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  • 1.
    Andersson, D. C.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Lindskog, P.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Inverse modeling applied for material characterization of powder materials2015In: Journal of Testing and Evaluation, ISSN 0090-3973, E-ISSN 1945-7553, Vol. 43, no 5, p. 1005-1019Article in journal (Refereed)
    Abstract [en]

    An investigation is performed concerning the applicability of inverse procedures, using optimization and simple experiments, for characterization of WC/Co powder materials. The numerical procedure is combined with uniaxial die-compaction experiments using an instrumented die, which allows direct measurement of the distribution of radial stress during the experiments. Finite-element (FE) methods and an advanced constitutive description of powder materials are relied upon to model the compaction experiment. Optimization using a surrogate model is used to determine some of the parameters in the constitutive description. These parameters in the material model are said to be found (with some accuracy) if the output from the FE simulation is similar to the experimental data. It is found that even though a complete constitutive description of the powder materials investigated cannot be achieved using this approach, many important material parameters can be determined with good accuracy.

  • 2.
    Andersson, Daniel C.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Cadario, Alessandro
    Lindskog, Per
    On the influence from punch geometry on the stress distribution at powder compaction2010In: Powder Technology, ISSN 0032-5910, E-ISSN 1873-328X, Vol. 202, no 1-3, p. 78-88Article in journal (Refereed)
    Abstract [en]

    A numerical analysis, using the finite element method, of the mechanical behavior at powder compaction at higher densities was performed. In this investigation the material behavior is modeled using an advanced macroscopic constitutive description initially presented by Brandt and Nilsson [1]. This material model, like many other models describing powder compaction at higher densities, includes a large number of constitutive parameters and as a result, a complete material characterization is a difficult task to perform or at least requires a large number of different experiments. A remedy to this problem is to apply inverse modeling, i.e. optimization, for determination of relevant material properties from comparatively simple experiments. It is then of course important, in order to achieve high accuracy results from the optimization procedure, that the stress fields produced during the experiments involves high gradients of stress. Adhering to simple uniaxial die compaction experiments the main parameter that can be used in order to achieve such a feature is the geometry of the punch used for load application. In the present investigation a number of punch profiles are studied and it is found that a skewed punch geometry is the most appropriate one to be used for experimental die compaction aiming at a constitutive description of the powder material based on inverse modeling. The main efforts are devoted towards an analysis based on the previously mentioned material model by Brandt and Nilsson [1] but also relevant results for another type of constitutive model will be presented. (C) 2010 Elsevier B.V. All rights reserved.

  • 3.
    Andersson, Daniel C.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Lindskog, Per
    Staf, Hjalmar
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    A Numerical Study of Material Parameter Sensitivity in the Production of Hard Metal Components Using Powder Compaction2014In: Journal of materials engineering and performance (Print), ISSN 1059-9495, E-ISSN 1544-1024, Vol. 23, no 6, p. 2199-2208Article in journal (Refereed)
    Abstract [en]

    Modeling of hard metal powder inserts is analyzed based on a continuum mechanics approach. In particular, one commonly used cutting insert geometry is studied. For a given advanced constitutive description of the powder material, the material parameter space required to accurately model the mechanical behavior is determined. These findings are then compared with the corresponding parameter space that can possibly be determined from a combined numerical/experimental analysis of uniaxial die powder compaction utilizing inverse modeling. The analysis is pertinent to a particular WC/Co powder and the finite element method is used in the numerical investigations of the mechanical behavior of the cutting insert.

  • 4.
    Andersson, Daniel
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Determination of yield surfaces in advanced constitutive powder models using inverse modeling2011In: Proceedings of the Euro PM 2011 Congress and Exhibition, European Powder Metallurgy Association , 2011, Vol. 3, p. 247-252Conference paper (Refereed)
    Abstract [en]

    In order to decrease the extensive experimental work in product development of WC/Co powder tooling equipment, an investigation of the applicability of inverse procedures to industrially relevant material models is performed. The powder die compaction process of WC/Co powder is modeled using the finite element method and an advanced plasticity-based constitutive model. An angled indenter is used to increase the sensitivity of constitutive parameters with respect to the measurable data from experiment, which is done using an instrumented die. Here, the inverse modeling (optimization) is performed (using iterative reduction of variable space and a combination of genetic (GA) and gradient search algorithms) in order to determine the yield surface of the investigated material. The results indicate that inverse modeling can be a useful tool in order to reduce the experimental efforts at material characterization of powder materials described by advanced material models.

  • 5.
    Andersson, Daniel
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Cadario, Alessandro
    Sandvik Tooling AB, Sweden.
    Lindskog, Per
    Sandvik Tooling AB.
    Inverse modeling for parameter determination when using advanced material models to describe powder compaction2010In: Proceedings of the World Powder Metallurgy Congress and Exhibition, World PM 2010, European Powder Metallurgy Association , 2010, Vol. 5, p. 77-84Conference paper (Refereed)
    Abstract [en]

    In order to decrease the amount of experimental work at material characterization of powder mixtures, optimization procedures are often used. In the present study, characterization of WC/Co powders described by an advanced plasticity model is at issue. In particular, uniaxial die compaction is analyzed numerically in order to determine the correlation between material parameters, scalar and functional, and measurable information from experiments. Such information include radial (contact) pressure between powder and die walls, press force as function of indentation depth and frictional effects between powder and die walls. The commercial finite element solver LS-Dyna and the optimization module LS-OPT are used in the present investigation.

  • 6.
    Andersson, Daniel
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Cadario, Alessandro
    Sandvik Tooling AB, Sweden .
    Lindskog, Per
    Sandvik Tooling AB.
    Parameter Sensitivity at Advanced Constitutive Modeling of Powder Materials2009In: Proceedings of the Euro International Powder Metallurgy Congress and Exhibition, Euro PM 2009, European Powder Metallurgy Association (EPMA) , 2009, Vol. 3, p. 293-298Conference paper (Refereed)
    Abstract [en]

    Dry pressing powder compaction is analyzed using the finite element method (FEM) and in particular then the explicit commercial FEM program LS-DYNA. The aim is then to determine the sensitivity of mechanical local and global parameters with respect to different constitutive as well as geometrical variables. A very advanced constitutive description (not available as standard in commercial FEM packages but implemented into LS-DYNA for the present investigation) is used in the numerical analysis, Brandt and Nilsson [1], and the results are particularly helpful for a forthcoming inverse analysis where it is crucial, for reasons of efficiency, to reduce the number of variables in the optimization procedure aiming at a accurate description of the mechanical behavior of the powder material. It should be clearly stated that the geometrical parameters to be investigated include different possible press geometries to be used for experimental verification of the results.

  • 7.
    Barbier, Christophe
    et al.
    KTH, Superseded Departments, Solid Mechanics.
    Larsson, Per-Lennart
    KTH, Superseded Departments, Solid Mechanics.
    Östlund, Sören
    KTH, Superseded Departments, Solid Mechanics.
    Experimental investigation of damage at folding of coated papers2002In: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 17, no 1, p. 34-38Article in journal (Refereed)
    Abstract [en]

    An experimental investigation of damage occuring at folding of coated paper has been performed. For this purpose an experimental device was constructed in such a way that close resemblance with an industrial situation was achieved. During the experiments the influence on the damage levels in the coating from such features as delamination, humidity and paper thickness have been studied using an optical microscope. The behaviour of two different paper materials has been investigated. A stress (or strain) based fracture criterion is relevant for the present problem but biaxiality of stresses as well as in-plane anisotropy must be taken into account. It was observed that cracking of the coating would not lead to subsequent cracking of the paper substrate and that delamination occurred during folding, in the base stock and not at the paper/coating interface, but its quantitative influence as regards cracking could not be determined. The influence from sheet grammage was investigated and it was found that the only case when (visible) cracks did not appear was at low values. High humidity did not affect the cracking.

  • 8.
    Barbier, Christophe
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Östlund, Sören
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Numerical investigation of folding of coated papers2005In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 67, no 4, p. 383-394Article in journal (Refereed)
    Abstract [en]

    Folding of coated paper is examined numerically using the finite element method. Particular emphasis is put on the behaviour of field variables relevant for cracking of the coating layers. In the numerical analysis, the basepaper is modelled as an anisotropic elastic-plastic material (both elastic and plastic anisotropy is accounted for) while the constitutive behaviour of the coating layers are approximated by classical (Mises) elastoplasticity. The numerical results suggest, among other things, that particular forms of plastic anisotropy can substantially reduce the maximum strain levels in the coating. It is also shown that delamination buckling, in the present circumstances, will have a very small influence on the strain levels in the coating layer subjected to high tensile loading.

  • 9.
    Barbier, Christophe
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Östlund, Sören
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On dynamic effects at folding of coated papers2005In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 67, no 4, p. 395-402Article in journal (Refereed)
    Abstract [en]

    Folding of coated papers is examined numerically using the finite element method. The analysis is focused on the influence from dynamic effects on the folding process. In particular, the behaviour of field variables relevant for cracking of the coating layers are studied in some detail. The results presented indicate that dynamic effects are of little importance as regards maximum strain levels in the coating but will influence the stress and strain distributions. Accordingly, a quasi-static analysis of the problem will be sufficient in order to describe many of the important features related to cracking.

  • 10.
    Barbier, Christophe
    et al.
    KTH, Superseded Departments, Solid Mechanics.
    Larsson, Per-Lennart
    KTH, Superseded Departments, Solid Mechanics.
    Östlund, Sören
    KTH, Superseded Departments, Solid Mechanics.
    On the effect of high anisotropy at folding of coated papers2004Report (Refereed)
  • 11.
    Barbier, Christophe
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Östlund, Sören
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On the effect of high anisotropy at folding of coated papers2006In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 72, no 3, p. 330-338Article in journal (Refereed)
    Abstract [en]

    A finite element procedure, developed in order to account for the effect of high anisotropy at folding of coated papers, is presented. The anisotropic behaviour (with very low stiffness in the thickness direction) is modelled using stiff structural elements (trusses and beams). The numerical results indicate that high elastic anisotropy leads to lower strain levels at folding than reported in previous analyses where this effect was not accounted for. High plastic anisotropy, on the other hand, will contradict this result.

  • 12.
    Barbier, Christophe
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Östlund, Sören
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Eklund, Johan
    DPC, MidSweden University.
    Folding of Printed Papers: Experiments and Numerical Analysis2003In: Preprints of the 2003 International Paper Physics Conference, 2003, p. 193-196Conference paper (Refereed)
  • 13.
    Barbier, Christophe
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Östlund, Sören
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Hallbäck, N.
    Karathanasis, M.
    On material characterization of paper coating materials by microindentation testing2005In: Journal of Coatings Technology Research, ISSN 1547-0091, Vol. 2, no 6, p. 463-471Article in journal (Refereed)
    Abstract [en]

    Microindentation as a method for determining important material properties of paper coating materials is studied experimentally and numerically The bulk of the investigation is concentrated upon the short-lived elastic part of a spherical indentation test, but determination of the failure stress of the coating is also discussed. The results indicate that microindentation can be a powerful tool for material characterization of these materials, but only if careful efforts arc, made to account for the influence from plasticity as well as from boundary effects.

  • 14. Carlsson, S.
    et al.
    Biwa, S.
    Larsson, Per-Lennart
    KTH, Superseded Departments, Solid Mechanics.
    On frictional effects at inelastic contact between spherical bodies2000In: International Journal of Mechanical Sciences, ISSN 0020-7403, E-ISSN 1879-2162, Vol. 42, no 1, p. 107-128Article in journal (Refereed)
    Abstract [en]

    Normal inelastic contact between spherical bodies is examined theoretically and numerically. The analysis is focused on viscoplastic material behaviour. In particular the effect of Coulomb friction is analysed in some detail, both regarding global and field variables. It is shown that the solution to the problem of contact between two deformable spherical bodies is provided by the solution of the fundamental problem of indentation of a viscoplastic half-space by a rigid sphere. The indentation analysis is based on self-similarity and cumulative superposition of intermediate flat die solutions as outlined in detail in a previous study by Storakers et al. (International Journal of Solids and Structures 1997;34:3061-83). The results show that frictional effects, when global properties such as the contact area and the mean contact pressure are at issue, will only be of importance at close to perfectly plastic material behaviour. Even in such circumstances the difference between values given by the solutions for frictionless and for full adhesive contact is no more than approximately 10%. Accordingly, it can be concluded that frictional effects are essentially negligible, when, for example, material characterization of viscoplastic solids by Brinell indentation is of interest. The situation is, however, quite different when field variables are at issue. In this case, stress and strain fields can be substantially influenced by friction with possible implications for features such as crack initiation and crack growth,

  • 15. Carlsson, S.
    et al.
    Larsson, Per-Lennart
    KTH, Superseded Departments, Solid Mechanics.
    On the determination of residual stress and strain fields by sharp indentation testing. Part I: Theoretical and numerical analysis2001In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 49, no 12, p. 2179-2191Article in journal (Refereed)
    Abstract [en]

    Sharp indentation tests, presently represented by cone and Vickers indenters, are analysed theoretically and numerically in order to explore how equi-biaxial residual stress and strain fields can be determined from the global properties, i.e. the size of the contact area between indenter and material and the hardness. given by such tests. It is shown that the residual strain fields can be accurately correlated with the hardness value while residual stresses are related to the size of the contact area. The latter feature is explained by the Fact that the size of the: contact area is sensitive to elastic effects. The results are summarized in simple closed form relations. well-suited to be used in an experimental situation, and the range of validity for the resulting formulae is discussed. The predictions are compared with corresponding results taken from the literature and good agreement is found. An experimental scheme for determination of residual fields by indentation is also suggested.

  • 16. Carlsson, S.
    et al.
    Larsson, Per-Lennart
    KTH, Superseded Departments, Solid Mechanics.
    On the determination of residual stress and strain fields by sharp indentation testing. Part II: Experimental investigation2001In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 49, no 12, p. 2193-2203Article in journal (Refereed)
    Abstract [en]

    An experimental investigation has been carried out in order to study how residual stress and strain fields can be determined by sharp indentation testing. Aiming at a thorough understanding of the influence from general residual surface stress: and strain fields on global indentation parameters, i.e. hardness and contact area, Vickers indentation tests have been performed on specimens first exposed to standard four-point bend (4PB) or single edge notch bend (SEN(B)) loading. The experimental results have been evaluated based on the findings in a parallel theoretical/numerical investigation and are compared with finite element simulations as well as with corresponding results taken from the literature. Good agreement between experiments and numerical results has been found, particularly in a situation with no or little plastic deformation due to preloading.

  • 17.
    Carlsson, Susanna
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On Microindentation of Viscoelastic Polymers1998In: Polymer testing, ISSN 0142-9418, E-ISSN 1873-2348, Vol. 17, no 1, p. 49-75Article in journal (Refereed)
  • 18. Eriksson, C. L.
    et al.
    Larsson, Per-Lennart
    KTH, Superseded Departments, Solid Mechanics.
    Rowciffe, D. J.
    Strain-hardening and residual stress effects in plastic zones around indentations2003In: Materials Science & Engineering: A, ISSN 0921-5093, E-ISSN 1873-4936, Vol. 340, no 02-jan, p. 193-203Article in journal (Refereed)
    Abstract [en]

    Plastic zones were revealed by polishing away Vickers indentations made in soda-lime glass, WC-11% Co, W and 7075 Al. Micro and nanohardness traces were used to explore the local mechanical response. The hardness value within the deformed zone increased up to 21% depending on the material. Soda-lime glass was the only material not to show a hardening effect, in fact it showed a small decrease in hardness. Finite element calculations were used to qualitatively determine the influence from residual stresses at indentation of soda-lime glass. The results are discussed in the context of the influence from work-hardening and residual stresses on indentation quantities.

  • 19.
    Fadil, Hassan
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering.
    Jelagin, Dennis
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering.
    Larsson, Per-Lennart
    KTH, Superseded Departments (pre-2005), Solid Mechanics. KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    On the Measurement of two Independent Viscoelastic Functions with Instrumented Indentation Tests2018In: Experimental mechanics, ISSN 0014-4851, E-ISSN 1741-2765, Vol. 58, no 2, p. 301-314Article in journal (Refereed)
    Abstract [en]

    In the present paper, a methodology for complete characterization of linear isotropic viscoelastic material with spherical instrumented indentation test is proposed. The developed method allows for measuring two independent viscoelastic functions, shear relaxation modulus and time-dependent Poisson's ratio, from the indentation test data obtained at non-decreasing loading, but otherwise arbitrary. Finite element modelling (FEM) is relied upon for validating the proposed methodology and for quantifying the influence of experimental variables on the measurements accuracy. Spherical indentation experiments are performed on several viscoelastic materials: polyoxymethylene, bitumen and bitumen-filler mastics. The viscoelastic material functions obtained with the indentation tests are compared with the corresponding results from the standard mechanical tests. Numerical and experimental results presented indicate that the methodology proposed allows mitigating the machine compliance and loading rate effects on the accuracy of the viscoelastic indentation tests.

  • 20.
    Fredriksson, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Wedge indentation of thin films modelled by strain gradient plasticity2008In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 45, no 21, p. 5556-5566Article in journal (Refereed)
    Abstract [en]

    A plane strain study of wedge indentation of a thin film on a substrate is performed. The film is modelled with the strain gradient plasticity theory by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. journal of the Mechanics and Physics of Solids 52, 1379-1406] and analysed using finite element simulations. Several trends that have been experimentally observed elsewhere are captured in the predictions of the mechanical behaviour of the thin film. Such trends include increased hardness at shallow depths due to gradient effects as well as increased hardness at larger depths due to the influence of the substrate. In between, a plateau is found which is observed to scale linearly with the material length scale parameter. It is shown that the degree of hardening of the material has a strong influence on the substrate effect, where a high hardening modulus gives a larger impact on this effect. Furthermore, pile-up deformation dominated by plasticity at small values of the internal length scale parameter is turned into sink-in deformation where plasticity is suppressed for larger values of the length scale parameter. Finally, it is demonstrated that the effect of substrate compliance has a significant effect on the hardness predictions if the effective stiffness of the substrate is of the same order as the stiffness of the film.

  • 21.
    Giannakopoulos, A.E.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Analysis of pyramid indentation of pressure-sensitive hard metals and ceramics1997In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 25, no 1, p. 1-35Article in journal (Refereed)
  • 22.
    Giannakopoulos, AE
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Vestergaard, R
    DTU, Denmark.
    Analysis of Vickers Indentation1994In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 31, no 19, p. 2679-2708Article in journal (Refereed)
  • 23.
    Hild, Francois
    et al.
    LMT Cachan, Paris, France.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Leckie, Frederick
    University of California, USA.
    Localization due to damage in fiber-reinforced composites1992In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 29, no 24, p. 3221-3238Article in journal (Refereed)
  • 24.
    Hild, Francois
    et al.
    LMT Cachan, Paris, France.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Leckie, Frederick
    University of California, USA.
    Uncoupled and coupled approaches to predict macrocrack initiation in fiber reinforced ceramic matrix composites1994In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 29, no 4, p. 365-377Article in journal (Refereed)
  • 25.
    Hild, Francois
    et al.
    LMT Cachan, Paris, France.
    Larsson, Per-Lennart
    Leckie, Frederick A.
    University of California, USA.
    Localization due to damage in two-direction fiber-reinforced composites1996In: Journal of applied mechanics, ISSN 0021-8936, E-ISSN 1528-9036, Vol. 63, no 2, p. 321-325Article in journal (Refereed)
  • 26.
    Hild, Francois
    et al.
    LMT Cachan, Paris, France.
    Leckie, Frederick
    University of California, USA.
    Larsson, Per-Lennart
    Criteria based on localization for the design of fiber reinforced brittle matrix composites1992Conference paper (Refereed)
  • 27.
    Jelagin, Denis
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Hertzian Fracture at Finite Friction: A Parametric Study2008In: Wear, ISSN 0043-1648, E-ISSN 1873-2577, Vol. 265, no 5-6, p. 840-848Article in journal (Refereed)
    Abstract [en]

    Friction has a profound influence on Hertzian fracture initiation when dissimilar materials are involved. Experimental studies show that the presence of friction results in higher fracture loads and fracture radii as compared to the frictionless case. It has also been shown recently that the experimental observations concerning Hertzian fracture initiation at unloading may be explained by the effect friction has on a surface tensile stress distribution. Presently a contact cycle between two dissimilar elastic bodies at finite Coulomb friction has been investigated numerically for a wide range of material parameters and contact geometries. Emphasis has been given to the surface tensile stress distribution which is assumed to be a governing parameter for Hertzian fracture initiation. In particular it was found that during loading the contact region divides into invariant stick and inward slip regions and the presence of outward frictional shear tractions reduces the maximum surface tensile stress and shifts it away from the contact contour as compared to the frictionless case. At unloading, the distributions of stick-slip zones were found to be severely history- and geometry-dependent and shear tractions reversed their direction over part of the contact area. Consequently, tensile stresses were found to grow at unloading. Results concerning the influence of the friction coefficient, Dundur's parameter and the specimen's Poisson's ratio on the absolute maximum surface tensile stress obtained at a frictional contact cycle are reported along with the magnitudes of the relative increase of maximum tensile stresses at unloading. Based on a critical stress fracture criterion it is discussed how the predicted increases will influence the critical loads required for crack initiation.

  • 28.
    Jelagin, Denis
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Transport Science, Highway and Railway Engineering.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Measurement of the Viscoelastic Properties of Bitumen Using Instrumented Spherical Indentation2013In: Experimental mechanics, ISSN 0014-4851, E-ISSN 1741-2765, Vol. 53, no 7, p. 1233-1244Article in journal (Refereed)
    Abstract [en]

    Indentation testing as a tool for determination of the viscoelastic mechanical properties of bitumen is examined in some detail using theoretical, numerical as well as experimental methods. In particular Brinell indentation is analysed and simple but rigorous formulae for a complete characterization of linear viscoelastic materials are presented. Numerical methods (finite element methods) are used in order to verify and substantiate these relations for an experimental situation. Indentation experiments are then performed on bitumen and special efforts are made in order to avoid size effects, i. e. anomalous results due to the fact that the indented specimens are too small and as a result, far field boundary conditions will influence the interpretation of the experimental output. The mechanical properties determined experimentally by indentation are compared with corresponding results from standard mechanical tests, and the results are encouraging considering the fact that non-linear effects are also influencing the outcome of the experiments.

  • 29.
    Jelagin, Denis
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Transport Science, Highway and Railway Engineering.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Nonlocal Frictional Effects at Indentation of Elastic Materials2013In: Tribology letters, ISSN 1023-8883, E-ISSN 1573-2711, Vol. 51, no 3, p. 397-407Article in journal (Refereed)
    Abstract [en]

    Indentation of elastic materials is investigated numerically using the finite element method. Large deformation theory is relied upon for accuracy. The study focuses on nonlocal frictional effects on relevant indentation quantities in the microindentation regime. The indentation quantities investigated include both local and global ones. It is shown that nonlocal frictional effects are small when global quantities are at issue, as is the case when conventional (Coulomb) theory of friction is used, also when these features are introduced at the ridges of a Vickers indenter where stress gradients are substantial. These effects are, however, shown to be of importance for particular indenter geometries as far as local field variables are concerned.

  • 30.
    Jelagin, Denis
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    On indentation and initiation of fracture in glass2008In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 45, no 10, p. 2993-3008Article in journal (Refereed)
    Abstract [en]

    The influence of indenter elasticity on Hertzian fracture initiation at frictional dissimilar elastic contact has been examined experimentally and numerically. In flat float glass specimens initiation of cone cracks has been observed and fracture loads measured with steel and tungsten carbide indenters at monotonically increasing loading and during a load cycle. The observed effect of indenter elasticity on fracture loads was found to be qualitatively different from the one predicted by the Hertz contact theory. This discrepancy may be explained by the presence of interfacial friction. The friction coefficient between the indenters and the specimen was measured and a contact cycle at finite Coulomb friction has been analyzed numerically. The influence of the indenter elasticity and the friction coefficient on the surface maximum tensile stress has been investigated and the results concerning the influence of these parameters on the fracture loads as given based on a critical stress fracture criterion. The obtained computational results were found to be in better agreement with experimental findings as compared to the predictions based on the frictionless contact theory. A remaining quantitative discrepancy was attributed to the well-known fact that a Hertzian macro-crack initiates from pre-existing defects on the specimen's surface. In order to account for the influence of the random distribution of these defects a Weibull statistics was introduced. The predicted critical loads corresponding to the 50% failure probability were found to be in close agreement with experimentally observed ones.

  • 31.
    Jelagin, Denis
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Transport Science, Highway and Railway Engineering.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On Indenter Boundary Effects at Elastic Contact2012In: Journal of Mechanics of Materials and Structures, ISSN 1559-3959, E-ISSN 2157-5428, Vol. 7, no 2, p. 165-182Article in journal (Refereed)
    Abstract [en]

    Axisymmetric contact problems at finite Coulomb friction and rounded profiles are examined for linear elastic solids. In previous analytical/numerical approaches to this problem often incremental procedures have been developed resulting in a reduced incremental problem corresponding to a rigid flat indentation of an elastic half-space. The reduced problem, being independent of loading and contact region, can be solved by a finite element method based on a stationary contact contour and characterized by high accuracy. Subsequently, with cumulative superposition procedures it is then possible to resolve the original problem in order to determine global and local field values. Such a procedure, when applied to for example to flat and conical profiles with rounded edges and apices, is exact save for the influence from boundaries close to the contact region. This influence could be exemplified by the indenter boundaries of a flat deformable profile with rounded edges indenting a linear elastic half-space. In the present analysis such effects are investigated qualitatively and quantitatively. In doing so, the results derived using previously discussed analytical/numerical approaches are compared with corresponding ones from full-field finite element calculations. Both local as well as global quantities are included in the comparison in order to arrive at a complete understanding of the boundary effects at elastic contact.

  • 32.
    Kamran, Yasir
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Second-order effects at microindentation of elastic polymers using sharp indenters2011In: Materials and Design, ISSN 0261-3069, Vol. 32, no 6, p. 3645-3653Article in journal (Refereed)
    Abstract [en]

    Sharp indentation of elastic polymers is investigated numerically using the finite element method. Large deformation theory is relied upon for accuracy. Both cone and Vickers indentation is considered and in particular, the study focuses on second-order effects on relevant indentation quantities in the micro-indentation regime. The second-order effects include indenter tip roundness, friction and also, for generality, effects due to different values on the included angle of the cone indenter, alpha. It is shown that frictional effects as well as effects due to indenter tip roundness are small at cone indentation but friction can substantially influence the results in case of Vickers indentation. The latter feature is most likely due to frictional effects at the ridges of the indenter and as such behavior is not accurately described using conventional theory of friction, a numerical approach for this purpose is discussed.

  • 33.
    Larsson, Per Lennart
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Olsson, Erik
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Elastic-plastic contact between hard metal particles2016In: Key Engineering Materials, 2016, p. 86-99Conference paper (Refereed)
    Abstract [en]

    In the present study contact between elastic-plastic dissimilar spherical particles are investigated. The investigation is based on analytical and numerical methods and in the latter case in particular the finite element method. The results presented are pertinent to force-displacement relations at contact when elastic and plastic deformations are of equal magnitude. Especially, hard metal particles are considered with a typical application area being analysis of powder compaction.

  • 34.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Correlation of global quantities for material characterization by sharp indentation testing of elastoplastic materials2016In: Journal of Testing and Evaluation, ISSN 0090-3973, E-ISSN 1945-7553, Vol. 44, no 6, p. 2293-2301Article in journal (Refereed)
    Abstract [en]

    Indentation problems pertinent to sharp indenters were examined. The analysis concerned classical elastic-plastic materials and, especially so, the details of the behavior of global contact quantities, such as mean contact pressure and the size of the contact area, in the transition region where elastic and plastic effects are of equal magnitude. The global contact quantities were correlated accurately using a single parameter, comprising both geometrical and mechanical properties, and presented using closed form expressions directly applicable to material characterization or measurements of residual mechanical fields by sharp indentation tests, but also for situations such as contact in gears or in electronic devices. The derived relations were based on highly accurate previous results from finite element studies of sharp indentation problems.

  • 35.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Influence from the inclined angle of the indenter for determination of residual stress and strain fields by sharp indentation testing2007In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 184, no 03-jan, p. 372-378Article in journal (Refereed)
    Abstract [en]

    In two previous articles by Carlsson and Larsson [S. Carlsson, P.-L. Larsson, On the determination of residual stress and strain fields by sharp indentation testing. Part I. Theoretical and numerical analysis, Acta Mater., 49 (2001) 2179-2191; S. Carlsson, R-L. Larsson, On the determination of residual stress and strain fields by sharp indentation testing. Part II. Experimental investigation, Acta Mater, 49 (2001) 2193-2203], sharp indentation tests were analysed experimentally, theoretically and numerically and it was found that biaxial residual stress and strain fields could be correlated with the global properties, i.e. hardness and size of the contact area, given by such tests. The practical usefulness of this finding is limited though due to the fact that the global properties are only weakly dependent of the residual stress state when standard indenter geometries are at issue. In order to find some guidance for improving upon this situation a numerical study of sharp indentation testing, based on the finite element method, was performed. The results derived indicate that the sensitivity of indentation variables to stress can be significantly increased by increasing the inclined angle of the sharp indenter and that this feature can be accurately captured by previously derived closed form relations directly applicable to a practical situation.

  • 36.
    Larsson, Per-Lennart
    KTH, Superseded Departments, Solid Mechanics.
    Investigation of sharp contact at rigid-plastic conditions2001In: International Journal of Mechanical Sciences, ISSN 0020-7403, E-ISSN 1879-2162, Vol. 43, no 4, p. 895-920Article in journal (Refereed)
    Abstract [en]

    Sharp contact problems are examined theoretically and numerically. The analysis is focused on elastic-plastic material behaviour and in particular the case when the local plastic zone arising at contact is so large that elastic effects on the mean contact pressure will be small or negligible. It is shown that, save for the particular case of a rigid-plastic power-law material, at such conditions, there is no single representative value on the uniaxial stress-strain curve that can be used in order to evaluate the global parameters at contact. However, the present numerical results indicate that good accuracy predictions for the mean contact pressure can be achieved when this variable is described by two parameters corresponding to the stress levels at, approximately, 2 and 35% plastic strain. Regarding the size of the contact area, it is shown that this quantity is very sensitive to elastic effects and any general correlation with material properties is complicated at best. The numerical analysis is performed by using the finite element method and the theoretical as well as the numerical results are compared with relevant experimental ones taken from the literature. From a practical point of view, the presented results are directly applicable to material characterization or measurements of residual mechanical fields by sharp indentation tests, but also for situations such as contact in gears or in electronic devices.

  • 37.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Modelling of sharp indentation experiments: some fundamental issues2006In: Philosophical Magazine, ISSN 1478-6435, E-ISSN 1478-6443, Vol. 86, no 33-35, p. 5155-5177Article in journal (Refereed)
    Abstract [en]

    Correct interpretation of sharp indentation experiments requires a fundamental understanding of the mechanics involved in the process. Such an understanding can only be achieved if an appropriate mechanical model is used to describe the problem. These models can, in rare cases, be purely analytical, but nowadays numerical modelling is a vital part of the mechanical approach. Furthermore, with the development of new materials and nanoindentation devices, material ( constitutive) modelling has becomes very important. The aim of the present paper is to present an overview of the modelling of sharp indentation experiments. Indentation of classical Mises elastoplastic behaviour, in particular, will be considered, in addition to indentation modelling of other types of materials. In addition, some fundamental issues in indentation modelling will be discussed. These issues include (1) the influence from large deformations, (2) differences and similarities between cone and pyramid indentation results, (3) the influence of residual stresses, (4) the effective elastic modulus at indentation and (5) the differences and similarities between indentation and scratch results. Most of these results have been published previously in international journals but their implications, in the author's opinion, have not been fully appreciated by the indentation community or, at least, not debated sufficiently.

  • 38.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On buckling of orthotropic compressed plates with circular holes1987In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 7, no 2, p. 103-121Article in journal (Refereed)
  • 39.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On buckling of orthotropic stretched plates with circular holes1989In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 11, no 2, p. 121-134Article in journal (Refereed)
  • 40.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On creep deformation at plane contact problems1997In: Cold Regions Science and Technology, ISSN 0165-232X, E-ISSN 1872-7441, Vol. 26, no 1, p. 67-82Article in journal (Refereed)
  • 41.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On delamination buckling and growth in circular and annular orthotropic plates1991In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 27, no 1, p. 15-28Article in journal (Refereed)
  • 42.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On multiple delamination buckling and growth in composite plates1991In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 27, no 13, p. 1623-1637Article in journal (Refereed)
  • 43.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    On representative stress correlation of global scratch quantities at scratch testing of elastoplastic materials2013In: MATER DESIGN, ISSN 0261-3069, Vol. 49, p. 536-544Article in journal (Refereed)
    Abstract [en]

    Scratch testing is studied aiming at correlation of global quantities in the context of a representative stress description. Previous investigations concerning this matter have shown that good accuracy predictions for different material classes, within the framework of classical Mises elastoplasticity, can be achieved by using a combination of stresses at different levels of plastic strains to define representative quantities at scratching. It is important to emphasize though that the correlation must account for the difference in mechanical behavior at elastoplastic and rigid plastic scratching and that pertinent results have only been presented for the normal scratch hardness. It is therefore the aim presently to investigate if such a correlation can be extended to apply also for global scratch quantities in general. From a practical point of view the results are valuable both when describing the mechanical behavior at scratching and at material characterization. Predictions based on the present study can within the framework of classical Mises elastoplasticity and quasi-static conditions, be made for a wide range of materials ranging from polymers and ceramics to metals.

  • 44.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On the correlation of scratch testing using separated elastoplastic and rigid plastic descriptions of the representative stress2013In: Materials and Design, ISSN 0261-3069, Vol. 43, p. 153-160Article in journal (Refereed)
    Abstract [en]

    The correlation of hardness values at scratch testing is studied within the framework of a differentiated description of representative stress values. The analysis is based on hardness values determined from a comprehensive finite element study of scratching of classical elastoplastic materials using a conical indenter. Large deformations are accounted for and the strain-hardening behaviour is varied in order to achieve generality of results. It is shown that good accuracy predictions for different material classes can be achieved by using a combination of stresses at different levels of plastic strains to define representative quantities at scratching. It is also shown that this correlation must account for the difference in mechanical behaviour at elastoplastic and rigid plastic scratching. From a practical point of view the results are valuable both when describing the mechanical behaviour at scratching and at material characterization. From the generality of the analysis, both elastoplastic and rigid plastic behaviour are accounted for, predictions based on the present study can be made for scratching of highly elastic materials such as polymers and ceramics but also for scratching of metals when plasticity dominates.

  • 45.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On the Determination of Biaxial Residual Stress Fields from Global Indentation Quantities2014In: Tribology letters, ISSN 1023-8883, E-ISSN 1573-2711, Vol. 54, no 1, p. 89-97Article in journal (Refereed)
    Abstract [en]

    In the present study, quantitative relations for the determination of surface residual stresses, using sharp indentation testing, are presented. The relations are based on previous results for equi-biaxial residual fields but further developed to apply also for a general situation. The present analysis relies on theoretical methods, but the results are validated using previous experimental and numerical findings. Cone indentation of classical Mises elastoplastic material behavior is assumed throughout the investigation for clarity but not out of necessity. Further development for a complete characterization of a general residual stress field is discussed in some detail.

  • 46.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On the Influence of Elastic Deformation for Residual Stress Determination by Sharp Indentation Testing2017In: Journal of materials engineering and performance (Print), ISSN 1059-9495, E-ISSN 1544-1024, Vol. 26, no 8, p. 3854-3860Article in journal (Refereed)
    Abstract [en]

    The determination of residual stresses in engineering materials using sharp indentation testing is studied analytically and numerically. The numerical part of the investigation is based on the finite element method. In particular, the effect from elastic deformations on global indentation properties is discussed in detail. This effect is essential when residual stresses are to be determined based on the change of the contact area due to such stresses. However, standard relations for this purpose are founded on the fact that the material hardness is invariant as regards residual (applied) stresses. Presently, this assumption is scrutinized and it is shown that it is only valid at dominating plastic deformation around the contact region. The hardness dependence of residual stresses can, however, be correlated in the same way as in the case of stress-free materials, indicating that the wealth of characterization formulas pertinent to indentation hardness is available also for the purpose of residual field determination. Only cone indentation of elastic-perfectly plastic materials is considered, but the generality of the results is discussed in some detail.

  • 47.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    On the mechanical behavior at sharp indentation of materials with compressive residual stresses2011In: MATER DESIGN, ISSN 0261-3069, Vol. 32, no 3, p. 1427-1434Article in journal (Refereed)
    Abstract [en]

    The correlation between residual stresses and the global properties, i.e. hardness and size of the contact area, given by a sharp indentation test have been studied quite frequently in recent years. The investigations presented have been based on experimental, theoretical and numerical methods and as a result, the basic features of the problem are now well understood. Furthermore, in this context quantitative relations, for the determination of residual stresses using sharp indentation, have been presented. Such relations have proven to be reliable in case of predominantly tensile residual stresses while the accuracy of predictions is much worse at compressive stress states. It is therefore the aim of the present study to investigate this matter in some detail and to present possible mechanisms for the difference in indentation behavior between tension and compression. Accordingly, the results are essentially qualitative but necessary and detailed investigations needed for a quantitative understanding are suggested. The present analysis is based on theoretical and numerical methods and in the latter case, the finite element method (FEM) is relied upon. Classical Mises elastoplastic material behavior is assumed throughout the investigation.

  • 48.
    Larsson, Per-Lennart
    KTH, Superseded Departments, Solid Mechanics.
    On the mechanical behavior of global parameters in material characterization by sharp indentation testing2004In: Journal of Testing and Evaluation, ISSN 0090-3973, E-ISSN 1945-7553, Vol. 32, no 4, p. 310-321Article in journal (Refereed)
    Abstract [en]

    Sharp contact problems are examined theoretically and numerically. The analysis is focused on elastic-plastic materials and, in particular, the behavior of global contact quantities, such as mean contact pressure and the size of the contact area, in the transition region where elastic and plastic effects are of equal magnitude. It is shown that under these circumstances, the global contact quantities can be correlated accurately using a single parameter, comprising both geometrical and mechanical properties, if the uniaxial stress-strain curve of the material is represented by the stress level(s) at appropriate value(s) of the accumulated plastic strain. From a practical point of view, the presented results are directly applicable to material characterization or measurements of residual mechanical fields by sharp indentation tests, but also for situations such as contact in gears or in electronic devices. The numerical analysis is performed by using the finite-element method.

  • 49.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Plastic Zone Size at Sharp Indentation of Classical Elastic-Plastic Materials: Behavior at Ideally Plastic Hardening2016In: Journal of engineering materials and technology, ISSN 0094-4289, E-ISSN 1528-8889, Vol. 138, no 1Article in journal (Refereed)
    Abstract [en]

    Sharp indentation problems are examined based on finite element methods (FEMs) and self-similarity considerations. The analysis concerns classical elastic-plastic materials with low, or no, strain-hardening and especially the details of the behavior of the size of the plastic zone are at issue. The results are correlated using a single parameter, comprising both geometrical and mechanical properties, and compared with previously presented semi-analytical findings. The numerical analysis is restricted to cone indentation of elastic-ideally plastic materials.

  • 50.
    Larsson, Per-Lennart
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Similarity methods for analysing indentation contact problems - Advantages and disadvantages2008In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 202, no 1-3, p. 15-21Article, review/survey (Refereed)
    Abstract [en]

    In this review article similarity methods for analysing indentation contact problems are explored and related advantages and disadvantages discussed in some detail. In particular, combined elastic and plastic effects, together with, and also taken separately from, the influence from large deformations, are discussed in the context of a self-similarity analysis. The main conclusion of the present investigation is that a self-similarity approach to indentation problems is of significant advantage at many circumstances while, however, limitations of such methods have to be carefully accounted for at application.

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