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  • 1. Ambrosi, D.
    et al.
    Ateshian, G. A.
    Arruda, E. M.
    Cowin, S. C.
    Dumais, J.
    Goriely, A.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
    Humphrey, J. D.
    Kemkemer, R.
    Kuhl, E.
    Olberding, J. E.
    Taber, L. A.
    Garikipati, K.
    Perspectives on biological growth and remodeling2011In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 59, no 4, p. 863-883Article, review/survey (Refereed)
    Abstract [en]

    The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

  • 2. Borvik, T.
    et al.
    Olovsson, L.
    Hanssen, A. G.
    Dharmasena, K. P.
    Hansson, Håkan
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Concrete Structures.
    Wadley, H. N. G.
    A discrete particle approach to simulate the combined effect of blast and sand impact loading of steel plates2011In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 59, no 5, p. 940-958Article in journal (Refereed)
    Abstract [en]

    The structural response of a stainless steel plate subjected to the combined blast and sand impact loading from a buried charge has been investigated using a fully coupled approach in which a discrete particle method is used to determine the load due to the high explosive detonation products, the air shock and the sand, and a finite element method predicts the plate deflection. The discrete particle method is based on rigid, spherical particles that transfer forces between each other during collisions. This method, which is based on a Lagrangian formulation, has several advantages over coupled Lagrangian-Eulerian approaches as both advection errors and severe contact problems are avoided. The method has been validated against experimental tests where spherical 150 g C-4 charges were detonated at various stand-off distances from square, edge-clamped 3.4 mm thick AL-6XN stainless steel plates. The experiments were carried out for a bare charge, a charge enclosed in dry sand and a charge enclosed in fully saturated wet sand. The particle-based method is able to describe the physical interactions between the explosive reaction products and soil particles leading to a realistic prediction of the sand ejecta speed and momentum. Good quantitative agreement between the experimental and predicted deformation response of the plates is also obtained.

  • 3.
    Dahlberg, Carl F.O.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Saito, Y.
    Öztop, M.S.
    Kysar, J. W.
    Geometrically necessary dislocation density measurements at a grain boundary due to wedge indentation into an aluminum bicrystal2017In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 105, p. 131-149Article in journal (Refereed)
    Abstract [en]

    An aluminum bicrystal with a symmetric tilt Σ43 (3 3 5)[1 1 0] coincident site lattice grain boundary was deformed plastically via wedge indentation under conditions that led to a plane strain deformation state. Plastic deformation is induced into both crystals and the initially straight grain boundary developed a significant curvature. The resulting lattice rotation field was measured via Electron Backscatter Diffraction (EBSD). The Nye dislocation density tensor and the associated Geometrically Necessary Dislocation (GND) densities introduced by the plastic deformation were calculated. The grain boundary served as an impediment to plastic deformation as quantified through a smaller lattice rotation magnitude and smaller GND density magnitudes in one of the crystals. There is evidence that the lattice rotations in one grain brought a slip system in that grain into alignment with a slip system in the other grain, upon which the impediment to dislocation transmission across the grain boundary was reduced. This allowed the two slip systems to rotate together in tandem at later stages of the deformation. Finite element crystal plasticity simulations using classical constitutive hardening relationship capture the general features observed in the experiments.

  • 4.
    Elaguine, Denis
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Brudieu, Marie-Anne
    Ecole Polytechnique, Palaiseau, France.
    Storåkers, Bertil
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Hertzian fracture at unloading2006In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 54, no 11, p. 2453-2473Article in journal (Refereed)
    Abstract [en]

    Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.

  • 5.
    Faleskog, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Stec, Mateusz
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Micromechanics and probabilistic modeling of cleavage microcrack nucleation and growth caused by particle cracking2008In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782Article in journal (Other academic)
  • 6. Franceschini, G.
    et al.
    Bigoni, D.
    Regitnig, P.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Brain tissue deforms similarly to filled elastomers and follows consolidation theory2006In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 54, no 12, p. 2592-2620Article in journal (Refereed)
    Abstract [en]

    Slow, large deformations of human brain tissue-accompanying cranial vault deformation induced by positional plagiocephaly, occurring during hydrocephalus, and in the convolutional development-has surprisingly received scarce mechanical investigation. Since the effects of these deformations may be important, we performed a systematic series of in vitro experiments on human brain tissue, revealing the following features. (i) Under uniaxial (quasi-static), cyclic loading, brain tissue exhibits a peculiar nonlinear mechanical behaviour, exhibiting hysteresis, Mullins effect and residual strain, qualitatively similar to that observed in filled elastomers. As a consequence, the loading and unloading uniaxial curves have been found to follow the Ogden nonlinear elastic theory of rubber (and its variants to include Mullins effect and permanent strain). (ii) Loaded up to failure, the shape of the stress/strain curve qualitatively changes, evidencing softening related to local failure. (iii) Uniaxial (quasi-static) strain experiments under controlled drainage conditions provide the first direct evidence that the tissue obeys consolidation theory involving fluid migration, with properties similar to fine soils, but having much smaller volumetric compressibility. (iv) Our experimental findings also support the existence of a viscous component of the solid phase deformation. Brain tissue should, therefore, be modelled as a porous, fluid-saturated, nonlinear solid with very small volumetric (drained) compressibility.

  • 7.
    Fredriksson, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Gudmundson, Peter
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Modelling of the interface between a thin film and a substrate within a strain gradient plasticity framework2007In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 55, no 5, p. 939-955Article in journal (Refereed)
    Abstract [en]

    Interfaces play an important role for the plastic deformation at the micron scale. In this paper, two types of interface models for isotropic materials are developed and applied in a thin film analysis. The first type, which can also be motivated from dislocation theory, assumes that the plastic work at the interface is stored as a surface energy that is linear in plastic strain. In the second model, the plastic work is completely dissipated and there is no build-up of a surface energy. Both formulations introduce one length scale parameter for the bulk material and one for the interface, which together control the film behaviour. It is demonstrated that the two interface models give equivalent results for a monotonous, increasing load. The combined influence of bulk and interface is numerically studied and it is shown that size effects are obtained, which are controlled by the length scale parameters of bulk and interface.

  • 8.
    Gudmundson, Peter
    KTH, Superseded Departments, Solid Mechanics.
    A unified treatment of strain gradient plasticity2004In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 52, no 6, p. 1379-1406Article in journal (Refereed)
    Abstract [en]

    A theoretical framework is presented that has potential to cover a large range of strain gradient plasticity effects in isotropic materials. Both incremental plasticity and viscoplasticity models are presented. Many of the alternative models that have been presented in the literature are included as special cases. Based on the expression for plastic dissipation, it is in accordance with Gurtin (J. Mech. Phys. Solids 48 (2000) 989; Int. J. Plast. 19 (2003) 47) argued that the plastic flow direction is governed by a microstress q(ij) and not the deviatoric Cauchy stress sigma'(ij) that has been assumed by many others. The structure of the governing equations is of second order in the displacements and the plastic strains which makes it comparatively easy to implement in a finite element programme. In addition, a framework for the formulation of consistent boundary conditions is presented. It is shown that there is a close connection between surface energy of an interface and boundary conditions in terms of plastic strains and moment stresses. This should make it possible to study boundary layer effects at the interface between grains or phases. Consistent boundary conditions for an expanding elastic-plastic boundary are as well formulated. As examples, biaxial tension of a thin film on a thick substrate, torsion of a thin wire and a spherical void under remote hydrostatic tension are investigated.

  • 9.
    Gudmundson, Peter
    KTH, Superseded Departments, Solid Mechanics.
    Acoustic emission and dynamic energy release rate for steady growth of a tunneling crack in a plate in tension1999In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 47, no 10, p. 2057-2074Article in journal (Refereed)
    Abstract [en]

    The dynamic steady state growth of tunneling cracks in membrane loaded isotropic Kirchhoff plates is considered. Explicit solutions for the asymptotic displacement and velocity fields are presented. It is shown that the asymptotic fields are inversely proportional to the square root of distance from the crack tip, and that a wake may or may not develop behind the crack tip depending on the static membrane state. If the crack tip velocity is smaller than a certain critical velocity, the asymptotic solution will completely vanish. An explicit solution for the dynamic energy release rate is also presented. Due to elastic waves radiated from the crack tip, the dynamic energy release rate will generally be smaller than the corresponding static energy release rate.

  • 10.
    Gudmundson, Peter
    KTH, Superseded Departments, Solid Mechanics.
    Anisotropic microcrack nucleation in brittle materials1990In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 38, no 4, p. 531-551Article in journal (Refereed)
    Abstract [en]

    A constitutive model for anisotropic microcracking in brittle materials is developed. The model is based on a stress controlled microcrack nucleation criterion, which can vary in a random way between different microcracks. The effects of microcrack closure and a random distribution of residual stresses are included in the analysis. The resultant inelastic strains are determined using a standard homogenization technique Numerical results are presented for three simple loading cases : pure tension, biaxial tension and triaxial tension. Crack tip shielding resulting from microcrack nucleation is also analysed, and numerical results of are presented for two different microcrack nucleation criteria.

  • 11.
    Gudmundson, Peter
    BBC Brown Boveri Research Centre.
    Eigenfrequency changes of structures due to cracks, notches or other geometrical changes1982In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 30, no 5, p. 339-353Article in journal (Refereed)
    Abstract [en]

    A first order perturbation method is presented which predicts the changes in resonance frequencies of a structure resulting from cracks, notches or other geometrical changes. The eigenfrequency changes due to a crack are shown to be dependent on the strain energy of a static solution which is easily obtainable for small cracks and other small cut-outs. The method has been tested for three different cases, and the predicted results correlate very closely to experimental and numerical results.

  • 12.
    Gudmundson, Peter
    Brown, Boveri and Co. Ltd., Research Cente.
    The dynamic behaviour of slender structures with cross-sectional cracks1983In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 31, no 4, p. 329-345Article in journal (Refereed)
    Abstract [en]

    A dynamic model for beams with cross-sectional cracks is discussed. It is shown that a crack can be represented by a consistent, static flexibility matrix. Two different methods for the determination of the flexibility matrix are discussed. If the static stress intensity factors are known, the flexibility matrix can be determined from an integration of these stress intensity factors. Alternatively, static finite element calculations can be used for the determination of the flexibility matrix. Both methods are demonstrated in the present paper. The mathematical model was applied to an edge-cracked cantilevered beam and the eigenfrequencies were determined for different crack lengths and crack positions. These results were compared to experimentally obtained eigenfrequencies. In the experiments, the cracks were modelled by sawing cuts. The theoretical results were, for all crack lengths, in excellent agreement with the experimental data. The dynamic stress intensity factor for a longitudinally vibrating, centrally cracked bar was determined as well. The results compared very well with dynamic finite element calculations. The crack closure effect was experimentally investigated for an edge-cracked beam with a fatigue crack. It was found that the eigenfrequencies decreased, as functions of crack length, at a much slower rate than in the case of an open crack.

  • 13. Guo, T. F.
    et al.
    Faleskog, Jonas
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Shih, C. F.
    Continuum modeling of a porous solid with pressure-sensitive dilatant matrix2008In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 56, no 6, p. 2188-2212Article in journal (Refereed)
    Abstract [en]

    The pressure-sensitive plastic response of a material has been Studied in terms of the intrinsic sensitivity of its yield stress to pressure and the presence and growth of cavities. This work focuses on the interplay between these two distinctly different mechanisms and the attendant material behavior. To this end, a constitutive model is proposed taking both mechanisms into account. Using Gurson's homogenization, an tipper bound model is developed for a voided solid with a plastically dilatant matrix material. This model is built around a three-parameter axisymmetric velocity field for a unit sphere containing a spherical void. The void is also subjected to internal pressure; this can be relevant for polymeric adhesives permeated by moisture that vaporizes at elevated temperatures. The plastic response of the matrix material is described by Drucker-Prager's yield criterion and an associated flow rule. The resulting yield surface and porosity evolution law of the homogenized constitutive model are presented in parametric form. Using the solutions to special cases as building blocks, approximate models with explicit forms are proposed. The parametric form and an approximate explicit form are compared against full-field Solutions obtained from finite element analysis. They are also studied for loading under generalized tension conditions. These computational simulations shed light on the interplay between the two mechanisms and its enhanced effect on yield strength and plastic flow. Among other things, the tensile yield strength of the porous solid is greatly reduced by the internal void pressure, particularly when a liquid/vapor phase is the source of the internal pressure.

  • 14.
    Kroon, Martin
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    A continuum mechanics framework and a constitutive model for remodelling of collagen gels and collagenous tissues2010In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 58, no 6, p. 918-933Article in journal (Refereed)
    Abstract [en]

    Collagen is a very important protein of the human body and is responsible for the structural stability of many body components. Furthermore, collagen fibre networks are able to grow and remodel themselves, which enables them to adjust to varying physiological conditions. This remodelling is accomplished by fibre-producing cells, such as fibroblasts. The ability to adjust to new physiological conditions is very important, for example in wound healing. In the present paper, a theoretical framework for modelling collagenous tissues and collagen gels is proposed. Continuum mechanics is employed to describe the kinematics of the collagen, and affine deformations of fibres are assumed. Biological soft tissues can be approximated as being hyperelastic, and the constitutive model for the collagen fabric is therefore formulated in terms of a strain energy function. This strain energy function includes a density function that describes the distribution of the collagen fibre orientation. The density function evolves according to an evolution law, where fibres tend to reorient towards the direction of maximum Cauchy stress. The remodelling of the collagen network is also assumed to include a pre-stretching of collagen fibres, accomplished by fibroblasts. The theoretical framework is applied to experiments performed on collagen gels, where gels were exposed to remodelling under both biaxial and uniaxial constraints. The proposed model was able to predict both the resulting collagen distribution and the resulting stress-strain relationships obtained for the remodelled collagen gels. The influence of the most important model parameters is demonstrated, and it appears that there is a fairly unique set of model parameters that gives an optimal fit to the experimental data.

  • 15.
    Kroon, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Faleskog, Jonas
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Micrornechanics of cleavage fracture initiation in ferritic steels by carbide cracking2005In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 53, no 1, p. 171-196Article in journal (Refereed)
    Abstract [en]

    Cleavage fracture in ferritic steels is often initiated in brittle carbides randomly distributed in the material. The carbides break as a result of a fibre loading mechanism in which the stress levels in the carbides are raised, as the surrounding ferrite undergoes plastic deformation. The conditions in the vicinity of the nucleated micro-crack will then determine whether the crack will penetrate or be arrested by the ferrite. The ferrite is able to arrest nucleated cracks through the presence of mobile dislocations, which blunt and shield the microcrack and thus lowers the stresses at the crack tip. Hence, the macroscopic toughness of the material directly depends on the ability of the ferrite to arrest nucleated micro-cracks and in turn on the plastic rate sensitivity of the ferrite. The initiation of cleavage fracture is here modelled explicitly in the form of a micro-crack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder or in a few cases an elastic sphere and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, where the tractions are governed by a modified exponential cohesive law. It is shown that the critical stress, required to propagate a microcrack from a broken carbide, increases with decreasing plastic rate sensitivity of the ferrite. The results also show that a low stress triaxiality and a high aspect ratio of the carbide promote the initiation of cleavage fracture from a broken carbide.

  • 16. Latourte, Felix
    et al.
    Gregoire, David
    Zenkert, Dan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Wei, Xiaoding
    Espinosa, Horacio D.
    Failure mechanisms in composite panels subjected to underwater impulsive loads2011In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 59, no 8, p. 1623-1646Article in journal (Refereed)
    Abstract [en]

    This work examines the performance of composite panels when subjected to underwater impulsive loads. The scaled fluid-structure experimental methodology developed by Espinosa and co-workers was employed. Failure modes, damage mechanisms and their distributions were identified and quantified for composite monolithic and sandwich panels subjected to typical blast loadings. The temporal evolutions of panel deflection and center deflection histories were obtained from shadow Moire fringes acquired in real time by means of high speed photography. A linear relationship of zero intercept between peak center deflections versus applied impulse per areal mass was obtained for composite monolithic panels. For composite sandwich panels, the relationship between maximum center deflection versus applied impulse per areal mass was found to be approximately bilinear but with a higher slope. Performance improvement of sandwich versus monolithic composite panels was, therefore, established specially at sufficiently high impulses per areal mass (I(0)/(M) over bar > 170 m s(-1)). Severe failure was observed in solid panels subjected to impulses per areal mass larger than 300 m s(-1). Extensive fiber fracture occurred in the center of the panels, where cracks formed a cross pattern through the plate thickness and delamination was very extensive on the sample edges due to bending effects. Similar levels of damage were observed in sandwich panels but at much higher impulses per areal mass. The experimental work reported in this paper encompasses not only characterization of the dynamic performance of monolithic and sandwich panels but also post-mortem characterization by means of both non-destructive and microscopy techniques. The spatial distribution of delamination and matrix cracking were quantified, as a function of applied impulse, in both monolithic and sandwich panels. The extent of core crushing was also quantified in the case of sandwich panels. The quantified variables represent ideal metrics against which model predictive capabilities can be assessed.

  • 17.
    Murtada, Sae-Il
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Kroon, Martin
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Modeling the dispersion effects of contractile fibers in smooth muscles2010In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 58, no 12, p. 2065-2082Article in journal (Refereed)
    Abstract [en]

    Micro-structurally based models for smooth muscle contraction are crucial for a better understanding of pathological conditions such as atherosclerosis, incontinence and asthma. It is meaningful that models consider the underlying mechanical structure and the biochemical activation. Hence, a simple mechanochemical model is proposed that includes the dispersion of the orientation of smooth muscle myofilaments and that is capable to capture available experimental data on smooth muscle contraction. This allows a refined study of the effects of myofilament dispersion on the smooth muscle contraction. A classical biochemical model is used to describe the cross-bridge interactions with the thin filament in smooth muscles in which calcium-dependent myosin phosphorylation is the only regulatory mechanism. A novel mechanical model considers the dispersion of the contractile fiber orientations in smooth muscle cells by means of a strain-energy function in terms of one dispersion parameter. All model parameters have a biophysical meaning and may be estimated through comparisons with experimental data. The contraction of the middle layer of a carotid artery is studied numerically. Using a tube the relationships between the internal pressure and the stretches are investigated as functions of the dispersion parameter, which implies a strong influence of the orientation of smooth muscle myofilaments on the contraction response. It is straightforward to implement this model in a finite element code to better analyze more complex boundary-value problems.

  • 18.
    Olsson, Erik
    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 force-displacement relations at contact between elastic-plastic adhesive bodies2013In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 61, no 5, p. 1185-1201Article in journal (Refereed)
    Abstract [en]

    The loading-unloading of dissimilar adhesive elastic-plastic bodies is studied both analytically and numerically, including elastic-ideal plastic and deformation hardening behavior. The contacting bodies are assumed to be spherical in the region of contact and consequently the presented model is partly based on results pertinent to Brinell indentation. The problem of adhesive unloading is solved in two steps; first the unloading in the absence of adhesion is studied and then an adhesive pressure term is added. The analytical model is derived using fracture mechanics arguments and is based on one parameter, the fracture energy. The model is finally verified with finite element simulations by introducing a cohesive behavior between the modeled spheres. The analytical model shows very good agreement with the FE-simulations both during loading and unloading and also concerning the case of force and displacement at separation.

  • 19.
    Patil, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Instabilities of wrinkled membranes with pressure loadings2016In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 94, p. 298-315Article in journal (Refereed)
    Abstract [en]

    Wrinkling can affect the functionality of thin membranes subjected to various loadings or boundary conditions. The concept of relaxed strain energy was studied for isotropic, hyperelastic, axisymmetric membranes pressurized by gas or fluid. Non-intuitive instabilities were observed when axisymmetric wrinkled membranes were perturbed with angle dependent displacement fields. A linearized theory showed that static equilibrium states of pressurized membranes, modelled by a relaxed strain energy formulation, are unstable, when the wrinkled surface is subjected to pressure loadings. The theory is extended to the non-axisymmetric membranes and it is shown that these instabilities are local phenomena. Simulations for the pressurized cylindrical membranes with non-uniform thickness and hemispherical membranes support the claims in both theoretical and numerical contexts including finite element simulations.

  • 20.
    Storåkers, Bertil
    et al.
    KTH, Superseded Departments, Solid Mechanics.
    Larsson, Per-Lennart
    KTH, Superseded Departments, Solid Mechanics.
    On Brinell and Boussinesq indentation of creeping solids1994In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 42, no 2, p. 307-332Article in journal (Refereed)
    Abstract [en]

    As an alternative to traditional tensile testing of materials subjected to creep, indentation testing is examined. Axisymmetric punches of shapes defined by smooth homogeneous functions are analysed in general at power law behaviour both from a theoretical and a computational point of view. It is first shown that by correspondence to nonlinear elasticity and self-similarity the problem to determine time-dependent properties admits reduction to a stationary one. Specifically it is proved that the creep rate problem posed depends only on the resulting contact area but not on specific punch profiles. As a consequence the relation between indentation depth and contact area is history independent. So interpreted, the solution for a flat circular cylinder (Boussinesq) is not only of intrinsic interest but serves as a reference solution to generate results for various punch profiles. This is conveniently carried out by cumulative superposition and in particular ball indentation (Brinell) is analysed in depth. A carefully designed finite element procedure based on a mixed variational principle is used to provide a variety of explicit results of high accuracy pertaining to stress and deformation fields. Universal relations for hardness at creep are proposed for Boussinesq and Brinell indentation in analogy with the celebrated formula by Tabor for indentation of strain-hardening plastic materials. Quantitative comparison is made with a diversity of experimental data attained by earlier writers and the relative merits of indentation strategies are discussed.

  • 21.
    Tjahjanto, Denny D.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.). ABB AB, Sweden.
    Girlanda, O.
    Östlund, Stefan
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Anisotropic viscoelastic-viscoplastic continuum model for high-density cellulose-based materials2015In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 84, p. 1-20Article in journal (Refereed)
    Abstract [en]

    A continuum material model is developed for simulating the mechanical response of high-density cellulose-based materials subjected to stationary and transient loading. The model is formulated in an infinitesimal strain framework, where the total strain is decomposed into elastic and plastic parts. The model adopts a standard linear viscoelastic solid model expressed in terms of Boltzmann hereditary integral form, which is coupled to a rate-dependent viscoplastic formulation to describe the irreversible plastic part of the overall strain. An anisotropic hardening law with a kinematic effect is particularly adopted in order to capture the complex stress-strain hysteresis typically observed in polymeric materials. In addition, the present model accounts for the effects of material densification associated with through-thickness compression, which are captured using an exponential law typically applied in the continuum description of elasticity in porous media. Material parameters used in the present model are calibrated to the experimental data for high-density (press)boards. The experimental characterization procedures as well as the calibration of the parameters are highlighted. The results of the model simulations are systematically analyzed and validated against the corresponding experimental data. The comparisons show that the predictions of the present model are in very good agreement with the experimental observations for both stationary and transient load cases.

  • 22.
    Wikström, Adam
    et al.
    KTH, Superseded Departments, Solid Mechanics.
    Gudmundson, Peter
    KTH, Superseded Departments, Solid Mechanics.
    Suresh, Subra
    Dept. of Mat. and Sci. and Eng., Massachusetts Inst. of Technology.
    Thermoelastic analysis of periodic thin lines deposited on a substrate1999In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 47, no 5, p. 1113-1130Article in journal (Refereed)
    Abstract [en]

    Thermoelastic stresses and curvatures arising from patterned thin lines on initially flat isotropic substrates are analyzed. A connection is made between substrates with patterned lines and laminated anisotropic composites containing transverse matrix cracks. Using this analogy along with anisotropic plate theories, approximate analytical expressions are derived for volume-averaged stresses as well as curvatures along and normal to the lines, for any thickness, width and spacing of the lines. The predictions of the analysis are shown to compare favorably with finite element simulations of stresses and curvatures for Si substrates with Al, Cu or SiO2 lines. The predictions also match prior experimental measurements of curvatures along and normal to patterned SiO2 lines on Si wafers, and further capture the general experimental trends reported previously for curvature evolutions in Si wafers with Al lines. The model presented here thus provides a very convenient and simple analytical tool for extracting stresses in thin lines on substrates from a knowledge of experimentally determined film stress, thereby circumventing the need for detailed computations for a wide range of unpassivated line geo metries of interest in microelectronic applications.

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