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  • 1. Daehli, Lars Edvard Bryhni
    et al.
    Faleskog, Jonas
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Borvik, Tore
    Hopperstad, Odd Sture
    Unit cell simulations and porous plasticity modelling for strongly anisotropic FCC metals2017In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 65, p. 360-383Article in journal (Refereed)
    Abstract [en]

    The macroscopic behaviour of anisotropic porous solids made from an aggregate of spherical voids embedded in a plastically anisotropic matrix material is investigated by means of unit cell simulations. Plastic yielding of the polycrystalline matrix is governed by the anisotropic yield criterion Yld2004-18p. Generic texture components for face-centred cubic crystals resembling those that typically emerge during rolling and annealing processes are applied in the study. A numerical method for systematic prescription of external stress states is presented and employed in the unit cell calculations. To preclude shear effects in the unit cell model, the material symmetry axes are restricted to coincide with the principal stress directions. This excludes the possibility to properly study the ductile failure mechanism and the current work is thus mainly concerned with the void growth phase. Various stress states ranging from biaxial tension to highly constrained regions in the vicinity of crack tips are employed in the study. The numerical results demonstrate that the matrix anisotropy has a marked effect on the unit cell response, both in terms of void growth and stress-strain curves. Furthermore, the void shape evolves quite differently depending upon the direction of the major principal stress relative to the material axes. A heuristic extension of the Gurson model that incorporates matrix plastic anisotropy is presented and subsequently used to describe the constitutive behaviour of the porous ductile solid. Numerical data from the unit cell analyses are used as target curves in the calibration process of the porous plasticity model. A sequential least-square optimization procedure is invoked to minimize the overall discrepancy between the unit cell calculations and the homogenized response of the plastically anisotropic porous solid for all the imposed stress states. The anisotropic porous plasticity model demonstrates predictive capabilities for the range of stress states covered in this study.

  • 2.
    Dahlberg, Carl F. O.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Faleskog, Jonas
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Strain gradient plasticity analysis of the influence of grain size and distribution on the yield strength in polycrystals2014In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 44, p. 1-16Article in journal (Refereed)
    Abstract [en]

    Plane strain models of polycrystalline microstructures are investigated using strain gradient plasticity (SGP) and a grain boundary (GB) deformation mechanism. The microstructures are constructed using a non-linear constrained Voronoi tessellation so that they conform to a log-normal distribution in grain size. The SGP framework is used to model the grain size dependent strengthening and the GB deformation results in a cut-off of this trend below a certain critical grain size. Plastic strain field localization is discussed in relation to the non-local effects introduced by SGP and a material length scale. A modification of the Hall-Petch relation that accounts for, not only the mean grain size, but also the statistical size variation in a population of grains is proposed.

  • 3.
    Dahlberg, Carl F. O.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Ortiz, M.
    Fractional strain-gradient plasticity2019In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 75, p. 348-354Article in journal (Refereed)
    Abstract [en]

    We develop a strain-gradient plasticity theory based on fractional derivatives of plastic strain and assess its ability to reproduce the scaling laws and size effects uncovered by the recent experiments of Mu et al. (2014, 2016, 2017) on copper thin layers undergoing plastically constrained simple shear. We show that the size-scaling discrepancy between conventional strain-gradient plasticity and the experimental data is resolved if the inhomogeneity of the plastic strain distribution is quantified by means of fractional derivatives of plastic strain. In particular, the theory predicts that the size scaling exponent is equal to the fractional order of the plastic-strain derivatives, which establishes a direct connection between the size scaling of the yield stress and fractionality.

  • 4.
    Gasser, T. Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Modeling the propagation of arterial dissection2006In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 25, no 4, p. 617-633Article in journal (Refereed)
    Abstract [en]

    Arterial dissections are frequently observed in clinical practice and during road traffic accidents. In particular, the lamellarly arrangement of elastin, collagen, in addition to smooth muscle cells in the middle arterial layer, the media, favors dissection failure. Experimental studies and related biomechanical models are rare in the literature. Finite strain kinematics is employed, and the discontinuity in the displacement field accounts for tissue separation. Dissection is regarded as a gradual process in which separation between incipient material surfaces is resisted by cohesive traction. Two variational statements together with their consistent linearizations form the basis for a finite element implementation. We combine the cohesive crack concept with the partition of unity finite element method, where nodal degrees of freedom adjacent to the discontinuity are enhanced. The developed continuum mechanical and numerical frameworks allow the analysis of the propagation of dissections within general nonlinear boundary-value problems, where the constitutive description for the continuous and the cohesive material is considered independent from each other. The continuous material is modeled as a fiber-reinforced composite with the fibers corresponding to the collagenous component which are assumed to be embedded in a non-collagenous isotropic groundmatrix. Dispersion of the collagen fiber orientation is considered in a continuum sense by one structure parameter. A novel cohesive potential per unit undeformed area is used to derive a traction separation law appropriate for the description of the mechanical properties of medial dissection. The cohesive stiffness contribution to the element stiffness matrix is explicitly derived. In particular, the dissection propagation of a rectangular strip of a human aortic media is investigated. Cohesive material properties are quantified by comparing the experimentally measured load with the computed dissection load.

  • 5.
    Gudmundson, Peter
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Modelling of length scale effects in viscoelastic materials2006In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 25, no 3, p. 379-388Article in journal (Refereed)
    Abstract [en]

    A length scale dependent linear viscoelastic constitutive model is developed. First, a generalized Maxwell model that can describe standard linear viscoelasticity is considered. The model is then generalized to include effects of. viscous strain gradients. The formulation of additional boundary conditions resulting from the strain gradient terms is discussed. It is shown that the boundary conditions can be formulated in terms of a surface energy. As an example, the thermal expansion of a thin polymeric film on an elastic substrate is analyzed. It is shown that the relative thermal expansion in the thickness direction of the film decreases for sufficiently small film thicknesses, in accordance with experimental observations. This effect cannot be captured by a standard thermo-viscoelastic theory, which gives a constant thermal expansion independent of film thickness.

  • 6.
    Hamedzadeh, Amir
    et al.
    Univ Calgary, Grad Programme Mech Engn, 2500 Univ Dr NW, Calgary, AB T2N 1N4, Canada..
    Gasser, T. Christian
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Federico, Salvatore
    Univ Calgary, Dept Mech & Mfg Engn, 2500 Univ Dr NW, Calgary, AB T2N 1N4, Canada..
    On the constitutive modelling of recruitment and damage of collagen fibres in soft biological tissues2018In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 72, p. 483-496Article in journal (Refereed)
    Abstract [en]

    The aim of this work is to propose a recruitment and damage constitutive model for collagen fibres in soft biological tissues. Similarly to other published models, our model employs probability distribution functions in order to capture the progressive recruitment and damage of fibrils in a collagen fibre. We rigorously investigate the continuum mechanical treatment of recruitment and damage using a multiplicative decomposition of the deformation gradient. Our proposed model stems from the correction, generalisation and extension to damage of the recruitment model proposed by Martufi and Gasser (2011, J. Biomech., 44, 2544-2550). We demonstrate that the generalised model is equivalent to the recruitment and damage model proposed by Hurschler et al. (1997, J. Biomech. Eng., 119, 392-399). Finally, we explore the sensitivity of the proposed model to the parameters describing recruitment and damage, implement the model into Finite Elements and show an example of application, which gives good agreement with published experimental data.

  • 7. Holzapfel, Gerhard A.
    et al.
    Gasser, T. Christian
    Stadler, M.
    A structural model for the viscoelastic behavior of arterial walls: Continuum formulation and finite element analysis2002In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 21, no 3, p. 441-463Article in journal (Refereed)
    Abstract [en]

    In this paper we present a two-layer structural model suitable for predicting reliably the passive (unstimulated) time-dependent three-dimensional stress and deformation states of healthy young arterial walls under various loading conditions. It extends to the viscoelastic regime a recently developed constitutive framework for the elastic strain response of arterial walls (see Holzapfel et al. (2001)). The structural model is formulated within the framework of nonlinear continuum mechanics and is well-suited for a finite element implementation. It has the special merit that it is based partly on histological information, thus allowing the material parameters to be associated with the constituents of each mechanically-relevant arterial layer. As one essential ingredient from the histological information the constitutive model requires details of the directional organization of collagen fibers as commonly observed under a microscope. We postulate a fully automatic technique for identifying the orientations of cellular nuclei, these coinciding with the preferred orientations in the tissue. The biological material is assumed to behave incompressibly so that the constitutive function is decomposed locally into volumetric and isochoric parts. This separation turns out to be advantageous in avoiding numerical complications within the finite element analysis of incompressible materials. For the description of the viscoelastic behavior of arterial walls we employ the concept of internal variables. The proposed viscoelastic model admits hysteresis loops that are known to be relatively insensitive to strain rate, an essential mechanical feature of arteries of the muscular type. To enforce incompressibility without numerical difficulties, the finite element treatment adopted is based on a three-field Hu-Washizu variational approach in conjunction with an augmented Lagrangian optimization technique. Two numerical examples are used to demonstrate the reliability and efficiency of the proposed structural model for arterial wall mechanics as a basis for large scale numerical simulations.

  • 8. Larsson, R.
    et al.
    Wysocki, M.
    Toll, Staffan
    Chalmers University of Technology, Sweden.
    Process-modeling of composites using two-phase porous media theory2004In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 23, no 1, p. 15-36Article in journal (Refereed)
    Abstract [en]

    A biphasic continuum model is proposed for the modeling of a family of forming processes for fiber composites. The processes considered involve deformation of a fiber bundle network, wetting by penetration of resin into fiber bundles, and resin flow through the fiber bundle network. The continuum model represents three (or more) actual micro constituents as two continuous phases: a solid phase being the fiber network plus any extra void within the fiber bundles and a fluid phase being the liquid matrix. The model framework thus comprises the continuum formulation of a nonlinear compressible porous solid saturated with an incompressible fluid phase. Guided by the entropy inequality, we specify constitutive relations concerning three different mechanisms pertinent to the forming process: effective stress response of the fiber bundle network, compaction of the solid phase, and Darcian interaction between the two phases. We are particularly concerned with the compaction of the fiber-bundles of the solid phase, consisting of elastic packing combined with a viscous wetting process driven by the fluid pressure. The paper is concluded with a couple of numerical examples, where the volumetric deformation-pressure response of a fluid saturated fiber bundle network at undrained conditions is considered. Both volumetric relaxation and volumetric creep tests are analyzed. In particular, the response for different loading rates is assessed. As a final example, a finite element analysis of a relaxation test for the macroscopically undrained compression of a fluid-filled fibernetwork specimen is carried out.

  • 9.
    Nygårds, Mikael
    et al.
    KTH, Superseded Departments, Solid Mechanics.
    Gudmundson, Peter
    KTH, Superseded Departments, Solid Mechanics.
    Numerical investigation of the effect of non-local plasticity on surface roughening in metals2004In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 23, no 5, p. 753-762Article in journal (Refereed)
    Abstract [en]

    A non-local crystal plasticity theory that incorporates strain gradients in the hardening moduli has been implemented in a finite element program. It is proposed that a gradient term enters the hardening modulus through a square-root dependence, which introduces an internal length scale. The relation has resemblance to the Hall-Petch relation. Simulations of polycrystalline materials are performed through a numerical finite element model that partition the mesh into grains through a discrete version of the Voronoi algorithm. Numerical simulations are performed and the surface roughness of an initially flat free surface is evaluated. The effects of microstructure, the internal length scale, anisotropy and hardening are presented. It is shown that the local surface roughness decreases as the ratio between internal length scale and grain size increases, since the non-local term accelerates hardening. By studies of three different materials (Al, Cu and Pu) with varying degree of anisotropy and hardening it is shown that there is a more pronounced roughening effect in anisotropic materials, the same effect is also seen for material softening.

  • 10.
    Patil, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Wrinkling of cylindrical membranes with non-uniform thickness2015In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 54, p. 1-10Article in journal (Refereed)
    Abstract [en]

    Thin membranes are prone to wrinkling under various loading, geometric and boundary conditions, affecting their functionality. We consider a hyperelastic cylindrical membrane with non-uniform thickness pressurized by internal gas or fluid. When pre-stretched and inflated, the wrinkles are generated in a certain portion of the membrane depending on the loading medium and boundary conditions. The wrinkling is determined through a criterion based on kinematic conditions obtained from non-negativity of Cauchy principal stresses. The equilibrium solution of a wrinkled membrane is obtained by a specified combination of standard and relaxed strain energy function. The governing equations are discretized by a finite difference approach and a Newton-Raphson method is used to obtain the solution. An interesting relationship between stretch induced softening/stiffening with the wrinkling phenomenon has been discovered. The effects of pre-stretch, inflating medium, thickness variations and boundary conditions on the wrinkling patterns are clearly delineated. (C) 2015 Elsevier Masson SAS. All rights reserved.

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