Journal ArticleDOI
Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate
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In this paper, it was shown that there exist approximations of the Hencky (logarithmic) finite strain tensor of various degrees of accuracy, having the following characteristics: (1) the tensors are close enough to the HSTT for most practical purposes and coincide with it up to the quadratic term of the Taylor series expansion; (2) are easy to compute (the spectral representation being unnecessary) ; and (3 ) exhibit tension-compression symmetry (i.e., the strain tensors of the inverse transformation is minus theAbstract:
It is shown that there exist approximations of the Hencky (logarithmic) finite strain tensor of various degrees of accuracy, having the following characteristics: (1) The tensors are close enough to the Hencky strain tensor for most practical purposes and coincide with it up to the quadratic term of the Taylor series expansion; (2) are easy to compute (the spectral representation being unnecessary) ; and ( 3 ) exhibit tension-compression symmetry (i.e., the strain tensor of the inverse transformation is minus the original strain tensor). Furthermore, an additive decomposition of the proposed strain tensor into volumetric and deviatoric (isochoric) parts is given. The deviatoric part depends on the volume change, but this dependence is negligible for materials that are incapable of large volume changes. A general relationship between the rate of the approximate Hencky strain tensor and the deformation rate tensor can be easily established.read more
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Micromechanical analysis of quasi-brittle materials using fracture-based interface elements
TL;DR: In this article, a microstructural model for the mechanical behavior of quasi-brittle materials is developed and verified for concrete and bone specimens, based on interface elements equipped with a constitutive law representing non-linear fracture, while continuum elements remain linear elastic.
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Elastoplasticity beyond small deformations
Heng Xiao,O. T. Bruhns,A. Meyers +2 more
TL;DR: In this article, an integrated viewpoint based on certain coherent threads running through various formulations of rate-independent elastoplasticity is presented, with a focus on new issues and new understanding, and on physically pertinent variables and formulations.
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An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity
TL;DR: In this article, a novel constitutive formulation is developed for finitely deforming hyperelastic materials that exhibit isotropic behavior with respect to a reference configuration, where the strain energy per unit reference volume, W, is defined in terms of three natural strain invariants, K1,K2,K3, which respectively specify the amount of dilatation, the magnitude of distortion, and the mode of distortion.
Journal ArticleDOI
The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity
Patrizio Neff,Ionel-Dumitrel Ghiba,Ionel-Dumitrel Ghiba,Ionel-Dumitrel Ghiba,Johannes Lankeit +4 more
TL;DR: In this paper, a family of isotropic volumetric-isochoric decoupled strain energies was investigated and the rank-one convexity of these energies was shown in plane elastostatics.
Journal ArticleDOI
The computation of the exponential and logarithmic mappings and their first and second linearizations
TL;DR: The first and second linearizations of the exponential and logarithmic mappings provided here are based directly on the exponential formula for the solutions of linear ODEs.
References
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Non-Linear Elastic Deformations
TL;DR: In this paper, the influence of non-linear elastic systems on a simple geometric model for elastic deformations is discussed, and the authors propose a planar and spatial euler introduction to nonlinear analysis.
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Introduction to the mechanics of a continuous medium
TL;DR: In this article, the authors propose a linearized theory of elasticity for tensors, which they call Linearized Theory of Elasticity (LTHE), which is based on tensors and elasticity.
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Localized necking in thin sheets
Sigurd Støren,James R. Rice +1 more
TL;DR: Using a simplified constitutive model of a pointed vertex on subsequent yield loci, the onset of localized necking under biaxial stretching has been predicted and this result supports the hypothesis of vertex-formation on the yield locus under continued plastic flow.
Journal ArticleDOI
Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis
Thomas J. R. Hughes,James Winget +1 more
TL;DR: In this article, an improved algorithm is presented for integrating rate constitutive equations in large deformation analysis, and the algorithm is shown to be "objective" with respect to large rotation increments.