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On Eshelby's Inclusion Problem in Nonlinear Anisotropic Elasticity

The recent literature of finite eignestrains in nonlinear elastic solids is reviewed, and Eshelby's inclusion problem at finite strains is revisited. The subtleties of the analysis of combinations of finite eigenstrains for the example of  combined finite radial, azimuthal, axial, and twist eigenstrains in a finite circular cylindrical bar are discussed. The stress field of a spherical inclusion with uniform pure dilatational eigenstrain in a radially-inhomogeneous spherical ball made of arbitrary incompressible isotropic solids is analyzed.

arash_yavari's picture

The mathematical foundations of anelasticity: Existence of smooth global intermediate configurations

A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption is on unsatisfactory ground.

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Small-on-Large Geometric Anelasticity

In this paper we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems.

computational nonlinear elasticity references

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I will be developing constitutive material models into commercial FE codes for nonlinear elasticity and searching for good books to get started for computational aspects. There are many good books for computational plasticity but I did not find any for nonlinear elasticity. Suggestion for good books or references is welcome.

Large anelasticity and associated energy dissipation in single-crystalline nanowires

Guangming Cheng, Chunyang Miao, Qingquan Qin, Jing Li, Feng Xu, Hamed Haftbaradaran, Elizabeth C. Dickey, Huajian Gao & Yong Zhu Nature Nanotechnology 10687–691 (2015) doi:10.1038/nnano.2015.135

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