The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

We present a machine learning framework to train and validate neural networks to predict
the anisotropic elastic response of a monoclinic organic molecular crystal known as β β …

We consider a family of isotropic volumetric–isochoric decoupled strain energies F ↦ W_\rm
eH (F):= W _\rm eH (U):=\left {μ k\, e^ k\, ‖\rm dev _n\rm log U ‖^ 2+ κ 2 ̂ k\, e^ ̂ k\,\rm tr …

We consider the class of non-negative rank-one convex isotropic integrands on R n× n
which are also positively p-homogeneous. If p≤ n= 2 we prove, conditional on the …

In this paper we improve the result about the polyconvexity of the energies from the family of
isotropic volumetric-isochoric decoupled strain exponentiated Hencky energies defined in …

Necessary and sufficient conditions are given for the convexity of a scalar valued function of
tensors that is proper isotropic, or invariant under rotations. These conditions are also …

Rotationally invariant functions can be represented as functions of the (signed) singular
values of their tensor arguments. In two dimensions, the paper expresses the ordinary …

We provide some new necessary and sufficient conditions for regular isotropic rank-one
convex functions on M 2+={2× 2 matrices such that det M≥ 0}. It is well known that isotropic …

Finite element simulations are widely used to study the non-linear mechanical behavior of
various biomaterials. Constructing an anisotropic strain energy function within the framework …

Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity -
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