Tensors, as geometric objects that describe linear or multi-linear relations between
geometric vectors, scalars, and other tensors, have provided a concise mathematical …

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 …

The deformation of an infinite bar subjected to a self-equilibrated load distribution is
investigated using the peridynamic formulation of elasticity theory. The peridynamic theory …

T he notion of the driving traction on a surface of strain discontinuity in a continuum
undergoing a general thermomechanical process is defined and discussed. In addition, the …

Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers
whose mechanical properties are altered by the application of external magnetic fields. Due …

The development of additive manufacturing methods, such as 3D printing, allows the design
of more complex architectured materials. Indeed, the main structure can be obtained by …

We investigate a family of isotropic volumetric-isochoric decoupled strain energies F ↦ W_
eH (F):= W _ eH (U):=\left {μ ke^ k ‖ dev _n U ‖^ 2+ κ 2 ke^ k tr (\log U)^ 2 & if\det F> …

This paper studies the so-called biquadratic optimization over unit spheres
x∈R^n,y∈R^m1≦i,k≦n,\,1≦j,l≦mb_ijklx_iy_jx_ky_l, subject to ‖x‖=1, ‖y‖=1. We …

In this paper, we derive necessary and sufficient conditions for the strong ellipticity condition
of anisotropic elastic materials. We first observe that the strong ellipticity condition holds if …

The strong ellipticity condition plays an important role in nonlinear elasticity and in materials.
In this paper, we define M-eigenvalues for an elasticity tensor. The strong ellipticity condition …