James K. Knowles

TL;DR: In this article, ESHELBY deduced a surface-integral representation for the force on an elastic singularity or inhomogeneity, which gives rise to a conservation law for regular elastostatic fields appropriate to homogeneous but not necessarily isotropic solids in the presence of infinitesimal deformations.

TL;DR: In this paper, the authors provide an overview of the recent developments concerning Saint-Venant's principle and present an exact solution for the exact solution of the second-order problem.

TL;DR: The notion of the driving traction on a surface of strain discontinuity in a continuum undergoing a general thermomechanical process is defined and discussed in this paper, and the associated constitutive notion of a kinetic relation, in which the normal velocity of propagation of the surface of discontinuity may be a given function of driving traction and temperature, is introduced for the special case of a thermoelastic material.

TL;DR: In this article, the authors construct explicitly a Helmholtz free energy, a kinetic relation and a nucleation criterion for a one-dimensional thermoelastic solid, capable of undergoing either mechanically or thermally-induced phase transitions.

TL;DR: In this article, an infinite slab containing a crack and deformed at infinity to a state of finite simple shear is considered, where the material of the slab is taken to be homogeneous, isotropic, elastic, and incompressible, and the analysis is carried out for the fully nonlinear equilibrium theory of finite elasticity.