The intent of this expository paper is to draw the attention of the applied mathematics
community to an interesting two-dimensional mathematical model arising in solid mechanics …

This book is motivated by stimulating problems in contact mechanics, emphasizing antiplane
frictional contact with linearly elastic and viscoelastic materials. It focuses on the essentials …

A computational method is proposed for the dynamics of solids capable of twinning and
phase transitions. In a two-dimensional, sharp-interface model of twinning, the stored …

In this work, we apply a phase-field modeling framework to elucidate the interplay between
nucleation and kinetics in the dynamic evolution of twinning interfaces. The key feature of …

This is an introductory survey of some selected topics in finite elasticity. Virtually no previous
experience with the subject is assumed. The kinematics of finite deformation is characterized …

This paper describes recent work by the authors on a continuum model for crystal twinning.
Twinning is described as an anti-plane shear deformation with discontinuous strains …

The purpose of the present research is to investigate how the nonlinearity and the boundary
conditions have the power to influence the coupling of the various modes of deformation …

Many composite materials, including biological tissues, are modeled as non-linear elastic
materials reinforced with elastic fibers. In the current paper, the full set of dynamic equations …

A classical problem in the framework of nonlinear elasticity theory is the characterization of
the materials that may sustain a pure state of anti-plane shear in the absence of body forces …

It is well known that rotational shear deformations, though not universal, are controllable in
specific kinds of compressible and incompressible materials. For incompressible materials, it …