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 paper studies coherent, energy-minimizing mixtures of two linearly elastic phases with
identical elastic moduli. We derive a formula for the “relaxed” or “macroscopic” energy of the …

Over the last few years, a continuum model based on finite or nonlinear thermoelasticity has
been developed and successfully used to study crystalline solids that undergo a martensitic …

This paper addresses the non-uniqueness pointed out by Ericksen in his classical analysis
of the equilibrium of a one-dimensional elastic bar with non-convex energy. According to …

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 …

We investigate the behavior of a continuum model designed to provide insight into the
dynamical development of microstructures observed during displacive phase …

A new constitutive model for plastic deformation of crystalline materials deforming by slip
and twinning has been formulated, and implemented in a finite-element program. The …

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 …

We derive a new general jump condition on a broken Weierstrass–Erdmann extremal of a
vectorial variational problem. Such extremals, containing surfaces of gradient discontinuity …

Laser powder bed fusion additive manufacturing (L-PBF AM) technology holds notable
advantages regarding raw material reusability. Nonetheless, a notable gap exists in …