One-dimensional motion of a material with a strain theshold

Abstract

We consider the one-dimensional shearing motion of a material exhibiting elastic behaviour when the stress is below some threshold. The threshold represents a limit to the deformability, i.e. no further deformation can occur on increasing the stress. The mathematical formulation leads to a free boundary problem for the wave equation, whose structure depends on whether the stress (and the velocity) are continuous across the propagating interface for the strain threshold .Local existence and uniqueness are proved for the continuous case (in which the interface propagation is subsonic). Some explicit solutions are calculated for another case (with a supersonic interface). It is shown that the model with strain threshold is never the limit of hyperelastic systems.

Keywords

• Implicit constitutive theories
• Free boundary problems
• Wave equation