Mathematical Modeling the Nonlinear 1D Dynamics of Elastic Heteromodular and Porous Materials

Abstract

Approaches to mathematical modeling of nonlinear strain dynamics in heteromodular and porous materials are discussed; the mechanical properties of media are described in terms of the simple piecewise linear elastic models. Several nonstationary 1D boundary value problems show that the singularity of model relationships gives rise to shock waves and centered Riemann waves in generalized solutions. Nonstationary load modes leading to the listed nonlinear effects are indicated separately for heteromodular and porous media.

Shock Loading of Heteromodular Elastic Materials under Plane-Strain Condition

“…This feature called heteromodularity has an effect to dynamic deformation processes especially. The one-dimensional dynamics of heteromodular materials has been described in reasonable detail, for example, in [5][6][7] and other works. The purpose of this paper is to study the dynamical processes in the heteromodular materials under plane strain.…”