A model of heterogeneous thermoviscoplastic material preserving uniform normal strains under combined compression, tension (or compression) and shearing. Instability and homogenization results

Abstract

In this paper, we present the special solution of the two-dimensional problem of a continuously graded composite made of thermovisco- rigid plastic materials under combined biaxial quasistatic compression and tension (or compression) and shear, that preserves prescribed uniform normal strains. The related reference initial-boundary value problem is fully defined and the corresponding solution is analyzed and computed numerically. In the context of a linearized instability analysis, critical conditions, as the critical shear banding angle, in terms of the loading level and material heterogeneities, are presented. In the context of non-linear instability, these results are examined and explained. Additionally, in the same context of non-linear analysis, the destabilizing mechanism, the onset of instability and the critical time for prescribed lower and upper bounds of equivalent strain-rate and upper bound of equivalent strain are defined and related to the lateral normal stress. The limitations of linearized analysis results are also revealed. Moreover, a semi-analytical homogenization scheme for a periodically-graded plate is presented. The related results are used for the derivation of a homogenized problem of a multilayered composite with continuously graded interlayers.