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

Georges Chatzigeorgiou (1) , Nicolas Charalambakis (2, 3)

1 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
2 School Civil Engineering [Thessaloniki]
3 Aristotle University of Thessaloniki

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 thecorresponding 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.

Mots clés: Continuously graded structures; Thermo-visco-plasticity; Instability; Homogenized problem

Domaines: Mécanique des matériaux [physics.class-ph]; Mécanique des solides [physics.class-ph]

Georges Chatzigeorgiou, Nicolas Charalambakis. A model of heterogeneous thermoviscoplastic material preserving uniform normal strains under combined compression, tension (or compression) and shearing. Instability and homogenization results. Composites Part B: Engineering, 2019, 167, pp.267-273. ⟨10.1016/j.compositesb.2018.12.022⟩. ⟨hal-01963542⟩