Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The role of material non-homogeneities on the formation and evolution of strain non-uniformities in thermoviscoplastic shearing

Authors: Theocharis Baxevanis and Nicolas Charalambakis
Journal: Quart. Appl. Math. 62 (2004), 97-116
MSC: Primary 74C10; Secondary 35B30, 35B40, 74E05, 74F05
DOI: https://doi.org/10.1090/qam/2032574
MathSciNet review: MR2032574
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Abstract: In this paper we present the effect of macroscopic non-homogeneities on the distribution and evolution of strain non-uniformities during the shearing of thermoviscoplastic materials. The thermomechanical parameters (strain hardening, strain rate sensitivity, and thermal softening), as well as all of the material parameters are supposed to depend explicitly on the space variable. We show that, even under stability conditions, the strain exhibits intense, time-increasing non-uniformities, following the non-homogeneities, in a specific rate, which depends on the degree of non-homogeneity exhibited by the thermomechanical parameters. By considering both the isothermal and anisothermal cases, we obtain results indicating that non-uniformity measures, based on the control of the strain gradient, are more suitable to give stability conditions of non-homogeneous materials. Moreover, we present numerical results concerning the interplay between material non-homogeneities, initial defects, and boundary conditions for two specific cases: the shearing of a reinforced slab and the shearing of a plate composed of several thin layers of periodic structure. The results are in complete agreement with the analytical behavior of the model.

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DOI: https://doi.org/10.1090/qam/2032574
Article copyright: © Copyright 2004 American Mathematical Society

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