Micromorphic approach for gradient-extended thermo-elastic-plastic solids in the logarithmic strain space. (English) Zbl 1392.74069
Summary: The coupled thermo-mechanical strain gradient plasticity theory that accounts for microstructure-based size effects is outlined within this work. It extends the recent work of C. Miehe et al. [Comput. Methods Appl. Mech. Eng. 268, 704–734 (2014; Zbl 1295.74014)] to account for thermal effects at finite strains. From the computational viewpoint, the finite element design of the coupled problem is not straightforward and requires additional strategies due to the difficulties near the elastic-plastic boundaries. To simplify the finite element formulation, we extend it toward the micromorphic approach to gradient thermo-plasticity model in the logarithmic strain space. The key point is the introduction of dual local-global field variables via a penalty method, where only the global fields are restricted by boundary conditions. Hence, the problem of restricting the gradient variable to the plastic domain is relaxed, which makes the formulation very attractive for finite element implementation as discussed in [S. Forest, “Micromorphic approach for gradient elasticity, viscoplasticity, and damage”, J.
Eng. Mech. 135, No. 3, 117–131 (2009; doi:10.1061/(ASCE)0733-9399(2009)135:3(117))] and [C. Miehe et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 374, No. 2066, Article ID 20150170, 18 p. (2016; Zbl 1353.74065)].
MSC:
| 74M25 | Micromechanics of solids |
| 74F05 | Thermal effects in solid mechanics |
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
Keywords:
size effects; finite gradient plasticity; micromorphic regularization; thermo-mechanical processesReferences:
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