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Micromorphic approach for gradient-extended thermo-elastic–plastic solids in the logarithmic strain space

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Abstract

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 Miehe et al. (Comput Methods Appl Mech Eng 268:704–734, 2014) 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 Forest (J Eng Mech 135:117–131, 2009) and Miehe et al. (Philos Trans R Soc A Math Phys Eng Sci 374:20150170, 2016).

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Authors and Affiliations

  1. Institute of Applied Mechanics (Civil Engineering), Chair I, University of Stuttgart, Pfaffenwaldring 7, 70569, Stuttgart, Germany

    Fadi Aldakheel

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  1. Fadi Aldakheel
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Correspondence to Fadi Aldakheel.

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Communicated by Andreas Öchsner.

This paper is dedicated to the memory of the late Professor Christian Miehe

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Aldakheel, F. Micromorphic approach for gradient-extended thermo-elastic–plastic solids in the logarithmic strain space. Continuum Mech. Thermodyn. 29, 1207–1217 (2017). https://doi.org/10.1007/s00161-017-0571-0

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