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Micromorphic theory and its finite element formulation

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Abstract

In this work, the kinematics and basic laws of microcontinuum field theories, including micromorphic theory and micropolar theory, are introduced. Then, constitutive equations for micromorphic thermo-visco-elastic solids, heat conducting fluids, and thermal plasticity are rigorously derived. The concept of material force, which may also be named as Eshelby mechanics, is briefly introduced. The balance law of pseudo-momentum, including the detailed expression of the material forces, for the mathematical theory of micromorphic plasticity is rigorously derived. Finally, a set of finite element equations for the coupling of finite displacement, micromotion, and temperature fields is rigorously formulated.

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Acknowledgements

The theoretical formulation in this work is supported through the Idaho National Laboratory (INL) Laboratory Directed Research & Development (LDRD) Program under the U.S. Department of Energy Idaho Operations Office Contract DE-AC07-05ID14517.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Idaho National Laboratory, Idaho Falls, ID, 83415, USA

    Jiaoyan Li

  2. Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, DC, 20052, USA

    Kerlin P. Robert & James D. Lee

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  1. Jiaoyan Li
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  2. Kerlin P. Robert
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  3. James D. Lee
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Correspondence to James D. Lee.

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Li, J., Robert, K.P. & Lee, J.D. Micromorphic theory and its finite element formulation. Acta Mech 231, 1253–1284 (2020). https://doi.org/10.1007/s00707-019-02496-7

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