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A Novel Mixed and Energy-Momentum Consistent Framework for Coupled Nonlinear Thermo-Electro-Elastodynamics
International Journal for Numerical Methods in Engineering
Swansea University Author: Antonio Gil
Accepted Manuscript under embargo until: 27th January 2024
DOI (Published version): 10.1002/nme.7209
A novel mixed framework and energy-momentum consistent integration scheme in the field of coupled nonlinear thermo-electro-elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of poly-convex strain energy functions. For this elastodynamic...
|Published in:||International Journal for Numerical Methods in Engineering|
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A novel mixed framework and energy-momentum consistent integration scheme in the field of coupled nonlinear thermo-electro-elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of poly-convex strain energy functions. For this elastodynamic framework, the properties of the so-called tensor cross product are exploited to derive a mixed formulation via a Hu-Washizu type extension of the strain energy function. Afterwards, a general path to incorporate non-potential problems for mixed formulations is demonstrated. To this end, the strong form of the mixed framework is derived and supplemented with the energy balance as well as Maxwell’s equations neglecting magnetic and time dependent effects. By additionally choosing an appropriate energy function, this procedure leads to a fully coupled thermo-electro-elastodynamic formulation which benefits from the properties of the underlying mixed framework. In addition, the proposed mixed framework facilitates the design of a new energy-momentum consistent time integration scheme by employing discrete derivatives in the sense of Gonzalez. A one-step integration scheme of second-order accuracy is obtained which is shown to be stable even for large time steps. Eventually, the performance of the novel formulation is demonstrated in several numerical examples.
Nonlinear thermo-electro-elastodynamics, polyconvexity, tensor cross product, non-potential mixed formulation, energy-momentum scheme
Faculty of Science and Engineering
DFG, German Research Foundation, project number 443238377
21132/SF/19, Fundación Séneca, Región de Murcia
Fundación Séneca, grant 20911/PI/18, and PID2021-125687OA-I00