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An energy momentum consistent integration scheme using a polyconvexity‐based framework for nonlinear thermo‐elastodynamics
Author(s) -
Franke M.,
Janz A.,
Schiebl M.,
Betsch P.
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5816
Subject(s) - discretization , thermoelastic damping , nonlinear system , finite element method , projection (relational algebra) , cauchy stress tensor , coupling (piping) , tensor (intrinsic definition) , tensor product , mathematics , energy (signal processing) , mathematical analysis , algorithm , physics , geometry , thermal , engineering , mechanical engineering , statistics , quantum mechanics , meteorology , pure mathematics , thermodynamics
Summary The present contribution provides a new approach to the design of energy momentum consistent integration schemes in the field of nonlinear thermo‐elastodynamics. The method is inspired by the structure of polyconvex energy density functions and benefits from a tensor cross product that greatly simplifies the algebra. Furthermore, a temperature‐based weak form is used, which facilitates the design of a structure‐preserving time‐stepping scheme for coupled thermoelastic problems. This approach is motivated by the general equation for nonequilibrium reversible‐irreversible coupling (GENERIC) framework for open systems. In contrast to complex projection‐based discrete derivatives, a new form of an algorithmic stress formula is proposed. The spatial discretization relies on finite element interpolations for the displacements and the temperature. The superior performance of the proposed formulation is shown within representative quasi‐static and fully transient numerical examples.