Relative Lagrangian Formulation of Finite Thermoelasticity

Authors

  • I-S. Liu Universidade Federal do Rio de janeiro
  • M. G. Teixeira Departamento de Ciência da Computação, Universidade Federal do Rio de Janeiro
  • G. T. A. Pereira Programa de Pós-Graduação em Informática, Universidade Federal do Rio de Janeiro

DOI:

https://doi.org/10.5540/tcam.2021.022.04.00609

Keywords:

Relative Lagrangian formulation, thermoelastic solid, small on large deformation, successive linear approximation, boundary value problem

Abstract

The motion of a body can be expressed relative to the present configuration of the body, known as the relative motion description, besides the classical Lagrangian and the Eulerian descriptions. When the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system of boundary value problems becomes linear. This formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. In fact, the proposed method is a process of repeated applications of the well-known “small deformation superposed on finite deformation” in the literature. This article presents these ideas applied to thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Some applications of such a formulation in numerical simulations are briefly reviewed and a numerical result is shown.

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Published

2021-10-26

How to Cite

Liu, I.-S., Teixeira, M. G., & Pereira, G. T. A. (2021). Relative Lagrangian Formulation of Finite Thermoelasticity. Trends in Computational and Applied Mathematics, 22(4), 609–628. https://doi.org/10.5540/tcam.2021.022.04.00609

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Original Article