Open AccessRelative Lagrangian Formulation of Finite Thermoelasticity
Author(s) -
I-S. Liu,
Marcello G. Teixeira,
Gabriel Thomaz Aquino Pereira
Publication year - 2021
Publication title -
trends in computational and applied mathematics
Language(s) - English
Resource type - Journals
ISSN - 2676-0029
DOI - 10.5540/tcam.2021.022.04.00609
Subject(s) - nonlinear system , thermoelastic damping , lagrangian and eulerian specification of the flow field , boundary value problem , eulerian path , deformation (meteorology) , lagrangian , mathematics , classical mechanics , mathematical analysis , physics , quantum mechanics , thermal , meteorology
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.