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.
Highlights
In modern continuum thermodynamics, to deduce thermodynamic restrictions on constitutive functions two essential approaches are widely employed, i.e., Coleman-Noll procedure [3] and Muller-Liu procedure [8]
At each time step, the constitutive function is calculated at the present state of deformation which will be regarded as the reference configuration for the state, and assuming the deformation to the state is small, the constitutive function and the partial differential equation can be linearized
The application of the successive linear approximation for a Mooney-Rivlin thermoelastic material is presented in detail
Summary
To deduce thermodynamic restrictions on constitutive functions two essential approaches are widely employed, i.e., Coleman-Noll procedure [3] and Muller-Liu procedure [8]. The application of the successive linear approximation for a Mooney-Rivlin thermoelastic material is presented in detail It is presented the numerical result of a finite deformation problem with temperature variation by the finite element method. This article is divided as follows: Section 2 presents the basic concepts of Thermodynamics of elastic materials necessary to obtain the balance equations in Lagrangian description; Section 3 addresses the concept of relative motion description as a preparation for Section 4 which, presents the Relative Lagrangian formulation of the problems considering a Mooney-Rivlin thermoelastic material; Section 5 presents some comments on the SLA; Section 6 presents the numerical result of a finite strain problem subject to temperature variation by the finite element method and, Section 7 presents the final conclusions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
