The Second Law as a constraint and admitting the approximate nature of constitutive assumptions

TL;DR

This paper presents a variational framework that treats the Second Law of thermodynamics as a constraint in continuum thermomechanics, accounting for the approximate nature of constitutive assumptions and analyzing when it acts as an over-constraint or a necessary condition.

Contribution

It introduces a novel variational principle that incorporates the Second Law as a flexible constraint, addressing the approximate nature of constitutive models in thermomechanics.

Findings

The variational principle is unconstrained and concave.

The paper discusses cases where the Second Law is an over-constraint.

The paper analyzes when the Second Law acts as a necessary constraint.

Abstract

A scheme for treating the Second Law of thermodynamics as a constraint and accounting for the approximate nature of constitutive assumptions in continuum thermomechanics is discussed. An unconstrained, concave, variational principle is designed for solving the resulting mathematical problem. Cases when the Second Law becomes an over-constraint on the mechanical model, as well as when it serves as a necessary constraint, are discussed.