Thermomechanical constitution of spalling elastic bodies

Abstract

In this article we develop a theory of spallation of a brittle thermoelastic body, and of the interaction between propagating waves and accumulated damage. This theory is applied to the prediction of the effect of spall damage on the elastic stiffness and thermal conductivity of the material.

Damage model for jointed rock mass and its application to tunnelling

“…A comprehensive thermomechanical model based on the vectorial representation of the damage was formulated by Davison and Stevens [6]. The damage is locally de®ned as:…”

A continuum approach to brittle and fatigue damage: Theory and numerical procedures

“…These damage variables require the establishment of additional rate equations and criteria that indicate when the current state will change. The governing equations can be derived within a thermodynamical framework in a manner as discussed by Coleman and Gurtin (1967) and Davison and Stevens (1973). In this paper a restriction to isotropic damage is made.…”

Continuum damage mechanics: combining thermodynamics with a thoughtful characterization of the microstructure

“…However, in most cases, the free energy expression is not used to feed detailed information about crack dimensions on the thermodynamic state of the material, but is merely selected such that it coincides with the effective stress tensor assumption [6][7][8]. Also the representation theorem of tensor functions [14][15][16] has been used to arrive at general expressions to describe damage [3,5], but this, unfortunately, often leads to an abundant amount of material coefficients.…”

“…Budiansky and O'Connell [2] used a self-consistent procedure to arrive at a crack-density parameter to describe the reduction of the elastic constants that, in the case of an isotropic distribution of penny-shaped cracks, equals the number density of cracks times the average of the cube of the crack radius. Also vectors [3,4], second order tensors [5] and even eighth-order tensors [1] have been used to describe the evolution and orientation distribution of damage in materials. One of the most popular concepts in CDM is based on the notion of a so-called "effective stress" combined with the hypothesis of strain equivalence [6][7][8].…”

“…Typically, the usual balance laws of mass, momentum, moment of momentum and energy, combined with a detailed expression of the Helmholtz free energy as a function of all, including the hidden (damage) variables, are augmented with the Gibbs-Duhem inequality, specifying the non-negative entropy production density [3,4,8,11,12]. Applied in this manner, the thermodynamics of hidden variables to describe damage is formally analogous to the more well-known use of hidden variables to describe finite plasticity [13].…”