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

Abstract

We formulate a macroscopic description of the mechanics of damaged materials. To represent the microstructure, the distribution of crack sizes is captured by way of the Minkowski functionals, or so-called quermass integrals, while a second-rank tensor is used to describe the average orientation of the cracks. A two phase-type approach is adopted to distinguish elastically strained material from unstrained regions in the wake of the cracks. Using nonequilibrium thermodynamic techniques, the driving force for the growth of the microcracks is naturally identified. In particular, Griffith's law is generalized to assemblies of polydisperse crack sizes. Due to the detailed characterization of the microstructure, we are also able to account for the plastic zones at the rims of the cracks that are known to hamper the crack growth, and to discuss possible forms of the damage parameter. The presented approach separates in a transparent fashion the incorporation of fundamental thermodynamic and mechanic principles on one hand, from the specification of the material and details of the crack formation and growth on the other hand.

On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling

“…In the current formulation, the choice of the deformation field χ in the set of fundamental variables x is related to the dependence of the thermodynamic potentials on ∇χ . Indeed, the current choice x = (χ , m, θ) is related to the fact that densities like (9) and (14) induce functionals of the general form…”

“…Besides deriving the GENERIC-based form of this model in connection with its continuum thermodynamic counterpart, we take a closer look at the modeling of dissipation in both contexts than has been (to our knowledge) done in the previous work (see also, e.g., Muschik et al [13]). Generally speaking, the GENERIC-based approach offers a sufficiently rich structure to facilitate the formulation of models whose form is not known a priori (e.g., damage: Hütter and Tervoort [9]). From this point of view, connections between phenomenology-based continuum thermodynamics and statistical-mechanics-based "closed-form" approaches like the GENERIC such as those established in the current work may provide further insight into a means of exploiting GENERIC-based methods to formulate thermodynamic material models at the continuum level.…”

Mechanistic Analysis of Rock Damage Anisotropy and Rotation Around Circular Cavities

“…The fundamental principles of thermodynamics used to derive the DSID constitutive relationships are explained in detail e.g. by (Collins and Houlsby, 1997;Houlsby and Puzrin, 2006;Desmorat, 2006;Hütter and Tervoort, 2008;Keller and Hutter, 2011;Voyiadjis et al, 2011). Three functionals are needed for the model formulation:…”

A thermo-mechanical damage model for rock stiffness during anisotropic crack opening and closure

“…In fact a long-standing debate exists in thermodynamics of irreversible processes regarding the nature of the variables that shall be employed in energy potentials. Introducing non-plastic, purely damage-induced irreversible deformation raises thermodynamic consistency issues, some of which are explained in [21,36,41,46,81], to cite only a few references. Future theoretical work will be undertaken by the authors and their collaborators to derive a closed-form formulation from a single damage potential for both damage and damage-induced irreversible deformation, within a thermodynamically consistent framework.…”