Thermomechanics of damageable materials under diffusion: modelling and analysis

Abstract

We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat generation/consumption/transfer is considered. Damage is modelled as rate-independent. The applications include metalhydrogen systems with metal/hydride phase transformation, poroelastic rocks, structural and ferro/para-magnetic phase transformation, water and heat transport in concrete, and, if diffusion is neglected, plasticity with damage and viscoelasticity, etc. For the ensuing system of partial differential equations and inclusions, we prove existence of solutions by a carefully devised semi-implicit approximation scheme of the fractional-step type.

A general thermodynamical model for adhesive frictional contacts between viscoelastic or poro-viscoelastic bodies at small strains

“…e.g. [51]. In some situations, only solvent transport over the adhesive interface is relevant, while in other situations the transport inside the bulk accompanied with pronounced swelling effects may lead to delamination, cf.…”

A Temperature-Dependent Phase-Field Model for Phase Separation and Damage

“…Up to our knowledge, this is one of the first contributions on the analysis of a model encompassing all of the three processes (temperature evolution, damage, phase separation) in a thermoviscoelastic material. Recently, a thermodynamically consistent, quite general model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and rate-independent damage, beside possible visco-inelastic processes, has been studied in [43]. Let us highlight the main difference to our own model: the evolution of the damage process is therein considered rate-independent, which clearly affects the weak solution concept adopted in [43].…”

“…Recently, a thermodynamically consistent, quite general model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and rate-independent damage, beside possible visco-inelastic processes, has been studied in [43]. Let us highlight the main difference to our own model: the evolution of the damage process is therein considered rate-independent, which clearly affects the weak solution concept adopted in [43]. In particular, we may point out that dealing with a rate-dependent flow rule for the damage variable is one of the challenges of our own analysis, due to the presence of the quadratic nonlinearity in ε(u) on the right-hand side of (1.3c).…”

Existence results for a coupled viscoplastic-damage model in thermoviscoelasticity

“…it is rate-dependent. Conversely, in [RT15] damage evolves rate-independently, while the evolution of plasticity is rate-dependent. In a different spirit, a fully rate-independent system for the evolution of the damage parameter, coupled with a tensorial variable which stands for the transformation strain arising during damage evolution, is analyzed in [BRRT16].…”

“…damage, rate-dependendent plasticity, the heat equation, as well as the porosity and the water concentration variables. Here we shall neglect the latter two variables and tackle the weak solvability and the existence of solutions, for a (fully rate-dependent ) viscoplastic (gradient) damage model, with viscosity and inertia in the momentum balance (the first according to Kelvin-Voigt rheology), and with thermal effects encompassed through the heat equation, whereas in [RT15] the enthalpy equation was analyzed, after a transformation of variables. We plan to address the vanishing-viscosity and inertia analysis for our model, and discuss the weak solution concept thus obtained, in a future contribution.…”