An anisotropic thermomechanical damage model for concrete at transient elevated temperatures

Abstract

The behaviour of concrete at elevated temperatures is important for an assessment of integrity (strength and durability) of structures exposed to a high-temperature environment, in applications such as fire exposure, smelting plants and nuclear installations. In modelling terms, a coupled thermomechanical analysis represents a generalization of the computational mechanics of fracture and damage. Here, we develop a fully coupled anisotropic thermomechanical damage model for concrete under high stress and transient temperature, with emphasis on the adherence of the model to the laws of thermodynamics. Specific analytical results are given, deduced from thermodynamics, of a novel interpretation on specific heat, evolution of entropy and the identification of the complete anisotropic, thermomechanical damage surface. The model is also shown to be stable in a computational sense, and to satisfy the laws of thermodynamics.

Thermodynamics in solid mechanics: a commentary

“…The papers that follow are independent but with the underlying theme that they address aspects of thermodynamics in solid mechanics. They have been arranged to provide a flow from theoretical considerations of thermodynamic stability (Petryk 2005), generalized constitutive developments and continuum mechanics (Schreyer & Maudlin 2005), through to thermodynamic aspects of particular materials such as generalized granular media (Suiker & de Borst 2005), concrete (Lemarchard et al 2005;Baker & de Borst 2005), and steels (Vakili-Tahami et al 2005).…”

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

“…For more general expressions for the coupling term f 3 in the free energy, the reader is referred to the literature on the representation theorem of tensor functions [14][15][16]. It may be seen as part of our model that the form of the (N,F)-coupling must guarantee the symmetry of the stress tensor (11). If a free energy expression is used that leads to antisymmetric contributions in the stress tensor, all possible ramifications must be explored carefully, e.g., the conservation of the angular momentum.…”

“…Although this may seem as a limitation of our approach on the first sight, it comes with the invaluable benefit of respecting fundamental principles of mechanics and thermodynamics. In particular, the damage parameter D = ψ 2 ψ −1/3 0 /2 enters directly into e and s, possibly in an anisotropic manner in combination with N. This in turn does not only affect the stress tensor (11), but also the driving force for the formation and growth of cracks (20). For illustration of that point, we briefly discuss the stress tensor expression based on the free energy density (25), that has been introduced earlier to examine the driving force A.…”

“…However, most CDM treatments of this so-called "ductile damage" associate damage solely with changes in the elastic properties of the material, assuming additive contributions of damage and plastic deformation to the free energy expression [11,17], although also more elaborate couplings between damage and plastic deformation have been considered [18].…”

“…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].…”