Abstract

The objective of the present project is the development and numerical implemen- tation of constitutive equations for the coupled thermomechanical damage problem in the speci c context of the in nitesimal strain approximation, within the framework of the thermodynamics of irreversible processes. The basis of the linear coupled- eld analysis is reviewed within a thermodynamic framework, so that the balance equations governing the linearised coupled thermo- mechanical problem are obtained. In particular, a state potential is proposed from which the variables associated with the internal state variables can be derived. The Helmholtz free energy proposed consists of an additive expression of three terms: a mechanical and a thermal contribution, and a coupling term. To introduce the damage coupling, the mechanical contribution of the Helmholtz free energy has been modelled to describe an elastoplastic isotropic ductile damage behaviour. For this purpose, the Gurson-Tvergaard-Needleman (GTN) model has been revised to obtain an elastoplastic damage model which is consistent with the thermodynamic framework. The constitutive equations have been derived from the proposed state potential. Then, the GTN dissipation potential has been used to ob- tain the evolution laws of the state variables associated with the dissipative mecha- nisms. A strain driven algorithm has been developed to integrate the evolution laws through a Backward Euler scheme. Finally, the consistent elastoplastic tangent has been obtained by consistent linearisation of the discretised rate relations. The so-obtained model formulation and numerical algorithms have been imple- mented as a constitutive model in the C++ library MUESLI. The nite element solu- tion of the momentum and energy equations of the coupled thermomechanical prob- lem is obtained using a fully implicit monolithic scheme of the general nite element code IRIS. Finally, numerical simulations have been conducted to assess the features of the proposed model. Regarding the elastoplastic damage model behaviour, the comparative analysis with the GTN model has con rmed that both models exhibit a softening behaviour in the plastic region. The softening predicted by the proposed model is signi cantly higher. Additionally, it has been shown that the proposed formulation is able to account for the coupling between damage and softening, ma- terialised in a deterioration of the sti ness matrix. Finally, the isothermal and adia- batic virtual tests performed on notched specimens have shown that the implemented constitutive equations are suitable to simulate the fully coupled thermoelastoplastic damage problem, both in the static and rst-order transient approaches.