Finite deformation fracture modelling of a thermo-mechanical cohesive zone

In the present contribution, the development of a thermo-mechanical cohesive zone model is discussed in the context of a strong discontinuity formulation according to the concept of partitions of unity [

1

]. On the basis of our previous work, [

2

,

3

], and also the contributions, [

4

,

5

], the deformation map is thereby defined in terms of mutually independent continuous and discontinuous portions of the displacement. As an extension, we also introduce a similar subdivision of the temperature field in one continuous and one discontinuous part, separated by the internal crack surface. As a result, we consider the weak formulation of the equation of motion and the energy equation as consisting of four coupled equations on the structure level. In the paper, we will focus on the conditions for onset as well as continued (coupled) discontinuity development within a thermo-hyperelastoplastic continuum with isotropic plastic hardening as well as thermally softening response. In the case of continued discontinuity development, a cohesive zone law is specified for the representation of the decay of the traction vector combined with heat flux across the interface zone. Apart from the crucial fracture modelling, we also discuss the numerical treatment and aspects of computational implementation of the proposed approaches. A couple of numerical examples that illustrate the capabilities of the proposed approach to the modelling of the thermo-mechanical cohesive zone are included.