On adaptive refinement techniques in multi-field problems including cohesive fracture

This paper presents a generalized finite element formulation which incorporates solid and fluid phases together with a temperature field. The model is developed to obtain time-dependent solutions of complex 2-D cases, such as concrete gravity dams subjected to loading–unloading cycles, non-homogeneous specimens subjected to thermo-mechanical effects, etc. The solid behaviour incorporates a fully coupled cohesive-fracture discrete model, which includes thermal and hydraulic loads and the resulting crack nucleation and propagation is fully described. The evolution of fractures leads to continuous topological changes of the domain and these are handled by systematic local remeshing of the domain and a corresponding change of fluid and thermal boundary conditions. Optimality of the size of automatically generated finite elements is controlled, and the mesh density is adaptively adjusted on the basis of an a posteriori error estimation. For the process zone an element threshold number is introduced to obtain mesh independent results. The presented applications demonstrate the efficiency of the procedure and the importance of mesh refinement in multi-physics problems.