Maximum energy dissipation-based incremental approach for structural analyses involving discrete fracture propagation in quasi-brittle materials

A maximum energy dissipation-based incremental approach (MEDIA) is proposed to overcome limit points, e.g. strong snap-backs, in the fracture analysis of quasi-brittle materials. An optimisation step is applied using an expression proposed to compute the change of dissipated energy within the discretised body when moving from one state of equilibrium to another. This expression is developed at the integration point level and uses a binary pathway vector to define all the possible solutions within that step. Due to the unique way the problem is cast, a genetic algorithm is deployed to identify the solution leading to the highest energy dissipation while following applicable thermodynamic constraints. The resulting analysis is non-iterative and purely incremental. MEDIA is particularly applicable in combination with discrete crack models. In this case, meshes are relatively coarse and each crack can be individually handled to maintain the computational cost independent of the discretisation. The equations are also cast in a direct inverse method that avoids explicitly solving the inversion of the stiffness matrices for each chromosome in the genetic optimisation. Problems having multiple snap-back effects and non-proportional loading, as well as lightly and highly reinforced concrete beams, are used to assess the suitability and efficiency of the proposed method. In contrast with other available techniques, MEDIA is shown to follow the adopted constitutive models without any energy loss due to the solution-finding process while providing adequate structural responses.