Mechanical and Civil Engineering Seminar

The objective (mesh-independent) simulation of evolving discontinuities, such as cracks, is still today a challenging task. Indeed, current available techniques are highly complex and very often involve outrageous computational costs, thereby making simulations up to complete failure quite difficult. In order to circumvent this problem, we propose herein a new hybrid computational framework in which local continuum damage mechanics is adaptively coupled with peridynamics to achieve the objective simulation of all the steps related to material failure, i.e. damage nucleation, crack formation and propagation. Local continuum damage mechanics successfully describes the degradation related to distributed microscopic defects before the formation of a macroscopic crack. However, when damage localization occurs, spurious mesh dependency arises, making the simulation of crack propagation challenging. On the other hand, the peridynamic theory is very promising for the simulation of fracture, as it naturally allows embedding discontinuities within the displacement field. Here, we present a hybrid local-continuum damage/peridynamic model. Local-continuum damage mechanics is used to describe volume damage before localization. Once localization is detected at a point, the remaining part of the energy is dissipated through an adaptive peridynamic model capable of the transition to a surface degradation, typically a crack. We believe that this framework, which actually mimics the real physical process of crack formation, is the first bridge between continuum damage theories and peridynamics. Two-dimensional numerical examples are used to illustrate that an objective simulation of material failure can be achieved by this method.