An alternative bilinear peridynamic model to simulate the damage process in quasi-brittle materials

Abstract

The study of damage process in quasi-brittle materials (such as plain or reinforced concrete and composites formed by a brittle matrix with ductile filler) is a challenge for researchers, especially when neither linear fracture mechanics nor plasticity approaches can be used. Some quasi-brittle material effects such as localization, scale effects and interaction between a cluster of micro-cracks are difficult to be captured with the standard formulation of the Finite Element Method (FEM). A valid alternative in the study of damage consists in using Discrete Element Methods (DEM). Among different versions available, one proposed by Silling can be highlighted due to the consistent way to connect continuum and discontinuum behaviour. This approach considers the body as composed by a set of nodes with lumped masses that can interact with each other in a finite volume or neighbourhood by uniaxial laws, where the variation of distance between two nodes regulates the intensity of the interaction forces. In this context, a bilinear law to represent this interaction among the nodes is proposed. This law was used by the authors with success in other versions of the DEM. Simulations of sandstone specimens submitted to uniaxial tensile show an acceptable compliance with experimental results, thus verifying the bilinear model. The proposal reduces the computational cost in the simulations and makes the model calibration more flexible. Considerations of the material random nature were fundamental to obtain good results in the applications. Finally, the advantages of the new law implementation are discussed.