In this talk, we will present our recent work on peridynamics and its application. We consider a bond-based peridynamics with a nonlinear constitutive law relating the bond-strain to the pairwise force. For the model considered, we can show well-posedness and existence in the Hölder and Hilbert H2 space under appropriate conditions and obtain apriori bounds on the finite-difference and finite-element discretization. We will present the application of the model to mode-I and mixed-mode fracture problems. One particular topic of interest is the kinetic relation for the crack tip velocity in the peridynamics and its link to the local kinetic relation (LEFM theory). We recover the classical kinetic relation from the peridynamics formulation. We will present numerical results that support the theory. Another application of peridynamics recently gaining much attention is in the granular media. DEM based methods can describe the interaction in particulate media very well but cannot model the intra-particle fracture. Prior works have shown the possibility of using peridynamics for the deformation of individual particles and DEM-like laws for the inter-particle interaction. We will present our work on the development of a high-fidelity model that we refer to as PeriDEM for granular media that promises to handle the arbitrarily shaped particles and their breakage. We will present some numerical results that demonstrate the effectiveness of the PeriDEM model.
This talk is in honor of Dr. J. Tinsley Oden’s monumental contributions to computational mechanics (mini-symposium 103 organized by Dr. Romesh Batra).