Coupling of FEM meshes with Peridynamic grids

The original peridynamics formulation uses a constant nonlocal region, the horizon, over the entire domain. We propose here adaptive refinement algorithms for the bond-based peridynamic model for solving statics problems in two dimensions that involve a variable horizon size. Adaptive refinement is an essential ingredient in concurrent multiscale modeling, and in peridynamics changing the horizon is directly related to multiscale modeling. We do not use any special conditions for the “coupling” of the large and small horizon regions, in contrast with other multiscale coupling methods like atomistic-to-continuum coupling, which require special conditions at the interface to eliminate ghost forces in equilibrium problems. We formulate, and implement in two dimensions, the peridynamic theory with a variable horizon size and we show convergence results (to the solutions of problems solved via the classical partial differential equations theories of solid mechanics in the limit of the horizon going to zero) for a number of test cases. Our refinement is triggered by the value of the nonlocal strain energy density. We apply the boundary conditions in a manner similar to the way these conditions are enforced in, for example, the finite-element method, only on the nodes on the boundary. This, in addition to the peridynamic material being effectively “softer” near the boundary (the so-called “skin effect”) leads to strain energy concentration zones on the loaded boundaries. Because of this, refinement is also triggered around the loaded boundaries, in contrast to what happens in, for example, adaptive finite-element methods.

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Adaptive refinement and multiscalemodeling in 2d peridynamics

Static solution of crack propagation problems in Peridynamics

An improved coupled thermo-mechanical bond-based peridynamics with multirate time integration scheme is developed to study the thermal shock cracking behaviors in brittle solids. In the proposed numerical method, effects of the relative distance between material points on thermoelastic stiffness of a bond are considered in the deformed configuration . The periodical and hierarchical characteristics of thermal crack patterns of ceramics in quenching tests are accurately predicted in 2-D and 3-D cases. The present numerical results are in good agreement with the previous experimental observations and data. It is shown that the proposed numerical model is simple and efficient to simulate the periodical and hierarchical initiation and propagation of cracks in brittle solids under thermal shocks. The present numerical simulations provide direction observations on the whole processes of crack initiation and propagation , which is a quite difficult problem in the laboratory experiments.

Davide Tomasi

Papers

Coupling of FEM meshes with Peridynamic grids

An enhanced coupling of PD grids to FE meshes