Asymptotically compatible meshfree discretization of state-based peridynamics for linearly elastic composite materials
This work provides a convergent numerical method for simulating fracture in composite materials using peridynamics, addressing a long-standing challenge with singular integral operators.
The authors developed an asymptotically compatible meshfree discretization for state-based peridynamics that achieves second-order convergence for Dirichlet problems and first-order convergence for curvilinear free surfaces and composite materials, even in the near-incompressible limit.
State-based peridynamic models provide an important extension of bond-based models that allow the description of general linearly elastic materials. Meshfree discretizations of these nonlocal models are attractive due to their ability to naturally handle fracture. However, singularities in the integral operators have historically proven problematic when seeking convergent discretizations. We utilize a recently introduced optimization-based quadrature framework to obtain an asymptotically compatible scheme able to discretely recover local linear elasticity as the nonlocal interaction is reduced at the same rate as the grid spacing. By introducing a correction to the definition of nonlocal dilitation, surface effects for problems involving bond-breaking and free surfaces are avoided without the need to modify the material model. We use a series of analytic benchmarks to validate the consistency of this approach, illustrating second-order convergence for the Dirichlet problem, and first-order convergence for problems involving curvilinear free surfaces and composite materials. We additionally illustrate that these results hold for material parameters chosen in the near-incompressible limit.