A new meshfree method for accurate and efficient solutions to solid mechanics problems involving large deviatoric deformation, fracture, and fragmentation

We present a novel meshfree method for accurate and efficient solutions to solid mechanics problems involving large deviatoric deformation, fracture, and fragmentation. Central to the approach is a newly developed meshfree shape function that satisfies the Kronecker delta property, exhibits first-order consistency, is non-negative, and achieves C 1 smoothness. The formulation employs nodal integration which is desirable for problems with large topological changes. The combination of nodal integration and the Kronecker delta property leads to a naturally diagonal explicit equilibrium equation even in the presence of complex boundary and contact conditions. A key innovation is the introduction of shadow nodes, which, in conjunction with a local triangle removal strategy, enables the seamless handling of complex geometries and evolving discontinuities without explicit boundary representations. The method demonstrates excellent convergence and high accuracy across a range of linear and nonlinear benchmark problems. Its robustness and versatility are further illustrated through challenging simulations involving extreme fracture and fragmentation. • A meshfree shape function with the Kronecker delta property, first order consistency, non-negativity, and C 1 smoothness. • A local triangle removal method and shadow nodes that allow meshing complex geometries without boundary descriptions. • Excellent convergence in linear and nonlinear benchmark problems compared to existing methods. • Great robustness and versatility demonstrated through problems involving extreme fracture and fragmentation.