SPH as nonlocal regularisation method
Within the framework of continuum damage mechanics (CDM), mechanical loading leads to material damage and consequent degradation of material properties. Strain softening behaviour when implemented as a local model in the finite element (FE) method leads to an ill posed boundary value problem resulting in significant mesh sensitivity of the solution. It is well-known that the addition of a characteristic length scale to CDM models, a non-local approach, maintains the character of the governing equations. Similarities between the SPH method and nonlocal integral regularisation methods were investigated. Numerical experiments demonstrated that the width of the strain softening region is controlled by the smoothing length rather than the inter-particle distance in SPH. This demonstrates that the SPH method is inherently non-local and suggests that the smoothing length should be linked to the material characteristic length scale in solid mechanics simulations.