Mesh-free simulations of shear banding in large deformation

Mesh-free approximation is used in numerical simulations of strain localization under large deformation. An explicit displacement based mesh-free formulation is used in both two-dimensional and three-dimensional computations. The spatial isotropy of mesh-free interpolant is demonstrated through the numerical example to show that mesh-free methods possess certain “mesh objectivity” that alleviates the notorious mesh-alignment sensitivity associated with numerical simulation of strain localization. It is also demonstrated in the paper that mesh-free interpolants can accurately capture finite shear deformation under large mesh distortion without recourse to special mesh design and remeshing. Moreover, curved shear band surface and multiple shear band interactions are captured in numerical simulations.