Integral‐based averaging with spatial symmetries for non‐local damage modelling

Simulations utilizing local constitutive equations for strain-softening materials are known to be pathologically mesh-dependent. The rational solution this problem is use nonlocal material models. In paper, we discuss the application of integral-based approach simulation non-local damage accumulation and fracture. Various combinations non-localities with common spatial symmetries analysed analytically numerically. include plane strain axisymmetric cases, as well presence symmetry planes cyclic symmetries. Although not a symmetry, practically important case thin plates also analysed. We show that delocalization procedure should executed using symmetry-adapted averaging kernels. For considered symmetries, analytical closed-form expressions obtained. Moreover, new easy-to-use kernel suggested, same 3D, stress applications. To showcase procedures, consider ductile model, based on multiplicative decomposition deformation gradient, hyperelastic relations between stresses strains. FEM solutions series problems presented, including graduate accumulation, crack initiation