Material characteristic length insensitive nonlocal modelling: A computationally efficient scaled nonlocal integral method

Abstract

Nonlocal modelling has achieved notable progress in resolving mesh dependence but remains constrained by two persistent challenges: sensitivity to characteristic length parameters and high computational costs. This study presents a scaled nonlocal integral formulation coupled with an optimized computational framework to simultaneously address two limitations. We first analytically demonstrate that variations in characteristic length induce proportional scaling of load–displacement curves, revealing that apparent changes in structure softening rate are artifacts of this scaling. Building on this insight, a dimensionless scaling factor is derived to systematically eliminate characteristic length dependence, enabling consistent predictions across parameter choices. The proposed method is integrated with a Mohr-Coulomb plasticity damage model, employing a return mapping algorithm for plasticity and a novel hybrid local-nonlocal solver accelerated by octree spatial partitioning for damage evolution. Three benchmark boundary value problems, evaluated across diverse element sizes, characteristic lengths, and softening laws, validate the robustness of the method. The results demonstrate that the proposed nonlocal method achieves mesh- and length-invariant load–displacement responses while accommodating arbitrary softening functions. The presented nonlocal computation method also shows a remarkable computational efficiency compared to the traditional nonlocal computation method.