A displacement-spatial co-adaptive strategy for the meshfree simulation of brittle phase-field fracture

Abstract

While prior studies have typically explored displacement-adaptive (DA) or spatially adaptive (SA) strategies independently, few have achieved their integration within a unified phase-field framework. To our knowledge, this work presents the first integration of adaptive displacement step-size adjustment and damage-partitioned spatial refinement within the RPIM meshfree framework. For the DA component, we develop a variation-driven step-size adjustment algorithm, in which the next displacement increment is adaptively determined based on the maximum variations of the phase field and history strain energy between successive load steps, as well as the current step size. For the SA component, we embed our previously proposed damage-driven partitioned node refinement scheme [1], which automatically adjusts nodal density in low-, medium-, and high-damage zones without requiring prior knowledge of the crack path. By combining DA and SA with RPIM’s capabilities (including irregular geometry handling, accurate interpolation, and low mesh sensitivity), the unified DSA accelerates simulations through simultaneous reduction of displacement steps and spatial nodes, significantly improving computational efficiency over using DA or SA alone. Validation on 2D and 3D benchmarks confirms superior adaptivity, efficiency, and accuracy.