We propose a benchmark and methodology to assess numerical methods' ability to represent and maintain crack-free superposition states in linear and nonlinear structural simulations. The benchmark provides analytic reference solutions, test geometries, error metrics, and a curated suite of cases covering elastic, elastoplastic, and fracture-prone regimes. Results on representative discretizations (continuous FEM, discontinuous Galerkin, meshfree) show how approximation, stabilization, and time integration choices affect spurious crack nucleation and opening. We identify key failure modes and prescribe best-practice recommendations to avoid nonphysical cracking while preserving superposed solution fidelity.
| Limitation | Mitigation | |------------|-------------| | Non-linear material behavior (plasticity) | Use superposition only in elastic regime; if plasticity occurs, apply Neuber correction or switch to incremental superposition. | | Crack closure effects | Account for residual compressive stresses reducing $K_I$ — beneficial crack-free condition. | | Stress gradient sensitivity | Use critical distance method (TCD) rather than point stress. | | Anisotropic residual fields | Perform eigenstrain reconstruction from multiple measurements. | superposition benchmark crack free
More resources available at help.procreate.com