Multi-stage calibration framework for continuum damage mechanics models

We present a multi-stage calibration framework for determining material parameters in continuum damage models. The framework sequentially minimizes loss functions targeting bespoke performance metrics, like peak force and displacement, total work, and $L^2$ norm of experimental vs numerical curves. Incorporating two nonlinear solvers, Unified Arc-Length (UAL) and Newton–Raphson (NR), we examine our approach against several benchmark problems with various damage theories, equivalent strain definitions and evolving length scale regimes. Overall, UAL outperforms NR in computational efficiency and captures snap-backs on the equilibrium path. The proposed framework can be readily expanded to identify material model parameters for other constitutive model classes.