Bayesian inversion for unified ductile phase-field fracture

Abstract The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design fabrication metallic materials structures on a large scale. Numerical aspects dictate sub-optimal calibration plasticity- fracture-related parameters number material properties. These enter system partial differential equations as forward model. Thus, an accurate estimation enables precise determination response different stages, particularly post-yielding regime, where take place. In this work, we develop Bayesian inversion framework fracture to provide knowledge regarding effective mechanical parameters. To end, synthetic experimental observations used estimate posterior density unknowns. model behavior solid materials, rely phase-field approach fracture, which present unified formulation that allows recovering models variational basis. framework, incremental minimization principles class gradient-type dissipative derive governing equations. overall is revisited extended case anisotropic fracture. Three subsequently recovered by certain choices constitutive functions, later assessed through techniques. A step-wise method proposed determine unknowns process. function parameters, three common Markov chain Monte Carlo (MCMC) techniques employed: (i) Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, (iii) ensemble Kalman filter combined with MCMC. examine computational efficiency MCMC methods, employ $$\hat{R}{-}convergence$$ R ^ - c o n v e r g tool. resulting algorithmically described detail substantiated numerical examples.