Bayesian inversion for unified ductile phase-field fracture

TL;DR

This paper develops a Bayesian inversion framework using phase-field models to accurately estimate ductile fracture parameters in metallic materials, integrating experimental data with advanced MCMC techniques.

Contribution

It introduces a unified variational phase-field model for ductile fracture and applies Bayesian inversion with multiple MCMC methods to estimate material parameters.

Findings

Bayesian inversion effectively estimates ductile fracture parameters.

Unified phase-field model captures different ductile failure behaviors.

MCMC methods vary in computational efficiency for parameter estimation.

Abstract

The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. In this work, we develop a step-wise Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis-Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the R-convergence tool.