Bayesian inversion codes for various one-dimensional model problems in computational mechanics is provided here. Enjoy!
i Elasticity,
ii Heat equation with convection,
iii Elastoplasticity,
iv Phase-field fracture for brittle materials,
v Phase-field fracture for ductile materials (gradient-extended plasticity),
vi Phase-field fracture for thermoelasticity,
vii Phase-field fatigue fracture.
How to cite us: https://doi.org/10.5281/zenodo.6451942
Accepted for publication in Archives of Computational Methods in Engineering
abstract. The complexity of many problems in computational mechanics calls for reliable programming codes and accurate simulation systems. Typically, simulation responses strongly depend on material and model parameters, where one distinguishes between backward and forward models. Providing reliable information for the material/model parameters enables us to calibrate the forward model (e.g., a system of PDEs). Markov chain Monte Carlo methods are efficient computational techniques to estimate the posterior density of the parameters. In the present study, we employ Bayesian inversion for several mechanical problems and study its applicability to enhance the model's accuracy. Seven different boundary value problems in coupled multi-field (and multi-physics) systems are presented. To provide a comprehensive study, both rate-dependent and rate-independent equations are considered. Moreover, open-source codes are provided, constituting a convenient platform for future developments for, e.g., multi-field coupled problems. The developed package is written in MATLAB and provides useful information about mechanical model problems and the backward Bayesian inversion setting.