Colloquia

Summary

Multiscale structural modelling of microstructures requires upscaling of constitutive behavior from lower to higher scales.

The upscaling process for linear material behavior can be addressed with a homogenization approach in which averaged stress and strain of a lower scale is imposed on the higher scale. However, homogenization is incapable of capturing nonlinear effects. Instead, a Bayesian method that couples the respective scales in terms of energy observables can be employed. The probabilistic setting enables nonlinear updating of uncertain higher scale parameter priors and permits lower scale uncertainty to be propagated through the model.

In this work, a finite element model of the intricate microstructure of porous trabecular bone is considered as a lower scale model for a single higher scale homogeneous element. The Bayesian updating procedure is implemented using a Markov Chain Monte Carlo sampling algorithm and a custom likelihood function that incorporates existing finite element software.

The applicability of this procedure is successfully demonstrated in a case study using linear elastic material models with a stochastic lower scale material description.

This paves the way for further implementation of the probabilistic modelling practice into other deformation regimes such as plasticity and damage.