2026-08-14 –, Room 4
A common task in solid mechanics is to select and calibrate a constitutive model for a specific material. Constitutive model discovery seeks to automate this task. The framework statFEM-EUCLID.jl provides an unsupervised approach for constitutive model discovery from sparse and noisy measurements and global reaction forces. Using UMBridge.jl, the framework treats the finite element solution as a black box, such that any finite element solver can, in principle, be linked to it.
Starting point is a specific problem setting, e.g. a plate with a hole under tension. For this setting, a set of displacement and/or strain observations Y and global reaction forces must be available. The discovery loop starts with an initial guess for a constitutive model and its parameters, and goes as follows:
1) Sample traction forces from a distribution that reflects the uncertainties in reaction forces
2) Query the FEM black box through UMBridge and propagate uncertain traction onto forecasted displacements u_f using non-intrusive polynomial chaos expansion
3) Check if the distance between measurements Y and forecasted displacements is sufficiently small
3a) If yes, we have converged and the current material model is the best fit
3b) If not, continue
4) Bayesian updating of forecasted displacements u_f from given observations Y yields assimilated displacements u_a
5) Taking the mean of u_a, discover a new material model using the virtual field method VFM or EUCLID
In the talk, the basic ideas of the statFEM-EUCLID framework, design decisions of the package and the flexibility in using different FEM solvers through UMBridge will be addressed.
Jan Philipp Thiele is a Research Software Engineer in the digital science support lab of TU Braunschweig.