  A well-established approach for inferring full displacement and stress fields
from possibly sparse data is to calibrate the parameter of a given constitutive
model using a Bayesian update. After calibration, a (stochastic) forward
simulation is conducted with the identified model parameters to resolve
physical fields in regions that were not accessible to the measurement device.
A shortcoming of model calibration is that the model is deemed to best
represent reality, which is only sometimes the case, especially in the context
of the aging of structures and materials. While this issue is often addressed
with repeated model calibration, a different approach is followed in the
recently proposed statistical Finite Element Method (statFEM). Instead of using
Bayes' theorem to update model parameters, the displacement is chosen as the
stochastic prior and updated to fit the measurement data more closely. For this
purpose, the statFEM framework introduces a so-called model-reality mismatch,
parametrized by only three hyperparameters. This makes the inference of
full-field data computationally efficient in an online stage: If the stochastic
prior can be computed offline, solving the underlying partial differential
equation (PDE) online is unnecessary. Compared to solving a PDE, identifying
only three hyperparameters and conditioning the state on the sensor data
requires much fewer computational resources.
  This paper presents two contributions to the existing statFEM approach:
First, we use a non-intrusive polynomial chaos method to compute the prior,
enabling the use of complex mechanical models in deterministic formulations.
Second, we examine the influence of prior material models (linear elastic and
St.Venant Kirchhoff material with uncertain Young's modulus) on the updated
solution. We present statFEM results for 1D and 2D examples, while an extension
to 3D is straightforward.
