Quantification method for extrapolation errors of constitutive models and a demonstration on C/SiC composite

Phenomenological constitutive models are always used in structural analysis due to its simplicity in modeling and implementation. However, these models are always fitted from limited experimental curves, leading to errors and insufficient confidence in analysis results. Previous constitutive model error quantification methods rely on a-posteriori experimental observations. In this paper, a priori error quantification method for extrapolation errors of constitutive models is established. Gaussian Process models are fitted with stress states as inputs and strains as outputs. Prediction variations of the GP model are used as the error indicator. The method naturally leads to zero error at known load cases and larger error at load cases away from existing experimental data. It can be integrated with FEM analysis easily and provide error visualization capabilities along with stress fields. Stress states at large error areas provide directions for further experiments and constitutive refinement. The method is demonstrated on the constitutive model and FEM analysis of a C/SiC frame and showed good validity.