Uncertainty propagation in finite deformations––A spectral stochastic Lagrangian approach

This work proposes a method for quantifying uncertainty propagation in finite deformation problems using the spectral stochastic finite element method (SSFEM). A spectral expansion of the current configuration of a deforming body is proposed to compute the stochastic deformation gradient which is in turn used to compute the stochastic analogs of the various quantities which appear in large deformation analysis such as strain and stress measures and consistent moduli. A total Lagrangian approach to the stochastic large deformation problem is presented. Model problems in large deformation elasto-plasticity are considered highlighting the features of the methodology developed. Rigorous comparisons with Monte-Carlo solutions are presented. It is shown that the proposed approach can estimate the probability density function and response statistics of the field variables with satisfactory accuracy.