Stochastic constitutive modeling of elastic-plastic materials with uncertain properties

Abstract A new deterministic constitutive model is developed that has a form that is efficient for use in a stochastic constitutive model in which the material properties and the stress and stiffness fields are considered uncertain and modeled as random variables. Simplifications are made to the deterministic model to allow for efficient propagation of uncertainty of model inputs using the Polynomial Chaos (PC) method to quantify the effect of uncertainty in the model parameters on the system response. With large uncertainties in the model parameters that are typical in soil models, the use of a simplified model is justified because the effect of the simplification will be masked by the uncertainties in the model parameters. Each component of the stress and stiffness tensor is expanded along the PC basis, and a small number of PC coefficients are updated along loading/unloading increments. The simplified deterministic model gives similar results to other traditional models, but the equations it involves are computationally much more efficient when extended to the stochastic model and solved with PC. The results are PC coefficients of each stress and stiffness component along the loading/unloading parts of the curve, from which probability distributions of the stress and stiffness can be reconstructed. Compared with traditional Monte-Carlo simulation, the PC method gives similar results while being several orders of magnitude faster computationally. The PC expansion method can also be extended to the non-linear stochastic finite element method.