On probabilistic entropies application in uniaxial deformation of hyper‐elastic materials

Abstract

Uncertainty quantification and reliability assessment for uniaxial tension of some hyper‐elastic material characterized by a few different constitutive equations is analyzed in this paper. The stretch of hyper‐elastic material is adopted as the Gaussian input with given expected value's range relevant to the experimentation and constant standard deviation. This goal is achieved with the use of the stochastic perturbation technique to calculate the first two probabilistic moments of the increasing tensile stress. Additionally, the Shannon probabilistic entropy fluctuations are determined for this test. Finally, reliability index is calculated using the stress‐based limit function and two reliability approaches–the First Order Reliability Method and the Bhattacharyya relative entropy.