Finite element models for structures with hyperelastic materials experiencing microstructural changes

摘要

Microstructural material changes such as polymerization, crystallization, and cumulative damage are often modeled using a two-network theory. Theories describing two-network material models are discussed and the basic equations for two-network materials undergoing scission and reformation are derived. Finite element equations are developed for isotropic nonlinear hyperelastic materials undergoing microstructural changes assuming a plane stress condition. A Mooney-Rivlin material model is used in the development of the finite element equations. A solution procedure is presented which incorporates a two-network theory. Uniaxial, biaxial, and unequal biaxial extension problems are solved using single element and 9 element finite element models. Several values of percent material conversions are used in each sample problem. Additionally, a 6.5 inch square sheet with a.25 inch centrally located circular hole is evaluated. Numerical results are compared to the theoretical values for each case. Finite element results agree with previously published solutions.