ANCF Multiplicative-Decomposition Thermoelastic Approach for Arbitrary Geometry

Abstract

The classical approach for the thermal analysis of solids and fluids uses the strain additive decomposition to account for the effect of the temperature. This strain-based approach does not properly capture the effect of complex stress-free reference-configuration geometry, is applicable only to small deformation problems, and leads to simplified expression for the Green–Lagrange strain tensor. In view of the geometric description of the absolute nodal coordinate formulation (ANCF), a new ANCF gradient-based approach is proposed. This approach employs a multiplicative decomposition of the matrix of position-gradient vectors in the stress-free reference configuration into two position-gradient matrices. One matrix is associated with the reference-configuration geometry before the application of the thermal load, and the other accounts for the volumetric change due to the change in temperature. A numerical study demonstrated the implementation of the proposed gradient-based approach.