Decomposition of Elasticity Tensor on Material Constants and Mesostructures of Metal Plates

Most metal plates are orthorhombic aggregates of cubic crystallites. First, we discuss the representations of the stress tensor, the strain tensor, the elasticity tensor, and the rotation tensor under the Kelvin notation. Then, we give the decomposition of determining the material constants and the mesostructure tensors on the metal plate of cubic crystallites. Under the Voigt model and the Reuss model, we derive the volume average stiffness tensor and the volume average flexibility tensor’s inverse, respectively, of cubic crystallites based on the decomposition. The elasticity tensors of the Voigt model and the Reuss model are upper and lower bounds of the effective elasticity tensor, respectively. We make use of an FEM example to check the decomposition of the elasticity tensor on the material constants and the mesostructures. The results of our decomposition are consistent with the FEM simulation’s results.