Linear elastic orthotropic material model

Abstract

In this article a linear elastic constitutive model for orthotropic material is derived based on the invariant theory and expressed in a coordinate invariant form. The orthotropic symmetry group is defined by three mutually orthogonal unit vectors. For orthotropic elastic solid the strain energy or correspondingly the complementary strain energy depends on seven invariants. Thermodynamic restrictions for the material parameters and conditions for monotonicity of the modulae of elasticity are derived. Example parameter sets for balsa, Douglas fir, cortical bone of tibia and femur are given.