Appendix B Anisotropic Elasticity

Abstract

In linear elasticity theory, only small changes in shape are considered, and a macroscopichomogeneous, linear-elastic material is also assumed. Elastic deformations disappear completely after release. For orthotropic bodies the generalized Hooke’s law applies with nine effective elasticity constants: εxx = 1 E1 σxx − υ21 E2 σyy − υ32 E3 σzz, εyy = 1 E2 σyy − υ12 E1 σxx − υ32 E3 σzz, εzz = 1 E3 σzz − υ13 E1 σxx − υ23 E2 σyy, γyz = γzy = 1 G23 τyz = 1 G32 τzy γzx = γxz = 1 G31 τzx = 1 G13 τxz, γxy = γyx = 1 G12 τxy = 1 G21 τyx. (B.1)