Design and Analysis of Composite Structures for Automotive Applications

Appendix BAnisotropic Elasticity

B.1 Elastic Orthotropic Body

In linear elasticity theory, only small changes in shape are considered, and a macroscopic‐homogeneous, 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:

B.1

• E₁, E₂, E₃ modules of elasticity,
• G₂₃ = G₃₂,  G₁₃ = G₃₁,  G₁₂ = G₂₁ shear modules,
• ν₁₂, ν₂₁, ν₂₃, ν₃₂, ν₁₃, ν₃₁ Poisson numbers.

There is a relationship:

B.2

The linear‐elastic material behavior with respect to the associated material system can be characterized by nine elasticity constants C_ij, or the equivalent by nine stiffness constants S_ij:

B.3

The inverse of (B.3) is:

B.4

The relations between the elasticities C_ij and stiffnesses S_ij read:

B.5

and

B.6

The generalized Navier equations result from the equilibrium ...