Orthorhombic crystals and orthotropic elasticity

The unit cell of the orthorhombic crystal is brick-shaped. The elastic properties are therefore symmetric with respect to three perpendicular planes. In a coordinate system that is parallel to the edges of the unit cell, the compliance matrix (equation (2.31)) takes the form 

the unspecified components vanish. Altogether, there are nine independent elastic constants. It has to be noted that the compliance tensor is symmetric, so some parameters are related, for example —i/2i/ i = Nevertheless, it is useful to discriminate between 1/12 and 1/21, for they are defined by transversal contraction. 

In a coordinate system parallel to the edges of the unit cell, normal stresses can only cause normal strains, and shear stresses only shear strains. This is not valid anymore if the coordinate system is arbitrarily oriented, so normal strain and shear are coupled. 

The orthorhombic crystal lattice itself is not too important technically because there are only a small number of materials crystallising in this structure. Composites (chapter 9), however, frequently have the same symmetry because they may contain aligned fibres. Materials with the same symmetry as an orthorhombic crystal are called orthotropic. 

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