Abstract. In this paper the linearized finite theory of elasticity is applied to obtain linear constitutive equations for constrained materials reinforced by two orhogonal families of fibres. Explicit expressions for the three stress tensors are derived for inextensible in both fibre directions materials, for incompressible materials and finally for materials that are both incompressible and inextensible in the two fibre directions. Comparison with the corresponding constitutive equations provided by the classical approach shows that the classical equations are not accurate to first order in the strain.

Received: March 17, 2016

AMS Subject Classification: 74B99, 74E10, 74A10

Key Words and Phrases: constraints, linearized finite elasticity, constitutive equations, orthotropic symmetry

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