CONSTRAINED LINEARLY ELASTIC MATERIALS REINFORCED BY TWO FAMILIES OF FIBRES

In this paper the linearized finite theory of elas- ticity is applied to obtain linear constitutive equations for con- strained materials reinforced by two orhogonal families of fi- bres. Explicit expressions for the three stress tensors are de- rived for inextensible in both fibre directions materials, for in- compressible materials and finally for materials that are both incompressible and inextensible in the two fibre directions. Comparison with the corresponding constitutive equations pro- vided by the classical approach shows that the classical equa- tions are not accurate to first order in the strain.