An elastic–viscoplastic model with non-affine deformation and rotation of a distribution of embedded fibres

reinforced by a distribution of fibres has been formulated. The fibre distribution is a symmetric positive-definite tensor with unit trace that is determined by an evolution equation. This evolution equation includes a competition between tendencies for affine evolution of the distribution and non-affine evolution causing the distribution to align with the elastic distortional deformation tensor or to become isotropic. Two elastic deformation measures are introduced associated with the fibre distribution. Specifically, non-affine measures of elastic distribution stretch and non-coaxiality of the distribution cause anisotropic stress response. The resulting model describes a number of effects relevant to growth and remodelling of biological tissues as well as to additive manufacturing of artificial materials. For example, the equations model the smooth transition from isotropic to anisotropic response seen in many biological tissues.