  There has been increasing experimental evidence of non-affine elastic
deformation mechanisms in biological soft tissues. These observations call for
novel constitutive models which are able to describe the dominant underlying
micro-structural kinematics aspects, in particular relative motion
characteristics of different phases. This paper proposes a flexible and modular
framework based on a micromorphic continuum encompassing matrix and fiber
phases. It features in addition to the displacement field so-called director
fields which can independently deform and intrinsically carry orientational
information. Accordingly, the fibrous constituents can be naturally associated
with the micromorphic directors and their non-affine motion within the bulk
material can be efficiently captured. Furthermore, constitutive relations can
be formulated based on kinematics quantities specifically linked to the
material response of the matrix, the fibres and their mutual interactions.
Associated stress quantities are naturally derived from a micromorphic
variational principle featuring dedicated governing equations for displacement
and director fields. This aspect of the framework is crucial for the truly
non-affine elastic deformation description. In contrast to conventional
micromorphic approaches, any non-local higher-order material behaviour is
excluded, thus significantly reducing the number of material parameters to a
range typically found in related classical approaches. In the context of
biological soft tissue modeling, the potential and applicability of the
formulation is studied for a number of academic examples featuring anisotropic
fiber-reinforced composite material composition to elucidate the micromorphic
material response as compared with the one obtained using a classical continuum
mechanics approach.
