Local micromorphic non-affine anisotropy for materials incorporating elastically bonded fibers

TL;DR

This paper introduces a micromorphic continuum model with director fields to accurately describe non-affine elastic deformation in fiber-reinforced biological tissues, reducing complexity compared to traditional higher-order models.

Contribution

It develops a modular micromorphic framework incorporating non-affine fiber motion with fewer parameters, tailored for biological soft tissue modeling.

Findings

Efficient capture of non-affine fiber deformation

Reduced parameter set compared to classical models

Demonstrated applicability to anisotropic composite materials

Abstract

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.