Arxiv:2102.13492V2 [Physics.Comp-Ph] 3 Mar 2021
Local micromorphic non-affine anisotropy for materials incorporating elastically bonded fibers Sebastian Skatulla1,2, Carlo Sansour3, and Georges Limbert4,5 1Department of Civil Engineering, University of Cape Town, South Africa 2Center for Research in Computational and Applied Mechanics, University of Cape Town, South Africa 3Department of Mathematics, Bethlehem University, Bethlehem, Palestine 4National Centre for Advanced Tribology at Southampton (nCATS) and Bioengineering Science Research Group, Department of Mechanical Engineering, Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO17 1BJ, UK 5Laboratory of Biomechanics and Mechanobiology, Division of Biomedical Engineering, Department of Human Biology, Faculty of Health Sciences, University of Cape Town, Observatory 7935, Cape Town, South Africa March 4, 2021 Abstract There has been increasing experimental evidence of non-affine elas- tic deformation mechanisms in biological soft tissues. These observations call for novel constitutive models which are able to describe the dom- inant underlying micro-structural kinematics aspects, in particular rel- ative motion characteristics of different phases. This paper proposes a flexible and modular framework based on a micromorphic continuum en- compassing matrix and fiber phases. It features in addition to the dis- placement field so-called director fields which can independently deform and intrinsically carry orientational information. Accordingly, the fibrous arXiv:2102.13492v2 [physics.comp-ph] 3 Mar 2021 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 princi- ple featuring dedicated governing equations for displacement and director 1 fields.
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