The modelling of fibre reorientation in soft tissue |
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Authors: | Igor Kar?aj Carlo Sansour Jurica Sori? |
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Institution: | (1) Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, I.Lučića 5, 10000 Zagreb, Croatia;(2) School of Civil Engineering, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK |
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Abstract: | In this paper, a hyperelastic and thermodynamically consistent model for soft tissue is developed that is able to describe
the change of the initial orientation of the collagen fibres. Full numerical implementation is considered as well. The collagen
architecture is assumed to reorient driven by a specific thermodynamical force. The anisotropy is described by a strain energy
function, which is decomposed into a part related to the matrix and a part related to the fibres. The initial fibre orientation
is defined by a structural tensor, while the current orientation is described by a time-dependent structural tensor, which
results from the initial one by a rotational transformation. The rotation tensor is obtained via an integration process of
a rate tensor, which depends on an adequately defined thermodynamical force. The integration is achieved via an exponential
map algorithm, where it is shown that the rotation is necessarily a two-parametric one. Efficiency of the proposed formulation
is demonstrated using some numerical examples. |
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Keywords: | |
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