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A microsphere-based remodelling formulation for anisotropic biological tissues

In English

Författare

Summary, in English

Biological tissues possess the ability to adapt according to the respective local loading conditions, which results in growth and remodelling phenomena. The main goal of this work is the development of a new remodelling approach that, on the one hand, reflects the alignment of fibrous soft biological tissue with respect to representative loading directions. On the other hand, the continuum approach proposed is based on a sound micro-mechanically motivated formulation. To be specific, use of a worm-like chain model is made to describe the behaviour of long-chain molecules as present in, for instance, collageneous tissues. The extension of such a one-dimensional constitutive equation to the three-dimensional macroscopic level is performed by means of a microsphere formulation. Inherent with the algorithmic treatment of this type of modelling approach, a finite number of unit vectors is considered for the numerical integration over the domain of the unit sphere. As a key aspect of this contribution, remodelling is incorporated by setting up evolution equations for the referential orientations of these integration directions. Accordingly, the unit vectors considered now allow interpretation as internal variables, which characterize the material's anisotropic properties. Several numerical studies underline the applicability of the model that, moreover, nicely fits into iterative finite element formulations so that general boundary value problems can be solved.

Avdelning/ar

Publiceringsår

2009

Språk

Engelska

Sidor

3499-3523

Publikation/Tidskrift/Serie

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Science

Volym

367

Issue

1902

Dokumenttyp

Artikel i tidskrift

Förlag

Royal Society Publishing

Ämne

  • Mechanical Engineering

Nyckelord

  • anisotropic biological tissues
  • remodelling
  • adaptation
  • finite element
  • method

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 1364-503X