ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

A MULTI-SCALE ANISOTROPIC CONSTITUTIVE MODEL FOR
BIOLOGICAL SOFT TISSUES.
1. ABSTRACT
APPLICATION TO SKIN MECHANICS
G. Limbert 1,2
A multi-scale mathematical and computational orthotropic constitutive framework for
biological soft tissues based on tensor invariants is developed. The formulation features
full decoupling of deformation modes so that constitutive parameters are directly related
to physical measurements. The rheological response is based on physical multi-scale
geometrical/structural parameters that can be experimentally measured or determined ab
initio from molecular dynamic simulations. The constitutive model reproduces very
well the experimental multi-axial properties of rabbit skin whilst also predicting a
posteriori the stiffness of individual collagen molecules. This work is therefore a
positive step towards the development of physically-meaningful multi-scale predictive
models of tissues and organs.
2. INTRODUCTION
The characterisation and modelling of the multi-scale mechanical behaviour of
biological soft tissues is essential for the development of predictive computational
models to assist research in medicine, biology, tissue engineering, pharmaceutics,
consumer goods, cosmetics or transport safety. It is important to develop constitutive
models that can capture particular rheological mechanisms operating at specific length
scales so that these models are adapted for their intended applications.
In this study, a multi-scale constitutive framework for biological soft tissues with
transversely isotropic and orthotropic symmetries is developed. A notable feature of the
formulation is the full decoupling of shear, volumetric and along-the-fibre deformation
modes which lead to four orthogonal stress tensors: 1) a pure hydrostatic stress tensor,
2) a deviatoric along-the-fibre tension-free stress tensor, 3) a deviatoric fibre-tofibre/matrix-to-fibre
shear stress tensor and 4) a deviatoric cross-fibre shear stress
tensor. Another desirable feature of the constitutive equations is that the response is
based on physical geometrical/structural parameters that can be experimentally
measured or determined ab initio from molecular dynamic simulations. The constitutive
formulation is applied to model the orthotropic mechanical behaviour of (rabbit) skin
and a direct sensitivity analysis of the constitutive parameters is conducted for a
simulated indentation test. The results of the sensitivity analyses are presented in [1].
1 Assistant Professor, national Centre for Advanced Tribology at Southampton (nCATS), Faculty of
Engineering and the Environment, University of Southampton, Southampton SO17 1BJ,UK
2 Assistant Professor, Bioengineering Science Research Group, Faculty of Engineering and the
Environment, University of Southampton, Southampton SO17 1BJ,UK