Hall, C. L. and Menon, S. N. and McCue, S. W. and McElwain, D. L. S. (2011) A novel model for onedimensional morphoelasticity. Part I  Theoretical foundations. Journal of Mathematical Biology . (Submitted)

PDF
362kB 
Abstract
While classical continuum theories of elasticity and viscoelasticity have long been used to describe the mechanical behaviour of solid biological tissues, they are of limited use for the description of biological tissues that undergo continuous remodelling. The structural changes to a soft tissue associated with growth and remodelling require a mathematical theory of ‘morphoelasticity’ that is more akin to plasticity than elasticity. However, previouslyderived mathematical models for plasticity are difficult to apply and interpret in the context of growth and remodelling: many important concepts from the theory of plasticity do not have simple analogues in biomechanics.
In this work, we describe a novel mathematical model that combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. While our focus here is on onedimensional problems, our model builds on earlier work based on the multiplicative decomposition of the deformation gradient and can be adapted to develop a threedimensional theory. The foundation of this work is the concept of ‘effective strain’, a measure of the difference between the current state and a hypothetical state where the tissue is mechanically relaxed. We develop onedimensional equations for the evolution of effective strain, and discuss a number of potential applications of this theory. One significant application is the description of a contracting fibroblastpopulated collagen lattice, which we further investigate in Part II.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1394 
Deposited By:  Peter Hudston 
Deposited On:  09 Sep 2011 06:57 
Last Modified:  29 May 2015 19:05 
Repository Staff Only: item control page