Continuum PDE models for soft tissue mechanics derived by upscaling of arrays of hyper-elastic cells

Roxanna Barry (SofTMech)

Friday 22nd February 16:00-17:00 Maths 311B

Abstract

Constitutive models for the deformation of soft tissues are typically constructed by fitting phenomenological models to in vitro experimental measurements. However, a significant challenge is to rationally construct macroscale models of soft tissues which encode the properties of the cells and matrix which form the tissue. In this work I present a general framework to derive multiscale models for soft tissues which incorporate the properties of individual cells without assuming homogeneity or periodicity at the cell level. We consider a reduced mechanical model for an individual cell which can deform, grow and divide, and then couple these to form a network description of a one-dimensional line of cells, where each has independent material and mechanical properties. We utilise a discrete-to-continuum approach to upscale to form new (nonlinear) continuum PDE models for the tissue which allows for gradients in the cell properties, and show that these discrete and continuum formulations agree well in a variety of test problems.

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