In this paper a mathematical model is developed to describe the effect of nonuniform growth on the mechanical stress experienced by cells within an avascular tumour. The constitutive law combines the stress-strain relation of linear elasticity with a growth term that is derived by analogy with thermal expansion. To accommodate the continuous nature of the growth process, the law relates the rate of change of the stress tensor to the rate of change of the strain (rather than relating the stres...Expand abstract
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A mathematical model of the stress induced during avascular tumour growth.
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