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A Theory Of Volumetric Growth For Compressible Elastic Biological Materials, Stephen M. Klisch, Timothy J. Van Dyke, Anne Hoger

Mechanical Engineering

A general theory of volumetric growth for compressible elastic materials is presented. The authors derive a complete set of governing equations in the present configuration for an elastic material undergoing a continuous growth process. In particular, they obtain two constitutive restrictions from a work-energy principle. First, the authors show that a growing elastic material behaves as a Green-elastic material. Second, they obtain an expression that relates the stress power due to growth to the rate of energy change due to growth. Then, the governing equations for a small increment of growth are derived from the more general theory. The equations …