Multigenerational Interstitial Growth of Biological Tissues

The objective of this study is to formulate a theory for multigenerational interstitial growth of biological tissues whereby each generation has a distinct reference configuration determined at the time of its deposition. In this model, the solid matrix of a growing tissue consists of a multiplicity of intermingled bodies, each of which represents a generation, all of which are constrained to move together in the current configuration. This proposed framework builds on the concept of constrained mixtures of solids originally formulated by Humphrey and Rajagopal (2002). The specific aim is to determine the form of constitutive relations for the solid constituents of a multigenerational tissue, and provide simple illustrations of the theory.