Mechanics of Growth and Growth of Mechanics

Sunday, October 25, 2015 - 9:45am - 10:25am
Yi-Chao Chen (University of Houston)
The classical theories of mechanics have provided powerful tools in studying the mechanical aspects of growths of biological tissues. The physiological process of growths, in turn, presents special challenges to the theory of mechanics, and brings forth the growth of mechanics itself. In this talk we discuss some issues that have emerged in this process.

The existing kinematic theory of growth is based on the decomposition of the deformation gradient tensor into the so-called growth tensor and accommodation elastic tensor. A clear understanding is needed of the nature of the growth tensor, so as to explain why and how it can be used to provide a macroscopic description of the addition of material particles (cells). Also, in defining these kinematic quantities, a fixed reference configuration is often used. Such an approach is inconsistent with the physical processes in which some materials particles did not exist in a fixed reference configuration. In particular, this approach is incapable of modeling the surface growths in which change in topology can occur as a surface grows into a volume. We discuss possible ways to overcome these difficulties. The growth tensor is derived as a continuum description of the changes of particle distribution for a discrete system. Also, by using the current configuration as the reference, a constitutive theory can be developed that does not rely on the concepts of a natural state and a fixed reference configuration.
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