The research objective of this grant is to elucidate a differential/Riemannian geometric formulation for the mechanics of growing bodies. The proposed work is based on the concept of a changing material manifold whose dynamics predicts the evolution of the relaxed state of a material body. This theory is applicable to biological tissues in which growth and remodeling are coupled with large deformations. To achieve the research objective of this proposal, a theory of continuum mechanics based on a dynamic material manifold is introduced that couples the growth/remodeling of biological tissues with their large deformations. The proposed research will put growth and similar nonlinear problems into a unified geometric theory that has a dynamic material manifold.
One of the goals of this project is to promote the use of geometric techniques in the mechanics community by demonstrating some of their advantages and applications. The results of this project will be presented in a language accessible to engineers, and they will demonstrate the conceptual clarifications and modeling advantages brought by the geometric approach. A major educational impact of this research is the establishment of a general framework for learning and teaching growth mechanics in biology using the language of mathematics and mechanics, a context, which is currently missing in the biophysics. This project will foster opportunities for collaborative research between the University of Maine and Georgia Institute of Technology and facilitate broadening the participation of undergraduate students in the cutting edge research in the field of biomechanics.