Soft tissue mechanics modeling based on hyperelasticity
Abstract: Mechanics thinking certainly goes way back to the earliest reasoning about how the world works. Archimedes’ law of the lever remains fundamental to all students of mechanical engineering as codified in equilibrium moment balance as learned in statics and strength of materials, and angular momentum balance as learned in dynamics. As students continue in their studies, the question of mechanical response for different types of materials assumes increasing importance. Idealized material classes are posited, response ranges are codified, and failure modes identified. This gives rise to various material theories, and those theories that seem to work well eventually make their way into the engineer’s toolkit via, for example, finite element codes. Describing the behavior of complicated materials requires specialized tools. Living soft biological tissue is among the most complicated of materials. It is highly deformable and typically porous. It grows and remodels and is difficult to isolate as a ``free body” because, to remain healthy, it must inherently be part of an open system. This talk will focus on the role of nonlinear elasticity theory (hyperelasticity) in the mechanics modeling of soft tissue. Because of potentially large deformation, linear elasticity is limited in its ability to describe soft tissue response (although it is undeniably important for many aspects). Classical nonlinear elasticity (so called rubber elasticity) is the next logical upgrade, but it typically must be generalized in a variety of ways in order to address issues such as: inflammation (swelling), fibrous microstructure (collagen, elastin), rate effects (viscous behavior), growth and remodeling. Examples will be drawn especially from the presenter’s modeling treatments of swelling edema and collagen turnover. Organ systems that have been considered in this vein include the trachea and the cervix.
Bio: Tom Pence is a professor in the Department of Mechanical Engineering at Michigan State University which is where he earned his undergraduate degree. His graduate work in applied mechanics was at Caltech, and his postdocs were at the University of Wisconsin-Madison and the University of Paris. He has held sabbatical appointments as a visiting professor at the University of Rome and Glasgow University. His research is in continuum mechanics and nonlinear elasticity as it pertains to material modeling, with a current focus on soft biological tissue. He serves on the editorial boards of several journals, including the Journal of Elasticity, and the International Journal of Solids and Structures. He is currently serving a term as a member of the U. S. National Committee for Theoretical and Applied Mechanics.
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