Speaker: Prof. Gerard Ateshian

Abstract

Dissipative mechanisms in solid mechanics include damage mechanics, viscoelasticity, plasticity, and growth mechanics. Historically, the thermodynamics of dissipative processes has been analyzed using the framework of internal variable theory, introducing hidden variables and associated constitutive relations for their temporal evolution. In this presentation we examine an alternative approach where dissipative mechanisms are analyzed using reactions that alter the composition of a mixture of solid constituents, as well as the their reference configurations. Since composition is an observable measure, this approach strictly relies only on the framework of thermodynamics of observable state variables, using the axiom of mass balance to predict their temporal evolution. We describe how this classical framework needs to be extended to account for reactive processes, taking advantage of the simplifications arising from constraining all constituents to share the same velocity and temperature. Illustrations may be provided for damage mechanics, viscoelasticity, plasticity, thermoelasticity and growth mechanics.

Biography

Gerard Ateshian is the Andrew Walz Professor of Mechanical Engineering and Director of the Musculoskeletal Research Laboratory at Columbia University in New York City. His primary research is in the field of soft tissue mechanics, with an emphasis on cartilage mechanics, lubrication, and tissue engineering, and the formulation of growth theories for biological tissues. In collaboration with Prof. Clark T. Hung at Columbia, he has translated his findings on cartilage mechanics to the field of functional cartilage tissue engineering, with a particular focus on the role of mechanical loading in tissue growth. Together with Dr. Jeffrey A. Weiss at the University of Utah, he has developed open-source computational tools that facilitate the modeling of tissue mechanics, transport, and growth processes (febio.org). He has applied and validated these tools with the modeling of engineered cartilage growth.