Mixture theory models continua consisting of multiple constituents with independent motions. In constrained mixtures, all constituents share the same velocity, but they may have different reference configurations. The theory of constrained reactive mixtures was formulated to analyze growth and remodeling in living biological tissues. We have shown that it can also reproduce and extend classical frameworks of damage mechanics, viscoelasticity and plasticity under isothermal conditions, when modeling reactive constituents (molecular bonds) that can break and reform in response to loading. It can also model thermoelasticity by letting temperature transform a constituent into another, having different properties and reference configuration. This presentation provides an overview of the application of reactive mixture theory to these types of problems.
Gerard Ateshian is the Andrew Walz Professor of Mechanical Engineering at Columbia University. He received his B.S. (1986), M.S. (1987) and Ph.D. (1991) from Columbia. His current research interests include cartilage mechanics, biotribology and tissue engineering in relation to osteoarthritis, and fundamental theories of continuum mechanics as related to biomechanics.