Constitutive Laws

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We have learned that constitutive laws/relations are important for the study of continuum mechanics. In this course, the focus will be on how the behavior of a material can be captured by using constitutive relations.

This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

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In this course, we discuss the frame of reference and material symmetry and how it affects the constitutive relations. We also discuss the objectivity of several classes of materials such as elastic, hyperelastic solids, and viscous fluids. We also briefly discuss Navier Stokes equations which is an initial and boundary value problem in fluid mechanics.

This short course is intended to discuss the solution for boundary value problems. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we will begin by discussing the two laws of thermodynamics — the balance of energy law and the entropy inequality law. We then use the Legendre transformation to derive the Helmholtz free energy. Following this, we discuss the Clausius-Planck and the Clausius-Duhem inequalities. We then study thermoelasticity, which explains how a body stores internal energy as it deforms due to local temperature changes. Finally, we conclude this course by discussing the heat flux vector in current and reference configurations. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.