Continuum Physics

This learning track was developed by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys. The idea for these courses on continuum physics grew out of a short series of talks on materials physics at the University of Michigan. Those talks were aimed at advanced graduate students, post-doctoral scholars, and faculty colleagues. From this group, the suggestion emerged that a somewhat complete set of lectures on continuum aspects of materials physics would be useful. Given their origin, they are meant to be early steps on a path of research in continuum physics for the entrant to this area, and a second opinion for the more seasoned exponent of the science. Also, there is potential use of this series as an enabler of more widespread research in continuum physics.


In this course, we first discuss what exactly continuum physics means. Then we revisit vectors and revise concepts such as basic operations of vectors, basis vectors, etc.
This course was created for Ansys Innovation Courses by Professor Kresihna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

This course discusses the mathematical quantities called tensors and, their properties. Tensors and vector fields are discussed as well.
This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

This course starts with a discussion on the motion of continuum bodies — how to describe and analyze the motion. The lectures cover the study of kinematics of motion divided into four subcategories: Motion and Deformation, Lagrangian description, Eulerian description, and Material Derivatives. From basic representation, all the subcategories will be discussed in this course. 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 discuss how to mathematically describe the distortion that solids and fluids undergo. We cover important topics such as (i) deformation of curves, surfaces and volumes; (ii) measures of strain; (iii) polar decomposition and (iv) rate of deformation. On completing this course, we will have a better understanding of the kinematics that underlies continuum mechanics. 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, balance laws will be discussed, including the balance of mass, momentum, and energy. The balance of mass can be associated with diffusion. The balance of linear momentum is associated with Newton’s laws of motion, and the balance of angular momentum is associated with Euler’s equation. The balance of energy gives rise to the heat equation. 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 session, the balance of mechanical energy will be explored along with differing measures of stress.  We will then delve into the work conjugate relations. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

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.

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 talk about deriving linearized elasticity. This can be explained using kinematics, constitutive relations, and the balance of linear momentum. As we conclude our learning on the continuum mechanics, we will do a quick recap followed by giving due credits and discussing different books for this subject.

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.

In this course, we begin by discussing what variational principles are and how they can be applied to nonlinear elasticity. We then apply variational derivatives for nonlinear elasticity to develop the weak form of balance of linear momentum for static problems. Finally, we use integration by parts to transform this weak form into the strong form of nonlinear elasticity. 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 discuss mass transport by considering the transport of the substance through space. Next, we will talk about the constitutive relations for flux in mass transport. Then, we will set up the foundation for the treatment of mass transport in continuum physics. Lastly, we will discuss the role of interfacial free energy and the Cahn-Hilliard formulation. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.