Continuum Physics

This learning track was developed by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys. These courses on continuum physics grew out of a short series of talks on materials physics at the University of Michigan. They are aimed at advanced graduate students, post-doctoral scholars, and faculty colleagues and detail early steps on a path of research in continuum physics. They also provide a second opinion for the more seasoned explorer of the science.

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1
Innovation Course

Remembering Vectors

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 Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

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Innovation Course

Tensors

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.

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Innovation Course

Kinematics of Motion

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 the kinematics of motion divided into four subcategories: Motion and Deformation, Lagrangian description, Eulerian description, and...Read more

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Innovation Course

Deformation

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 th...Read more

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Innovation Course

Balance Laws in Continuum Physics

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 moment...Read more

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Innovation Course

Stress in Continuum Mechanics

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.

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Innovation Course

Constitutive Laws

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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Innovation Course

Objectivity and Material Symmetry

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 discus...Read more

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Innovation Course

Boundary Value Problems

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.

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Innovation Course

Linearized Elasticity

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 cred...Read more

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Innovation Course

Thermomechanics

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...Read more

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Innovation Course

Variational Principles

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...Read more

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Innovation Course

Mass Transport

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. ...Read more

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Continuum Physics — Learning Track Completion Badge

This badge is available upon successful completion of the "Continuum Physics" Learning Track.