Course Description
Continuum mechanics is concerned with the deformations and motions of continuous material media under the influence of external effects. This course will present various classic theories of solid and fluids. The theory of continuous media- the basic laws of motion and constitutive theory-will be discussed.
Athena Title
Continuum Mechanics
Prerequisite
ENGR 8103 or permission of school
Semester Course Offered
Offered every year.
Grading System
A - F (Traditional)
Course Objectives
By the end of this course, students will be able to: (1) Learn the basic knowledge of tensor analysis and concepts of continuum mechanics to the depth required to critique contemporary continuum mechanics literature. (2) Derive from first principles the fundamental mass, linear and angular momenta, energy, and entropy balance equations. (3) Formulate constitutive theories for various linear and non- linear solids and fluids based on the axiomatic approach. (4) Learn the principles and applications of objectivity and representation theorem for isotropic functions.
Topical Outline
(1) Introduction to Cartesian tensors. • Tensor product and contraction; • Isotropic tensors; • Eigenvalues and Eigenvectors of a second-order tensor; • Gradient of a tensor field; (2) Deformation, stress, kinematics of motions. • Strain tensors and displacement vector; strain invariants and principle directions; • Changes of volume and surface; • Time rates of vectors; • Kinematics of line, surface, and volume integrals; • Strain rate; (3) Balance laws of continuum systems. • Stress tensor; • Conservation of mass; • Balance of linear and angular moment; • Conservation of energy; • Principle of entropy; (4) Constitutive equations. • Axioms of constitutive theory; • Isotropic materials; (5) Elastic solid, thermo-visco-elastic solid, plasticity. • Isotropic elastic materials; • Linear constitutive equations; • Propagation of elastic waves; • Plasticity.
Syllabus
Public CV