May 27, 2024  
Graduate Record 2020-2021 
Graduate Record 2020-2021 [ARCHIVED RECORD]

AM 6130 - Mathematical Foundations of Continuum Mechanics

Describes the mathematical foundations of continuum mechanics from a unified viewpoint. The relevant concepts from linear algebra, vector calculus, and Cartesian tensors; the kinematics of finite deformations and motions leading to the definition of finite strain measures; the process of linearization; and the concept of stress. Conservation laws of mechanics yield the equations of motion and equilibrium and description of constitutive theory leading to the constitute laws for nonlinear elasticity, from which the more familiar generalized Hooke’s law for linearly elastic solid is derived. Constitutive laws for a Newtonian and non-Newtonian fluid are also discussed. The basic problems of continuum mechanics are formulated as boundary value problems for partial differential equations. Cross-listed as APMA 6130. Prerequisite: Linear algebra, vector calculus, elementary PDE (may be taken concurrently).

Credits: 3