COURSES
530.605
MECHANICS OF SOLIDS AND MATERIALS I
This course provides an introduction to the mathematical and theoretical foundations of the mechanics of solids and materials. We will begin with the mathematical preliminaries of continuum mechanics: vectors and tensors calculus, then introduce the kinematics of deformation and descriptions of stress in a continuum: Eulerian and Lagrangian descriptions, followed by conservation laws: mass, momentum, and energy balance, and entropy. These concepts will be applied to develop the concepts of constitutive relations: frame invariance, material symmetry, and dissipation. The second half of the class will be devoted to elasticity, both classical and finite elasticity, and solution methods for boundary value problems.
530.612
COMPUTATIONAL SOLID MECHANICS
This course teaches in-depth and hands-on understanding of numerical methods for solid mechanics problems. The course begins with a review of the fundamental concepts of the finite element method for linear boundary value problems (BVP) and initial boundary value problems (IBVP) in solid mechanics. Advanced methods for nonlinear BVPs are presented and applied to problems of material inelasticity and finite elasticity. Topics covered include the strong and weak statements of the BVP, weighted residual methods, time integration, Newton-type methods for nonlinear problems, and error estimation and convergence.
530.448
BIOMECHANICS II
This course teaches the fundamental concepts of mechanics and apply them to study the mechanical behavior of cells and soft tissues. Topics covered include mechanics of bone; elasticity and viscoelasticity of cells and connective tissues; structure-function relationship of connective tissues; and experimental methods in soft tissue mechanics.