2.072: Mechanics of Continuous Media

Fall | Graduate | 12 Units | Prereq: 2.071

Principles and applications of continuum mechanics. Kinematics of deformation. Thermomechanical conservation laws. Stress and strain measures. Constitutive equations including some examples of their microscopic basis. Solution of some basic problems for various materials as relevant in materials science, fluid dynamics, and structural analysis. Inherently nonlinear phenomena in continuum mechanics. Variational principles.

Fall 2020 Update: Fully Remote Classes - This subject will cover the foundations of continuum mechanics and thermodynamics: (i) Kinematics of deformation. (ii) Balance laws for (a)  mass,  (b) linear and angular momenta, and (c) energy.  (iii) An entropy imbalance that represents the second law of thermodynamics. and  (iv) The principle of material frame-indifference. The formulation of modern constitutive theories of materials, which will be based on  these foundations, will be  discussed. Specific constitutive theories to be discussed will  include: (i) Heat conduction; and (ii) Elastic solids under isothermal and non-isothermal conditions. In addition to these standard topics, because of the growing  importance  of the coupled multi-physics response of materials in modern technologies related to the environment and energy, as a new feature  this year I  will also cover coupled theories for (iii) Thermoelasticity;  (iv) Chemoelasticity; (v) Poroelasticity;  and  (vi) Piezoelectricity. Time-permitting, and depending on student interest, additional  constitutive theories to be discussed will  include: (vii) Compressible and incompressible, linearly viscous fluids; (viii) Non-Newtonian yield stress fluids; and (ix) Elastic-plastic and elastic-viscoplastic  solids. All lectures will be online on MW 11am to 12:30p. I will also conduct an online  recitation on Friday mornings from 11am to 12noon.