TAM 451: Intermediate Solid Mechanics

Class Description:

Analysis of stress and strain (definitions, transformation of axes, equilibrium equations, and symmetry of the stress tensor); linear materials, Hookes law; strain energy, potential energy, energy principles and methods; two-dimensional problems in elasticity (torsion, axisymmetric problems); the finite-element method for two- and three-dimensional boundary-value problems in linear elasticity; plasticity (introduction, yield criteria, elastic-plastic behavior, and limit-load calculations); linear-elastic fracture mechanics (introduction, Griffiths approach, stress intensity factor, and energy release rate). Prerequisite: TAM 251.

Topics:

Fundamentals
Analysis of strain: principal values and directions, compatibility (3 hr)
Analysis of stress: principal values and directions (3 hr)
Equilibrium equations, stress symmetry (1 hr)

Elasticity
Constitutive relations, isotropy (2 hr)
Plane problems of 2-D elasticity; torsion (4 hr)
Axisymmetric problems (2 hr)
Work and energy; energy methods (2 hr)
Introduction to the finite-element method (6 hr)

Plasticity
Yielding, yield surfaces, von Mises and Tresca yield criteria (3 hr)
Perfect plasticity, strain hardening (1 hr)
Limit loads, plastic deflection of beams, plastic torsion (5 hr)
Applications: plane strain, slip-line theory (3 hr)

Linear-elastic fracture mechanics
Crack-tip stresses and deformation fields in solids (2 hr)
Energetics of cracked bodies (3 hr)
The J integral (2 hr)
Theoretical strength, Griffith theory, Irwin approach (3 hr)
Small-scale yielding, fracture-toughness testing (size effect) (3 hr)

Instructor's option (10 hr)

Topics from one or more of the following areas:

  • Elasticity, e.g. the Rayleigh-Ritz method, Castigliano’s method, beams on elastic foundation, contact problems, thin film mechanics, dislocation theory
  • Plasticity, e.g. Drucker’s stability postulate, the normality rule, J2 flow theory (Prandtl-Reuss theory), applications
  • Viscoelasticity, e.g. simple models and their limitations
  • Fracture mechanics, e.g., compliance methods, cohesive zone models, elastic-plastic fracture (asymptotic results)
     

ME:  MechSE or technical elective.

EM:  Secondary field elective.

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TAM