TAM 552: Solid Mechanics II

Class Description:

Continuation of TAM 551. Selected topics in linear elasticity (including St. Venant beam theory and plane problems of elastostatics), plasticity (including yield surfaces, von Mises and Tresca yield criteria, Drucker|#39;s stability postulate, J-flow theory, perfect plasticity, limit analysis, and slip-line theory), and fracture mechanics (including linear elastic analysis, fracture criteria for elastic brittle fracture, and elastic-plastic fracture). Prerequisite: TAM 551. 4 graduate hours.

Textbook:
Robert J. Asaro and Vlado A. Lubarda, Mechanics of Solids and Materials, Cambridge University Press, 2011

Reference books:
Richard B. Hetnarski and Jozef Ignaczak, The Mathematical Theory of Elasticity, 2nd ed., CRC Press, 2011

Jacob Lubliner, Plasticity Theory, MacMillan Publishing (now also available as a Dover publication), 2008

D. Broek, Elementary Engineering Fracture Mechanics, Kluwer Academic Publishers, 2008

Topics:

St.-Venant beam theory (10 hr)
St.-Venant|rsquo;s principle, semi-inverse method, effect of weight; extension, pure bending, torsion; bending by transverse shear, flexure

The plane problem of linear elastostatics (12 hr)
Plane stress, plane strain, generalized plane stress; uniqueness; characterization of plane elastic states; Airy|rsquo;s solution, multiply connected regions, some polynomial stress functions, problems in cylindrical polar coordinates, singular elasticity solutions (isolated point force, concentrated line load, dislocation stress field, punch problems)

Theory of plasticity (19 hr)
Yielding, yield surface; von Mises, Tresca yield criteria; Drucker|rsquo;s stability postulate; strain or work hardening, normality rule, J2 flow theory (Prandtl|ndash;Reuss equations for isotropic materials with isotropic hardening), perfect plasticity, stress|ndash;strain law; torsion of a prism, limit analysis, plane-strain slip-line theory

Fracture mechanics (19 hr)
Linear elastic analysis (crack-tip stresses, deformation fields, energetics of cracked bodies, compliance methods for determining K, weight-function analysis, Jintegral); fracture criteria for elastic brittle fracture (theoretical strength, Griffith theory, Irwin approach, cohesive zone models, mode II criteria, estimate of plastic zone size based on K, small-scale yielding, fracture-toughness testing, thickness effects, Rcurves), elastic|ndash;plastic fracture (asymptotic results for crack-tip stress fields, J-integral analysis)

TOTAL HOURS: 60

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