TAM 529: Viscoelasticity Theory

Class Description:

Same as AE 529. See AE 529. 4 graduate hours.

Textbook:

Instructor's notes

Required readings:
Alfrey, Mechanical Behavior of High Polymers
Bland, The Theory of Linear Viscoelasticity
Gross, Mathematical Structure of the Theories of Viscoelasticity
Freudenthal, The Inelastic Behavior of Engineering Materials and Structures
Freudenthal and Geiringer, The mathematical theories of the inelastic continuum. In Handbuch der Physik 6
Various journal articles

Topics:

Linear viscoelasticity
Elastic|ndash;viscoelastic analogy, including dynamic problems; limitations (3 hr)
Creep and relaxation functions: Generalized Kelvin and Maxwell models; relations between creep and relaxation functions (3 hr)
Thermodynamics of viscoelastic media: Reciprocity relations, viscoelastic stress analysis (4 hr)
Variational principles: Energy theorems, applications; variational and Lagrangian methods (4 hr)
Model fitting to measured values of complex moduli: relationships between complex modulus and operator equations, between creep and relaxation functions and operator equations, between various methods of behavior representation (3 hr)
Quasi-static viscoelastic problems: Shear center motion in viscoelastic beams, thick walled hollow cylinders under inertia loads, elastically restrained cylinders under pressure and in the presence of material annihilation, sandwich plates (Biot|#39;s stability problem) (8 hr)
Dynamic viscoelastic problems: Propagation of viscoelastic waves; impact on infinite media and circular plates; vibration of viscoelastic bars, plates and shells; damping of flexural vibrations by alternate viscoelastic and elastic layers (8 hr)

Nonlinear viscoelasticity
Nonlinear relations: nonlinear stress-strain relations, nonlinear viscoelastic-elastic analogy, limitations (3 hr)
Nonlinear problems: tension of bars, creep rupture in tension, torsion of prismatic bars and rotationally symmetric shells, stress functions for nonlinear problems, finite difference and asymptotic solutions (7 hr)

TOTAL HOURS: 43

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