Viscoelastic Solids
 
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University of Wisconsin
EMA 630: Viscoelastic solids.
Time and place: Offered, Fall 2003, 2005, 2007. Planned offering: every other year; next offering Fall 2009.
For Fall 2009, Tue. Thurs. 11:00-12:15 2321 Engineering Hall
Timetable
Textbook: R. S. Lakes, Viscoelastic Materials,
Cambridge University Press, May 2009;
Viscoelastic Materials book outline
alternate, R. S. Lakes, Viscoelastic Solids, CRC Press, 1998.
Viscoelastic Solids book outline
References / reserve
Ferry, J. D., Viscoelastic Properties of Polymers
I. M. Ward and D. W. Hadley, Mechanical Properties of Solid Polymers
Coordinator: Rod Lakes, Professor of Engineering
Prerequisites: Intermediate mechanics of materials, such as the following.
EMA 506 advanced strength of materials or equivalent or EMA 303 and consent of instructor.
Description: Linear theory of viscoelasticity; non-aging materials; Boltzmann superposition principle; linear functionals; thermodynamic foundations; time-temperature superposition principle; boundary and initial value problems. Applications of viscoelastic materials are to be examined in connection with vibration damping, relaxation of stress in fasteners, creep, droop, and sag in structural members, sound absorption, creep buckling, settlement of foundations, tire mechanics, and shock attenuation.
Goals: To prepare seniors and graduate students to do advanced analysis and design using materials such as polymers and composites with time and frequency dependent viscoelastic properties or to do research with polymers, composites or biological materials; development of physical insight.
Grading: Grading is based on exams, a project report, and on homework. The scale is 90-100% - A, etc. Reports and homework must be in paper form, not electronic. Report grades will be reduced by 10% for each working week (2% per day) of additional
delay.
Interdisciplinary aspects
Engineering mechanics: All materials exhibit some viscoelastic response. Therefore understanding of elastic response should be supplemented with understanding of viscoelastic response.
Biomedical engineering: Tissues in the body are all viscoelastic. Most tissues exhibit large viscoelastic effects. These effects influence the performance of the tissue.
Materials science: Viscoelasticity results from physical processes such as dislocation motion, grain boundary slip, molecular motions, domain motion, or diffusion. Viscoelasticity is of use as a probe into such processes.
Mechanical engineering: Viscoelastic materials are used for control of vibration in machinery. Viscoelastic damping of materials can reduce noise. Creep and relaxation of materials can affect their performance in machinery.
Civil engineering: Viscoelasticity of soil and other earth materials is relevant to settlement of buildings.
Electrical engineering: Viscoelasticity in piezoelectric materials gives rise to energy dissipation, phase angles, and frequency dependence of properties. Vibration control in computer disk drives improves their performance.
- Course Outline:
- 1 Introduction. Viscoelastic phenomena. Creep. Hysteresis. Decay of vibrations. Viscoelastic solids and liquids. Relaxation. Phase shifts. Wave attenuation.
- 2 Constitutive relations for linear viscoelastic materials. Boltzmann superposition principle Delta functions. Convolutions. Boltzmann superposition integral. Fourier transforms.
Laplace transforms. Effect of temperature. Thermorheologically simple materials.
- 3 Dynamic behavior. Energy storage and dissipation. Phase shifts. Resonance. Wave attenuation. Internal friction.
- 4 Conceptual structure of the theory. Relations among the viscoelastic functions. Approximate interrelations. Physical meaning of the viscoelastic functions.
- 5 Solution of problems involving viscoelastic materials. Correspondence principle. Modified correspondence principle. Non-transform type problems.
- 6 Experimental methods. Transient methods for creep and relaxation. Dynamical methods: subresonant, lumped and distributed resonant. Waves. Temperature effects. Thermal activation.
- 7 Viscoelastic properties of materials. Viscoelastic polymers. Viscoelastic metals. Materials with high viscoelastic damping. Hard and soft biological tissues. Low damping materials. Creep resistant materials.
- 8 Causal mechanisms. Dislocations. Thermo-elasticity. Stress-induced fluid flow; Biot analysis. Snoek relaxation. Granato-Lucke relaxation. Grain boundary motion. Interfaces. Molecular motion in polymers. Phase transformations. Shape memory materials. Piezoelectric relaxation. Processes in biological tissues.
- 9 Viscoelastic composite materials. Structure-property relations. Bounds on properties. Fibrous, particulate, and cellular solids. Foams and honeycombs.
- 10 Applications. Earplugs. Medical diagnosis. Rolling friction. Protection of the human body. Vibration damping. Impact absorbers. Foundation settlement. Tire mechanics. Sound absorption. Ultrasound attenuation in non-destructive testing and in diagnostic ultrasound. Use of residual stress. Instrument mounts. Sway of buildings. Relaxation of fasteners. Gaskets. Diagnosis of disease. Concrete viscoelastic properties. Asphalt viscoelastic properties. Viscoelasticity of food products. Spacecraft and satellite performance related to viscoelasticity.
