(Department)  Biomedical Engineering         (Division)      
 (Level and Major)  

Course Title                VISCOELASTICITY              
Number of Credits       3             Prerequisite

Prerequisites: Advanced strength of materials or equivalent; Vibration

Goals: To prepare 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 final exam (60%), experimental project (30%), and on homework-based quiz (10%).

Tentative Outline:

Introduction: Viscoelastic phenomena. Creep. Hysteresis. Decay of vibrations. Viscoelastic solids and liquids. Relaxation. Phase shifts. Wave attenuation.

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.

Discrete models: (Maxwell, Kelvin, Voigt, standard linear solid, multi-parameters, generalized,....)

Dynamic behavior: Energy storage and dissipation. Phase shifts. Resonance. Wave attenuation. Internal friction.

Conceptual structure of the theory: Relations among the viscoelastic functions. Approximate interrelations. Physical meaning of the viscoelastic functions.

Solution of problems involving viscoelastic materials: Correspondence principle. Modified correspondence principle. Non-transform type problems. Temperature effects.

Experimental methods: Transient methods for creep and relaxation. Dynamical methods.

Viscoelastic properties of materials: Viscoelastic polymers. Viscoelastic metals. Materials with high viscoelastic damping. Hard and soft biological tissues. Low damping materials. Creep resistant materials.

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

References : Viscoelastic Materials, Roderic Lakes, Cambridge, University Press, 2009

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