Lectures on Viscoelasticity Theory

  title={Lectures on Viscoelasticity Theory},
  author={Allen C. Pipkin},
I. Viscoelastic Response in Shear.- II. Fourier and Laplace Transforms.- III. Relations Between Modulus and Compliance.- IV. Some One-Dimensional Dynamical Problems.- V. Stress Analysis.- VI. Thermal Effects.- VII. Large Deformations with Small Strains.- VIII. Slow Viscoelastic Flow.- IX. Viscometric Flow.- Solutions. 
Theory of Linear Viscoelasticity
This chapter mainly introduces theories of one-dimensional linear viscoelasticity based on Boltzmann superposition and the concept of linear response and phenomenological models such as spring–dashpot and parsimonious models.
Free vibrations of viscoelastic materials with high damping
The theoretical basis for the determination of dynamic moduli of viscoelastic materials using free vibrations is critically reviewed. A new method is proposed which consists in a Fourier analysis of
Nonlinear Constitutive Laws in Viscoelasticity
The aim of the present paper is to review the classical nonlinear viscoelastic models and provide a unifying framework using the continuum mechanics formalism to help in the description of materials which exhibit time dependent stress—strain behavior.
Stress Boundary Value Problem in Linear Viscoelasticity
Summary. - We will solve the following boundary value problem in linear viscoelasticity: given the value of the stress on (a part of) the boundary of the domain find the stress in the whole body at
Viscoelastic material models in peridynamics
How to define the storage and loss moduli for a rheologically nonlinear material?
A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the interrelation between the Fourier transform and the stress decomposition approaches is established.
Isothermal Boundary-Value Problems
This chapter contains a comprehensive discussion of the types of boundary-value problems encountered in linear viscoelasticity. The chapter presents detailed solution methods for compressible and
Equivalences and Contrasts of Thermo-Elasticity and Thermo-Viscoelasticity: A Comprehensive Critique
Similarities and differences between thermo-elasticity and thermo-viscoelas- ticity are critically examined and evaluated. Topics include, among others, constitutive relations, Poisson's ratio,
Methods of investigation of boundary value problems in viscoelasticity theory
The present paper is devoted to some classical and modern methods of solving boundary value problems of viscoelasticity theory, including the Volterra principle, Il’yushin’s approximation method,
Back to the thermodynamic admissibility of creep-relaxation functions in linear viscoelasticity
The recent discussion on admissibility criteria for the kernels of linear viscoelastic liquids is completed by the results for viscoelastic solids. The necessary and sufficient conditions of