Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

A concise, self-contained introduction to solid polymers, the mechanics of their behavior and molecular and structural interpretations. This updated edition provides extended coverage of recent developments in rubber elasticity, relaxation transitions, non-linear viscoelastic behavior, anisotropic mechanical behavior, yield behavior of polymers, breaking phenomena, and other fields.

Mechanical properties of solid polymers

Starting with specific constitutive equations, methods of evaluating material properties from experimental data are outlined and then illustrated for some polymeric materials; these equations have been derived from thermodynamic principles, and are very similar to the Boltzmann superposition integral form of linear theory. The experimental basis for two equations under uniaxial loading and the influence of environmental factors on the properties are first examined. It is then shown that creep and recovery data can be conveiently used to evaluate properties in one equation, while two-step relaxation data serve the same purpose for the second equation. Methods of reducing data to accomplish this characterization and to determine the accuracy of the theory are illustrated using existing data on nitrocellulose film, fiber-reinforced phenolic resin, and polyisobutylene. Finally, a set of three-dimensional constitutive equations is proposed which is consistent with nonlinear behavior of some metals and plastics, and which enables all properties to be evaluated from uniaxial creep and recovery data.

On the characterization of nonlinear viscoelastic materials

A fully three-dimensional finite-strain viscoelastic model is developed, characterized by: (i) general anisotropic response, (ii) uncoupled bulk and deviatoric response over any range of deformations, (iii) general relaxation functions, and (iv) recovery of finite elasticity for very fast or very slow processes; in particular, classical models of rubber elasticity (e.g. Mooney-Rivlin). Continuum damage mechanics is employed to develop a simple isotropic damage mechanism, which incorporates softening behavior under deformation, and leads to progressive degradation of the storage modulus in a cyclic test with increasing amplitude (Mullins' effect). A numerical integration procedure is proposed which trivially satisfies objectivity and bypasses the use of midpoint configurations. The resulting algorithm can be exactly linearized in closed form, and leads to symmetric tangent moduli. Quasi-incompressible response is accounted for within the context of a three-field variational formulation of the Hu-Washizu type.

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On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects

Physical aging of polymers

Two simple types of constitutive equations appropriate to materials exhibiting viscoelasticity are presented, one of a basic solid nature and one of a basic fluid nature. The predictions of the equations for a stress relaxation experiment are worked out and compared to the data from some experiments on various elastomers. The fluid theory is shown to be most appropriate in a certain sense.

A Study of Stress Relaxation with Finite Strain

Creep and recovery behaviour of ultra-high molecular weight polyethylene in the region of small uniaxial deformations

In 1963 Bernstein, Kearsley, and Zapas1 presented a theory of an elastic fluid which gave the correct stress-relaxation response for a large variety of elastomeric materials, including vulcanized rubbers. A principle attractiveness of this theory is its relative simplicity; with a single integral in time, it describes the stress-strain behavior for all types of deformation histories. In the case of simple extension, it predicts the behavior in any uniaxial strain history from the results of single step stress-relaxation experiments which cover the same range of extension and time. We designed a series of experiments to check the validity of this theory and found, as is shown in this paper, excellent agreement with experiment in all cases. We are aware that experiments cannot prove a theory. From our results, however, we feel strongly that a single integral expression with a nonlinear integrand such as the BKZ elastic fluid equation is sufficient to describe the stress-strain behavior of elastomer...

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Correlation of Large Longitudinal Deformations With Different Strain Histories.

A simple non.equilibrium thermodynamics is developed and a particular example is studied. The theory is formulated to describe a viscoelastic fluid, capable of finite deformation, which need not be locally in or near a state of thermodynamic equilibrium. This fluid may support shear stresses only when away from local thermodynamic equilibrium _ A notion of time-temperature superposition is contained in the formulation of the constitutive equations. Conservation of energy is obeyed and the second law of thermudynamics is satisfied as a consequence of simple requirements on the constitutive relations. In an adiabatic isochoric motion the temperature increases when work is done on the material and decreases when the material does work. For given volume and temperature, e ntropy decrea ses whe n the mate rial is deformed from equ il ibrium . It is s hown in what general way viscos it y depends upon te mperature . For infinites imal s train, the special form of the stress-s train relations are derived in order to de termine how t.e mpe rature and t ime-t e mperature supe rpos ition e nte r in thi s case.

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Thermodynamics of perfect elastic fluids

The BKZ elastic fluid theory is used to correlate experimental results obtained in biaxial strain and steady simple shear. With a heuristic potential function involving three material properties, excellent agreement is obtained between theory and experiment. In the special case where one of the material properties is dominant, the behavior in steady simple shear is calculated from dynamic measurements in the infinitesimal range and is compared with actual data.

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L. J. Zapas

Papers

A Study of Stress Relaxation with Finite Strain

Creep and recovery behaviour of ultra-high molecular weight polyethylene in the region of small uniaxial deformations

Correlation of Large Longitudinal Deformations With Different Strain Histories.

Thermodynamics of perfect elastic fluids

Viscoelastic Behavior Under Large Deformations.