Thermodynamic constitutive equations for materials with memory on a material time scale

We present a complete, self‐consistent set of thermodynamic constitutive equations for viscoelastic solid and fluid materials which can be applied during arbitrary, three‐dimensional deformations and thermal processes. Deformational and thermal histories are measured using a fading memory norm in a material time which provides a quantitative indication of the constitutive models’ ability to represent the dynamic response. The free energy constitutive equation is a Frechet expansion about the deformation and temperature histories of arbitrarily large but sufficiently slow departures from equilibrium in material time. The kinetic relationship between the laboratory and material time scales does not depend on equilibrium considerations. This approach greatly extends the applicability of low‐order memory expansions to nonequilibrium polymer states. Constitutive equations for stress, internal energy, entropy, enthalpy, and heat capacity are derived. All the required material properties can be evaluated unambig...

[1]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[2]  Ronald S. Rivlin,et al.  Further Remarks on the Stress-Deformation Relations for Isotropic Materials , 1955 .

[3]  Walter Noll,et al.  Foundations of Linear Viscoelasticity , 1961 .

[4]  J. Ferry.  Viscoelastic properties of polymers , 1961 .

[5]  L. Struik.  Physical aging in amorphous polymers and other materials , 1978 .

[6]  M. Litt,et al.  Cold flow of glassy polymers. III. Temperature dependence of yield elongation in BPA polycarbonate , 1967 .

[7]  E. Gruber.  L. G. E. Struik: Physical Aging in Amorphous Polymers and Other Materials. Elsevier Sci. Publ. Comp., Amsterdam-Oxford-New York 1978. 229 Seiten, 141 Abbildungen, Preis: US $ 42,50, Holl. Gulden 97,50. , 1978 .

[8]  W. V. Chang,et al.  On the theory of the viscoelastic behavior of soft polymers in moderately large deformations , 1976 .

[9]  B. Bernstein,et al.  Thermodynamics of perfect elastic fluids , 1964 .

[10]  George W. Scherer,et al.  Relaxation in Glass and Composites , 1986 .

[11]  J. Caruthers,et al.  A New Nonlinear Viscoelastic Constitutive Equation for Predicting Yield in Amorphous Solid Polymers , 1986 .

[12]  M. Litt,et al.  Cold flow of glassy polymers. II: Ductility, impact resistance, and unoccupied volume , 1967 .

[13]  R. Simha,et al.  On the Statistical Thermodynamics of Spherical and Chain Molecule Fluids , 1969 .

[14]  S. Newman,et al.  Stress-Strain Behavior of Rubber-Reinforced Glassy Polymers , 1965 .

[15]  H. Bair,et al.  Interpretation of shift of relaxation time with deformation in glassy polymers in terms of excess enthalpy , 1973 .

[16]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[17]  I. L. Hopkins.  Stress relaxation or creep of linear viscoelastic substances under varying temperature , 1958 .

[18]  Ronald S. Rivlin,et al.  The mechanics of non-linear materials with memory , 1959 .

[19]  R. Rivlin,et al.  Representation theorems in the mechanics of materials with memory , 1964 .

[20]  John E. McKinney,et al.  Dynamic Compressibility of Poly (Vinyl Acetate) and Its Relation to Free Volume , 1963, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[21]  Bernard D. Coleman,et al.  Thermodynamics of materials with memory , 1964 .

[22]  Walter Noll,et al.  A mathematical theory of the mechanical behavior of continuous media , 1958 .

[23]  A. Kovacs.  La contraction isotherme du volume des polymères amorphes , 1958 .

[24]  Richard Schapery.  An engineering theory of nonlinear viscoelasticity with applications , 1966 .

[25]  H. Bair,et al.  Analysis of non‐linear stress relaxation in polymeric glasses , 1978 .

[26]  Igor Emri,et al.  Volume change and the nonlinearly thermo‐viscoelastic constitution of polymers , 1987 .

[27]  A class of simple solids with fading memory , 1969 .

[28]  W. Knauss,et al.  Non-linear viscoelasticity based on free volume consideration , 1981 .

[29]  Bernard D. Coleman,et al.  On thermodynamics, strain impulses, and viscoelasticity , 1964 .

[30]  P. M. Naghdi,et al.  Linear non-isothermal viscoelastic solids , 1967 .

[31]  P. M. Naghdi,et al.  On thermal effects in a special class of viscoelastic fluids , 1973 .

[32]  A. Pipkin,et al.  Small Finite Deformations of Viscoelastic Solids , 1964 .

[33]  Leslie Morland,et al.  Stress Analysis for Linear Viscoelastic Materials with Temperature Variation , 1960 .

[34]  Richard Schapery.  On the characterization of nonlinear viscoelastic materials , 1969 .

[35]  P. M. Naghdi,et al.  On thermomechanics of polymers in the transition and rubber regions , 1978 .

[36]  R. Rivlin,et al.  Stress-Deformation Relations for Isotropic Materials , 1955 .

[37]  P. M. Naghdi,et al.  A class of non-isothermal viscoelastic fluids , 1972 .

[38]  G. Adam,et al.  On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids , 1965 .

[39]  R. Simha,et al.  Use of a theoretical equation of state to interpret time-dependent free volume in polymer glasses , 1981 .

[40]  P. M. Naghdi,et al.  ON 'THERMO-RHEOLOGICALLY SIMPLE' SOLIDS. , 1970 .

[41]  R. Simha,et al.  Configurational Thermodynamic Properties of Polymer Liquids and Glasses. Poly(vinyl acetate). II , 1974 .