Elasto/viscoplastic constitutive equations with memory and internal variables

Abstract A general elasto/viscoplastic constitutive equation of a material with memory and internal variables is proposed based on the concept of generalized simple body. The proposed theory can describe not only such rate-dependent behaviours as primary and secondary creep, but also accelerating (teritary) creep, in which strain rate increases under constant stress. The application of the proposed theory to elasto/viscoplastic material in uniaxial condition is given and numerically analyzed with respect to strain rate effect.

[1]  O. W. Dillon,et al.  Thermodynamics of Elastic‐Plastic Materials as a Theory with Internal State Variables , 1969 .

[2]  P. M. Naghdi,et al.  On the Mechanical Behavior of Viscoelastic/Plastic Solids , 1963 .

[3]  C. Wang.  Generalized simple bodies , 1969 .

[4]  Alfred M. Freudenthal,et al.  The Mathematical Theories of the Inelastic Continuum , 1958 .

[5]  P. Perzyna.  Memory effects and internal changes of a material , 1971 .

[6]  C. C. Wang,et al.  On a general representation theorem for constitutive relations , 1969 .

[7]  W. Prager,et al.  Introduction of Mechanics of Continua , 1962 .

[8]  Piotr Perzyna,et al.  The constitutive equations for rate sensitive plastic materials , 1963 .

[9]  岡 二三生,et al.  Constitutive Equations for Normally Consolidated Clay Based on Elasto-Viscoplasticity , 1982 .

[10]  J. Oden,et al.  A unified theory of thermoviscoplasticity of crystalline solids , 1973 .

[11]  P. Symonds,et al.  Dynamic Plasticity of Metals , 1970 .

[12]  P. Perzyna.  Thermodynamic Theory of Viscoplasticity , 1971 .

[13]  U. S. Lindholm,et al.  Mechanical behavior of materials under dynamic loads , 1968 .

[14]  M. Gurtin,et al.  Thermodynamics with Internal State Variables , 1967 .

[15]  S. Tanimura.  A practical constitutive equation covering a wide range of strain rates , 1979 .

[16]  Wu Han-Chin,et al.  A Theory of viscoplasticity , 1973 .

[17]  R. Bird,et al.  Rheological Properties of Three Solutions. Part II. Relaxation and Growth of Shear and Normal Stresses , 1967 .

[18]  Fusao Oka,et al.  CONSTITUTIVE EQUATIONS FOR NORMALLY CONSOLIDATED CLAY BASED ON ELASTO-VISCOPLASTICITY , 1982 .

[19]  L. E. Malvern.  Plastic wave propagation in a bar of material exhibiting a strain rate effect , 1951 .

[20]  N. Cristescu.  Dynamic Plasticity Under Combined Stress , 1968 .

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