Shannon definition of entropy as a measure of uncertainty represented by a probability distribution, showed that entropy becomes the primitive concept more fundamental than energy. Jaynes (1957) also proved that thermodynamic entropy is
identical with the information-theory entropy of the probability distribution except
for the presence of Boltzmann’s constant.
Valanis (1971) established irreversibility and existence of entropy as a state
function in Newtonian mechanics formulation. Valanis (1971) was able to prove
this for reversible and irreversible systems and processes, irrespective of the constitutive equations of the system. He postulated that, in the case of a reversible system,
entropy is a function of the deformation gradients (strains) and temperature; in the
case of an irreversible system, it is also a function of n internal variables necessary to
describe the irreversibility of the system. Valanis based his proof of the existence of
entropy as a consequence of the integrability of the differential form of the first law
using an extended form of the Caratheodory conjecture, to the effect that in the
neighborhood of a thermodynamic state there exist other states, which are not
accessible by processes, which are reversible and adiabatic. Based on this work
Valanis (1971) proposed the endochronic plasticity theory, which deals with the
plastic response of materials by means of memory integrals, expressed in terms of
memory kernels. Formulation of this theory is based on thermodynamics concepts
and provides a unified point of view to describe the elastic-plastic behavior of
material, since it places no requirement for a yield surface and “loading function”
to distinguish between loading and unloading. A key ingredient of the theory is that
the deformation history is defined with respect to a deformation memory scale called
intrinsic time. In the original version of the endochronic theory, proposed by Valanis
(1971), the intrinsic time was defined as the path length in the total strain space. The
so-called endochronic theory violates the second law of thermodynamics and leads
to constitutive relations, which characterize inherently unstable materials (Rivlin
1981). Aiming at the correction of this deficiency a new version of the endochronic
theory was developed by Valanis and Komkov (1980) in which the intrinsic time
was defined as the path length in the plastic strain space.
Rice (1971) used internal-variable thermodynamic formalism for description of
the microstructural rearrangements to characterize metal plasticity. Rice (1971)
postulated that the theoretical foundations of constitutive relations at finite strain
for metals exhibiting inelasticity is a consequence of specific structural
rearrangements on the microscale of the material, such as metals deforming plastically through dislocation motion. Rice (1971) is actually a generalization of his
earlier work Kestin and Rice (1970), where it is assumed that each microstructural
arrangement proceeds at a rate governed by its associated thermodynamic force. This
work became the framework for the time-dependent inelastic behavior in terms of a
flow potential, and reduces to statements on normality of plastic strain increment to
yield surface in the time-independent case. Rice (1971) approach assumes inelastic
deformation under macroscopically homogeneous strain and temperature as a
sequence of constrained equilibrium states. Using equilibrium thermodynamic formalism and thermodynamic potentials, Rice (1971) relates changes in the local
structural rearrangements to corresponding changes in the macroscopic stress or
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4 Unified Mechanics Theory
identical with the information-theory entropy of the probability distribution except
for the presence of Boltzmann’s constant.
Valanis (1971) established irreversibility and existence of entropy as a state
function in Newtonian mechanics formulation. Valanis (1971) was able to prove
this for reversible and irreversible systems and processes, irrespective of the constitutive equations of the system. He postulated that, in the case of a reversible system,
entropy is a function of the deformation gradients (strains) and temperature; in the
case of an irreversible system, it is also a function of n internal variables necessary to
describe the irreversibility of the system. Valanis based his proof of the existence of
entropy as a consequence of the integrability of the differential form of the first law
using an extended form of the Caratheodory conjecture, to the effect that in the
neighborhood of a thermodynamic state there exist other states, which are not
accessible by processes, which are reversible and adiabatic. Based on this work
Valanis (1971) proposed the endochronic plasticity theory, which deals with the
plastic response of materials by means of memory integrals, expressed in terms of
memory kernels. Formulation of this theory is based on thermodynamics concepts
and provides a unified point of view to describe the elastic-plastic behavior of
material, since it places no requirement for a yield surface and “loading function”
to distinguish between loading and unloading. A key ingredient of the theory is that
the deformation history is defined with respect to a deformation memory scale called
intrinsic time. In the original version of the endochronic theory, proposed by Valanis
(1971), the intrinsic time was defined as the path length in the total strain space. The
so-called endochronic theory violates the second law of thermodynamics and leads
to constitutive relations, which characterize inherently unstable materials (Rivlin
1981). Aiming at the correction of this deficiency a new version of the endochronic
theory was developed by Valanis and Komkov (1980) in which the intrinsic time
was defined as the path length in the plastic strain space.
Rice (1971) used internal-variable thermodynamic formalism for description of
the microstructural rearrangements to characterize metal plasticity. Rice (1971)
postulated that the theoretical foundations of constitutive relations at finite strain
for metals exhibiting inelasticity is a consequence of specific structural
rearrangements on the microscale of the material, such as metals deforming plastically through dislocation motion. Rice (1971) is actually a generalization of his
earlier work Kestin and Rice (1970), where it is assumed that each microstructural
arrangement proceeds at a rate governed by its associated thermodynamic force. This
work became the framework for the time-dependent inelastic behavior in terms of a
flow potential, and reduces to statements on normality of plastic strain increment to
yield surface in the time-independent case. Rice (1971) approach assumes inelastic
deformation under macroscopically homogeneous strain and temperature as a
sequence of constrained equilibrium states. Using equilibrium thermodynamic formalism and thermodynamic potentials, Rice (1971) relates changes in the local
structural rearrangements to corresponding changes in the macroscopic stress or
118
4 Unified Mechanics Theory