Q is positive inward, in Rice (1971) formulation, which we are quoting without
modification. It is assumed that heat entering from outside does not increase the
irreversible entropy generation. On the other hand, heat generated in the system and
dissipating outward leads to irreversible entropy generation.
The second law requirement that non-negative work rate of associated forces on
internal variables is given by
_
ξ α
∂ϕ E, θ, ξ
ð
Þ
∂ξ α
0
ð4:22Þ
Remember in Eq. (4.5) f α was defined as
f α ¼ ÀV
0 ∂ϕ E, θ, ξ
ð
Þ
∂ξ α
ð4:23Þ
Rice (1971) concludes by, “That is, the rates of internal arrangement actually
occurring during a process must be such that the free energy would decrease if strain
and temperature were held fixed at current values.”
In Newtonian mechanics, Eqs. (4.22) and (4.23) are primarily used to impose the
requirement that flow potential must be convex and smooth surface, and but are not
actually included in Newtonian laws to degrade the energy. Degradation is imposed
by empirical formulation with a damage potential obtained from experimental data.
Later, Rice (1977) derived thermodynamic restrictions on the quasi-static growth,
or healing of Griffith cracks. However as presented they were nothing beyond global
restriction on the detailed molecular kinetics of crack growth. Therefore, there was
no attempt to integrate these restrictions into Newton’s laws. Other work by Rice
(1977) on use of thermodynamics in theory of plasticity and fracture mechanics was
based on or a derivative of his work discussed here.
Bazant (1972) used thermodynamics for modeling mechanics of interfaces in
concrete structure, where a thermodynamically consistent formulation of interacting
continua with surfaces based on surface thermodynamics was proposed. He
accounted for creep, shrinkage and delayed thermal dilation and their interaction
with adsorbed water layers confined between two solid adsorbent surfaces
Kijalbaev and Chudnovsky (1970) and Chudnovsky (1973, 1984) proposed a
probabilistic model of the fracture process unifying the phenomenological study of
long-term strength degradation of materials, fracture mechanics and statistical
approach to fracture mechanics. Chudnovsky (1984) used irreversible thermodynamics to model the deterministic side of the failure phenomenon and stochastic
calculus to account for the failure mechanisms controlled by “chance,” particularly
the random roughness of fracture surfaces. Kijalbaev and Chudnovsky (1970) and
Chudnovsky (1973, 1984) derived the entropy production for an elastic medium
with damage. Citing Swalin (1972) on the invariance of the entropy jump during a
phase transition with respect to stresses and temperature, Chudnovsky (1973)
hypothesized that the entropy jump invariance can be used to predict the local
124
4 Unified Mechanics Theory
modification. It is assumed that heat entering from outside does not increase the
irreversible entropy generation. On the other hand, heat generated in the system and
dissipating outward leads to irreversible entropy generation.
The second law requirement that non-negative work rate of associated forces on
internal variables is given by
_
ξ α
∂ϕ E, θ, ξ
ð
Þ
∂ξ α
0
ð4:22Þ
Remember in Eq. (4.5) f α was defined as
f α ¼ ÀV
0 ∂ϕ E, θ, ξ
ð
Þ
∂ξ α
ð4:23Þ
Rice (1971) concludes by, “That is, the rates of internal arrangement actually
occurring during a process must be such that the free energy would decrease if strain
and temperature were held fixed at current values.”
In Newtonian mechanics, Eqs. (4.22) and (4.23) are primarily used to impose the
requirement that flow potential must be convex and smooth surface, and but are not
actually included in Newtonian laws to degrade the energy. Degradation is imposed
by empirical formulation with a damage potential obtained from experimental data.
Later, Rice (1977) derived thermodynamic restrictions on the quasi-static growth,
or healing of Griffith cracks. However as presented they were nothing beyond global
restriction on the detailed molecular kinetics of crack growth. Therefore, there was
no attempt to integrate these restrictions into Newton’s laws. Other work by Rice
(1977) on use of thermodynamics in theory of plasticity and fracture mechanics was
based on or a derivative of his work discussed here.
Bazant (1972) used thermodynamics for modeling mechanics of interfaces in
concrete structure, where a thermodynamically consistent formulation of interacting
continua with surfaces based on surface thermodynamics was proposed. He
accounted for creep, shrinkage and delayed thermal dilation and their interaction
with adsorbed water layers confined between two solid adsorbent surfaces
Kijalbaev and Chudnovsky (1970) and Chudnovsky (1973, 1984) proposed a
probabilistic model of the fracture process unifying the phenomenological study of
long-term strength degradation of materials, fracture mechanics and statistical
approach to fracture mechanics. Chudnovsky (1984) used irreversible thermodynamics to model the deterministic side of the failure phenomenon and stochastic
calculus to account for the failure mechanisms controlled by “chance,” particularly
the random roughness of fracture surfaces. Kijalbaev and Chudnovsky (1970) and
Chudnovsky (1973, 1984) derived the entropy production for an elastic medium
with damage. Citing Swalin (1972) on the invariance of the entropy jump during a
phase transition with respect to stresses and temperature, Chudnovsky (1973)
hypothesized that the entropy jump invariance can be used to predict the local
124
4 Unified Mechanics Theory