This note examines restrictions imposed by the second law of thermodynamics on peridynamics in both the bond-based and the state-based formulations. Our study was carried out in the framework of thermomechanics with internal variables. In bond-based peridynamics, there are two possible thermomechanical interpretations of the dissipation function. One interpretation only admits a thermodynamic orthogonality of Ziegler, while the other admits powerless forces within a representation theory of Edelen. The latter interpretation is admissible in state-based peridynamics. Since the dissipation function of peridynamics is set up in velocity space, a link to statistical mechanics of irreversible phenomena does not appear possible.

References

References
1.
Silling
,
S. A.
,
2000
, “
Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces
,”
J. Mech. Phys. Solids
,
48
,
pp.
175
209
.10.1016/S0022-5096(99)00029-0
2.
Demmie
,
P. N.
, and
Silling
,
S. A.
,
2007
, “
An Approach to Modeling Extreme Loading of Structures Using Peridynamics
,”
J. Mech. Mater. Struct.
,
2
(
10
),
pp.
1921
1944
.10.2140/jomms.2007.2.1921
3.
Ziegler
,
H.
,
1983
,
An Introduction to Thermomechanics
,
North-Holland, Amsterdam
.
4.
Maugin
,
G.A.
,
1999
,
The Thermomechanics of Nonlinear Irreversible Behaviors—An Introduction
,
World Scientific
,
Singapore
.
5.
Edelen
,
D. G. B.
,
1973
, “
On the Existence of Symmetry Relations and Dissipative Potentials
,”
Arch. Rat. Mech. Anal.
,
51
,
pp.
218
227
.10.1007/BF00276075
6.
Edelen
,
D. G. B.
,
1974
, “
Primitive Thermodynamics: A New Look at the Clausius–Duhem Inequality
,”
Int. J. Eng. Sci.
,
12
,
pp.
121
141
.10.1016/0020-7225(74)90012-3
7.
Ostoja-Starzewski
,
M.
, and
Zubelewicz
,
A.
,
2011
, “
Powerless Fluxes and Forces, and Change of Scale in Irreversible Thermodynamics
,”
J. Phys. A: Math. Theor.
,
44
,
p.
335002
(9 pp.)
.10.1088/1751-8113/44/33/335002
8.
Silling
,
S. A.
,
Epton
,
M.
,
Weckner
,
O.
,
Xu
,
J.
, and
Askari
,
E.
,
2007
, “
Peridynamic States and Constitutive Modeling
,”
J. Elast.
,
88
,
pp.
151
184
.10.1007/s10659-007-9125-1
You do not currently have access to this content.