Abstract
The concern of this work is the derivation of material conservation and balance laws for second gradient electroelasticity. The conservation laws of material momentum, material angular momentum and scalar moment of momentum on the material manifold are derived using Noether's theorem and the exact conditions under which they hold are rigorously studied. The corresponding balance laws are also presented.
Similar content being viewed by others
References
E.C. Aifantis, On the role of gradient in the localization of deformation and fracture. Internat. J. Engrg. Sci. 30 (1992) 1279–1299.
M. Epstein and G.A. Maugin, Energy-momentum tensor and J-integral in electrodeformable bodies. Internat. J. Appl. Electromagn. Materials 2 (1991) 141–145.
D.C. Fletcher, Conservation laws in linear elastodynamics. Arch. Rational Mech. Anal. 60 (1976) 329–353.
M.E. Gurtin, Configurational Forces as Basic Concepts of Continuum Physics, Applied Mathematical Sciences 137. Springer, New York (2000).
E.P. Hadjigeorgiou, V.K. Kalpakides and C.V. Massalas, A general theory for elastic dielectrics. Part II. The variational approach. Internat. J. Nonlinear Mech. 34 (1999) 967–480.
Y.-N. Huang and R.C. Batra, Energy-momentum tensors in nonsimple elastic dielectrics. J. Elasticity 42 (1996) 275–281.
N.H. Ibragimov, Transformation groups applied to mathematical physics. In: Mathematics and its Applications. D. Reidel, Dordrecht (1985).
V.K. Kalpakides and C.V. Massalas, Tiersten's theory of thermoelectroelasticity. An extension. Internat. J. Engrg. Sci. 31 (1993) 157–164.
V.K. Kalpakides, E.P. Hadjigeorgiou and C.V. Massalas, A variational principle for elastic dielectrics with quadrupole polarization. Internat. J. Engrg. Sci. 34 (1995) 793–801.
V.K. Kalpakides and G.A. Maugin, Canonical formulation and conservation laws of thermoelasticity without dissipation, submitted for publication.
J.K. Knowles and E. Sternberg, On a class of conservation laws in linearized and finite elastostatics. Arch. Rational Mech. Anal. 44 (1972) 187–211.
G.A. Maugin, Material Inhomogeneities in Elasticity, Applied Mathematics and Mathematical Computation. Chapman and Hall, London (1993).
G.A. Maugin and M. Epstein, The electroelastic energy-momentum tensor. Proc. Roy. Soc. London A 433 (1991) 299–312.
G.A. Maugin and V.K. Kalpakides, The slow march towards an analytical mechanics of dissipative materials. Technische Mechanik 22 (2002) 98–103.
G.A. Maugin and V.K. Kalpakides, A Hamiltonian formulation for elasticity and thermoelasticity, J. Phys. A: Math. Gen. 35 (2002) 10775–10778.
G.A. Maugin and C. Trimarco, Elements of field theory in inhomogeneous and defective materials. In: R. Kienzler and G. A. Maugin (eds), Configuratioanal Mechanics of Materials, CISM Udine Lectures. Springer, Wien (2001) pp. 55–128.
P.J. Olver, Applications of Lie Groups to Differential Equations. Graduate Texts inMathematics 107. Springer, New York (1993).
Y.E. Pak and G. Herrmann, Conservation laws and the material momentum tensor for the elastic dielectric. Internat. J. Engrg. Sci. 24 (1986) 1365–1374.
Y.E. Pak and G. Herrmann, Crack extension force in a dielectric medium. Internat. J. Engrg. Sci. 24 (1986) 1375–1388.
P. Steinmann, Application of material forces to hyperelastostatic fracture mechanics. I. Continuum mechanical setting. Internat. J. Solids Struct. 37 (2000) 7371–7391.
I. Vardoulakis, G. Exadaktylos and E. Aifantis, Gradient Elasticity with surface energy: mode- III crack problem. Internat. J. Solids Struct. 33 (1996) 4531–4558.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kalpakides, V., Agiasofitou, E. On Material Equations in Second Gradient Electroelasticity. Journal of Elasticity 67, 205–227 (2002). https://doi.org/10.1023/A:1024926609083
Issue Date:
DOI: https://doi.org/10.1023/A:1024926609083