Conservation laws and energy release rates for general strain-gradient elastic solids are derived in a finite deformation framework. With respect to the relevant literature new terms are derived modelling the energy release through the body edges. We show how the enlightened contributions and the presence of edge forces play a relevant role when estimating the J-integral of mode I and II crack opening problems.
RiceJR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech1965; 35: 379–386.
2.
EshelbyJD. The elastic energy-momentum tensor. J Elast1975; 5: 321–335.
3.
KnowlesJKSternbergE. On a class of conservation laws in linearized and finite elastostatics. Arch Ration Mech Anal1971; 44: 187–211.
4.
AtkinsonCLeppingtonFG. Some calculations of energy-release rate g for cracks in micropolar and couple-stress elastic media. Int J Fract1974; 10: 599–602.
5.
JaricJ. Conservation laws of the j-integral type in micropolar elastostatics. Int J Eng Sci1978; 16: 967–984.
BatraRC. The force on a lattice defect in an elastic body. J Elast1987; 17: 3–8.
11.
BudianskyBRiceJRConservation laws and energy-release rates. J Appl Mech1973; 40: 201–203.
12.
MindlinRD. Micro-structure in linear elasticity. Arch Ration Mech Anal1964; 16: 51–78.
13.
DuanHLWangJHuangZPKarihalooBL. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J Mech Phys Solids2005; 53: 1574–1596.
14.
DormieuxLKondoD. An extension of Gurson model incorporating interface stresses effects. Int J Eng Sci2010; 48: 575–581.
15.
SciarraGdell’IsolaFCoussyO. Second gradient poromechanics. Int J Solids Struct2007; 44: 6607–6629.
16.
CollinFChambonRCharlierR. A finite element method for poro-mechanical modelling of geotechnical problems using local second gradient models. Int J Numer Methods Eng2006; 65: 1749–1772.
RadiE. On the effects of characteristic lengths in bending and torsion on Mode III crack in couple stress elasticity. Int J Solids Struct2008; 45: 3033–3058.
19.
GourgiotisPAGeorgiadisHG. Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity. J Mech Phys Solids2009; 57: 1898–1920.
20.
GermainP. La méthode des puissances virtuelles en mécanique des milieux continus. I. Théorie du second gradient. J Mec1973; 12: 235–274.
21.
Dell’IsolaFSciarraGVidoliS. Generalized Hooke’s law for isotropic second gradient materials. Proc R Soc London A2009; 465: 2177–2196.
22.
Podio-GuidugliPVianelloM. Hypertractions and hyperstresses convey the same mechanical information. Continuum Mech Thermodyn2010; 22: 163–176.
23.
SokolowskiM. Theory of couple-stresses in bodies with constrained rotations. CISM Courses and Lectures 26. New York: Springer, 1970.
24.
DestuynderPDjaouaM. Sur une interprétation mathématique de l’intégrale de rice en théorie de la rupture fragile. Math Methods Appl Sci1981; 3: 70–87.
25.
LazarMMauginGA. Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity. Int J Eng Sci2005; 43: 1157–1184.
26.
JinZHBatraRC. R-curve and strength behavior of a functionally graded material. Mater Sci Eng1998; A242: 70–76.
27.
GourgiotisPSifnaiouMGeorgiadisH. The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity. Int J Fract2010; 166: 179–201.