On the generalized virial theorem and Eshelby tensors

International Journal of Solids and Structures - Tập 47 - Trang 1209-1220 - 2010
Jean-François Ganghoffer1
1LEMTA – ENSEM, 2, Avenue de la Forêt de Haye, BP 160, 54054 Vandoeuvre CEDEX, France

Tài liệu tham khảo

Askes, 2005, Higher-order continua derived from discrete media: continualisation aspects and boundary conditions, Int. J. Solids Struct., 42, 187, 10.1016/j.ijsolstr.2004.04.005 Born, 1954 Ciarlet, 1993 Callen, 1985 Chandrasekhar, 1953, Problems of gravitational stability in the presence of a magnetic field, Ap. J., 118, 116, 10.1086/145732 Chandrasekhar, 1962, The potentials and the superpotentials of homogeneous ellipsoids, Ap. J., 136, 1037, 10.1086/147456 Chang, 2002 Clausius, 1870, On a mechanical theorem applicable to heat, Phil. Mag. Ser., 4, 122, 10.1080/14786447008640370 Dittrich, 2001 Ericksen, 1984 Feyel, 2000, FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Comput. Methods Appl. Mech. Eng., 183, 309, 10.1016/S0045-7825(99)00224-8 Goodstein, 1975 Irving, 1950, The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics, J. Chem. Phys., 18, 817, 10.1063/1.1747782 Jouanna, 2001, Statistical approach of the stress tensor by the generalized virial, C.R. Acad. Sci., Paris, t. 329, 775 Jouanna, 2004, Partial stresses in heterogeneous media by a direct statistical approach, C.R. Mécanique, 332, 305, 10.1016/j.crme.2004.01.006 Kouznetsova, 2004, Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy, Comput. Methods Appl. Mech. Eng., 193, 5525, 10.1016/j.cma.2003.12.073 Ledoux, 1945, On the radial pulsation of gaseous stars, Ap. J., 102, 143, 10.1086/144747 Maugin, G.A., 1993. Material Inhomogeneities in Elasticity. Chapman et al., London. Mindlin, 1965, Second gradient in strain and surface tension in linear elasticity, Int. J. Solids Struct., 1, 417, 10.1016/0020-7683(65)90006-5 Milstein, 1982 Mourad, 2003, A nonlinearly elastic homogenized constitutive law for the myocardium, Comput. Fluid Solid Mech., 1779 Murdoch, 2007, A critique of atomistic definitions of the stress tensor, J. Elasticity, 88, 113, 10.1007/s10659-007-9121-5 Parker, 1954, Tensor virial equations, Phys. Rev., 96, 1686, 10.1103/PhysRev.96.1686 Poincaré, 1903 Pichugrin, 2008, Asymptotic equivalence of homogenisation procedures and fine-tuning of continuum theories, J. Sound Vib., 313, 858, 10.1016/j.jsv.2007.12.005 Schmidt, 1979 Steinmann, 2000, Application of material forces to hyperelastostatic fracture mechanics. I. Continuum mechanical setting, Int. J. Solids Struct., 37, 7371, 10.1016/S0020-7683(00)00203-1 Sunyk, 2003, On higher gradients in continuum-atomistic modelling, Int. J. Solids Struct., 40, 6877, 10.1016/j.ijsolstr.2003.07.001 Tadmor, 1996, Quasicontinuum analysis of defects in solids, Phil. Mag., A73, 1529, 10.1080/01418619608243000