Abstract
Firstly, typical gradient-dependent nonlocal inelastic models were briefly reviewed. Secondly, based on the principle of ‘gradient-dependent energy dissipation’, a gradient-dependent constitutive model for plasticity coupled with isotropic damage was presented in the framework of continuum thermodynamics. Numerical scheme for calculation of Laplacian term of damage field with the numerical results obtained by FEM calculation was proposed. Equations have been presented on the basis of Taylor series for both 2-dimensional and 3-dimensional cases, respectively. Numerical results have indicated the validity of the proposed gradient-dependent model and corresponding numerical scheme.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belytschko T, Chiang H Y, Plaskacz E. High resolution two-dimensional shear band computations: imperfections and mesh dependence[J].Comput Methods Appl Mech Engrg, 1994,137(1):1–15.
Besson, J, Steglich D, Brocks W. Modeling of crack growth in round bars and plane strain specimens [J].Internal J Solids and Structures, 2001,38(11):8259–8284.
Noll W. Materially uniform simple bodies with inhomogeneities[J].Arch Rational Mech Anal, 1967,27(1):1–32.
Nedjar B. Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects[J].Internat J Solids and Structures, 2001,38(9):5412–5451.
Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements[J].Comput. Mech, 1992,10(3):519–534.
Villon P. Contribution à L’optimisation[D]. Thèse Présentée Pour L’obtention du Grade de Docteur D’état. Universitéde Technologie de Compiègne, France, 1991.
Belytschko T, Krongauz Y, Organ D, et al.. Meshless methods: an overview and recent developments [J].Comput Methods Appl Mech Engrg, 1996,139(1):3–47.
Liu W K, Li S, Belytschko T. Moving least square kernel Galerkin method—(I): Methodology and convergence[J].Comput Methods Appl Mech Engrg, 1997,143(1):113–154.
Aifantis E C. On the role of gradient in the localization of deformation and fracture[J].Internat J Engrg Sci, 1992,30(4):1279–1299.
Comi C, Perego U. A generalized variable formulation for gradient dependent softening plasticity [J].Internat J Numer Methods Engrg, 1996,39(6):3731–3755.
Li X, Cescotto S. A mixed element method in gradient plasticity for pressure dependent materials and modelling of strain localization[J].Comput Methods Appl Mech Engrg, 1997,144(1):287–305.
Liebe T, Steinmann P, Benallal A. Theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage[J].Comput Methods Appl Mech Engrg, 2001,190(11):6555–6576.
Lemaitre J.A Course on Damage Mechanics[M]. Springer-Verlag, Berlin, 1992.
Maugin G A. Remarks on the thermomechanics of weakly nonlocal theories[A]. In:Nonlocal Aspects in Solid Mechanics, Abstracts of the EuroMech Colloquium 378[C]. Mulhouse, France, 1998, 2–9.
Hansen N R, Schreyer H L. A thermodynamically consistent framework for theories of elastoplasticity coupled with damage[J].Internat J Solids Structures, 1994,31(2):359–389.
Saanouni K, Forster C, Hatira F B. On the anelastic flow with damage[J].Internat J Dama Mech, 1994,3(1):140–169.
Grange M, Besson J Andrieu E. An anisotropic Gurson model to represent the ductile rupture of hydrided Zircaloy-4 sheets[J].Internat J Fracture, 2000,105(1):273–293.
Gurson A L. Continuum theory of ductile rupture by void nucleation and growth—Part I: Yield criteria and flow rules for porous ductile media[J].J Engng Mater Tech, 1977,99(1):2–15.
Kachanov L M.Introduction to Continuum Damage Mechanics[M]. Maritinus Nijhoff Dordrecht, the Netherlands, 1986.
Shen Xinpu, Shen Guoxiao, Chen Lixin. Investigation on elasto-plastic constitutive model coupled with damage for localization phenomena[J].Applied Mathematics and Mechanics (English Edition), 2004,25(12):1365–1373.
Brunet M, Morestin F, Walter H. Damage identification for anisotropic sheet-metals using a non-local damage model[A]. In:Proceedings of 2002 ASME-IMECE[C]. IMECE 2002-33088, Nov 17–22, 2002, New Orleans, 1–10.
Author information
Authors and Affiliations
Additional information
Communicated by YANG Gui-tong, Original Member of Editorial Committee, AMM)
Foundation item: the Natural Science Foundation of Liaoning Province of China (2001101023)
Biography: SHEN Xin-pu, Professor, Doctor, E-mail: xinpushen@vip.sina.com
Rights and permissions
About this article
Cite this article
Xin-pu, S., Guo-xiao, S., Li-xin, C. et al. Investigation on gradient-dependent nonlocal constitutive models for elasto-plasticity coupled with damage. Appl Math Mech 26, 218–233 (2005). https://doi.org/10.1007/BF02438245
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02438245