Implementing the New First and Second Differentiation of a General Yield Surface in Explicit and Implicit Rate-Independent Plasticity
محورهای موضوعی : EngineeringF Moayyedian 1 , M Kadkhodayan 2
1 - Mechanical Engineering Department, Ferdowsi University of Mashhad
2 - Mechanical Engineering Department, Ferdowsi University of Mashhad
کلید واژه: Rate-independent Euler backward/forward methods, Consistent elastic-plastic modulus, Internally pressurized thick walled cylinder,
چکیده مقاله :
In the current research with novel first and second differentiations of a yield function, Euler forward along with Euler backward with its consistent elastic-plastic modulus are newly implemented in finite element program in rate-independent plasticity. An elastic-plastic internally pressurized thick walled cylinder is analyzed with four famous criteria including both pressure dependent and independent. The obtained results are in good agreement with experimental results. The consistent/continuum elastic-plastic moduli for Euler backward method are also investigated.
[1] Krieg R.D., Krieg D.B., 1977, Accuracies of numerical solution methods for the elastic-perfectly plastic model, Journal of Pressure Vessel Technology -Transactions of the ASME 99:510-515.
[2] Schreyer H.L., Kulak R.F., Kramer J.M., 1979, Accurate numerical solutions for elastic-plastic models, Transactions of the ASME 101: 226-234.
[3] Simo J.C., Taylor R.L., 1985, Consistent tangent operators for rate-independent elastoplasticity, Computer Methods in Applied Mechanics and Engineering 48:101-118.
[4] Ortiz M., Popov E.P., 1985, Accuracy and stability of integration algorithms for elastoplastic constitutive relations, International Journal for Numerical Methods in Engineering 21:1561-1576.
[5] Potts D.M., Gens A., 1985, A critical assessment of methods of correcting for draft from the yield surface in elasto-plastic finite element analysis, International Journal for Numerical and Analytical Methods in Geomechanics 9:149-159.
[6] Ortiz M., Simo J.C., 1986, An analysis of a new class of integration algorithms for elastoplastic constitutive relations, International Journal for Numerical Methods in Engineering 23:353-366.
[7] Simo J.C., Taylor R.L., 1986, A return mapping algorithm for plane stress elastoplasticity, International Journal for Numerical Methods in Engineering 38:649-670.
[8] Dodds R.H., 1987, Numerical techniques for plasticity computations in finite element analysis, Computers & Structures 26:767-779.
[9] Ortiz M., Martin J.B., 1989, Symmetry-preserving return mapping algorithms and incrementally external paths: A unification of concepts, International Journal for Numerical Methods in Engineering 28:1839-1853.
[10] Gratacos P., Montmitonnet P., Chenot J.L., 1992, An integration scheme for Prandtl-Reuss elastoplastic constitutive equations, International Journal for Numerical Methods in Engineering 33:943-961.
[11] Ristinmma M., Tryding J., 1993, Exact integration of constitutive equations in elasto-plasticity, International Journal for Numerical Methods in Engineering 36:2525-2544.
[12] Kadkhodayan M., Zhang L.C., 1995, A consistent DXDR method for elastic-plastic problems, International Journal for Numerical Methods in Engineering 38:2413-2431.
[13] Foster C.D., Regueiro R.A., Fossum A.F., Borja R.I., 2005, Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials, Computer Methods in Applied Mechanics and Engineering 194:5109-5138.
[14] Kim J., Gao X., 2005, A generalised approach to formulate the consistent tangent stiffness in plasticity with application to the GLD porous material model, International Journal of Solid and Structures 42:103-122.
[15] Hu W., Wang Z.R., 2005, Multiple-factor dependence of the yielding behaviour to isotropic ductile material, Computational Materials Science 32:31-46.
[16] Ding K.Z., Qin Q.H., Cardew-Hall M., 2007, Substepping algorithms with stress correction for simulating of sheet metal forming process, International Journal of Mechanical Sciences 49:1289-1308.
[17] Nicot F., Darve F., 2007, Basic features of plastic strains: from micro-mechanics to incrementally nonlinear models, International Journal of Plasticity 23:1555-1588.
[18] Oliver J., Huespe A.E., Cante J.C., 2008, An implicit/explicit integration scheme to increase computability of non-linear material and contact/friction problems, Computer Methods in Applied Mechanics and Engineering 197:1865-1889.
[19] Ragione L.L., Prantil V.C., Sharma I., 2008, A simplified model for inelastic behaviour of an idealized granular material, International Journal of Plasticity 24:168-189.
[20] Kosa A., Szabo L., 2009, Exact integration of the von mises elastoplasticity model with combined linear isotropic/kinematic hardening, International Journal of Plasticity 25:1083-1106.
[21] Tu X., Andrade J.E., Chen Q., 2009, Return mapping for nonsmooth and multiscale elastoplasticity, Computer Methods in Applied Mechanics and Engineering 198:2286-2296.
[22] Valoroso N., Rosti L., 2009, Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity, International Journal of Solid and Structures 46:74-91.
[23] Gao X., Zhang T., Hayden M., Roe C., 2009, Effects of the stress state on plasticity and ductile failure of an aluminium 5083 alloy, International Journal of Plasticity 25:2366-2382.
[24] Cardoso R.P.R., Yoon J.W., 2009, Stress integration method for a nonlinear kinematic/isotropic hardening model and its characterization based on polycrystal plasticity, International Journal of Plasticity 25: 1684-1710.
[25] Ghaie A., Green D.E., 2010, Numerical implementation of Yoshida-Uemori two-surface plasticity model using a fully implicit integration scheme, Computational Material Sciences 48:195-205.
[26] Ghaei A., Green D.E., Taherizadeh A., 2010, Semi-implicit numerical integration of Yoshida-Uemori two-surface plasticity model, International Journal of Mechanical Sciences 52:531-540.
[27] Kossa A., Szabo L., 2010, Numerical implementation of a novel accurate stress integration scheme for the von Mises elastoplasticity model with combined linear hardening, Finite Element in Analysis and Design 46:391-400.
[28] Rezaiee-Pajand M., Sharifan M., 2011, Accurate and approximate integrations of Drucker-Prager plasticity with linear isotropic and kinematic hardening, European Journal of Mechanics A/Solids 30:345-361.
[29] Becker R., 2011, An alternative approach to integrating plasticity relations, International Journal of Plasticity 27:1224-1238.
[30] Moayyedian F., Kadkhodayan M., 2013, A general solution in Rate-Dependant plasticity, International Journal of Engineering 26:391-400.
[31] Moayyedian F., Kadkhodayan M., 2014, A study on combination of von mises and tresca yield loci in non-associated viscoplasticity, International Journal of Engineering 27:537-545.
[32] Owen D.R.J., Hinton E., 1980, Finite Elements in Plasticity: Theory and Practice, Pineridge Press Limited.
[33] Souza Neto E.D., Peric D., Owen D.R.J., 2008, Computational Methods for Plasticity, Theory and Applications, John Wiley and Sons, Ltd.
[34] Simo J.C., Hughes T.J.R., 1998, Computational Inelasticity, Springer-Verlag New York, Inc.
[35] Zienkiewicz O.C., Taylor R.L., 2005, The Finite Element Method for Solid and Structural Mechanics, Elsevior Butterworth-Heinemann, sixth edition.
[36] Crisfield M.A., 1997, Non-Linear Finite Element Analysis of Solids and Structures, New York , John Wiley.
[37] Hill R., 1950, The Mathematical Theory of Plasticity, Oxford University Press, New York.
[38] Chakrabarty J., 1987, Theory of Plasticity, McGraw-Hill, New York.
[39] Chen W.F., Zhang H., 1936, Structural Plasticity Theory, Problems and CAE Software, Springer-Verlag, New York.
[40] Khan A., Hung S., 1995, Continuum Theory of Plasticity, John Wiley & Sons, Canada.
[41] Marcal P.V., 1965, A note on the elastic-plastic thick cylinder with internal pressure in the open and closed-end condition, International Journal of Mechanical Sciences 7:841-845.
