Adaptive analysis of inelastic problems with Bodner-Partom constitutive model

• Autorzy: Cecot W.
• Konferencja: Polish Conference on Computer Methods in Mechanics (16 ; 21-24.06.2005 ; Częstochowa, Poland
• Języki publikacji: EN

Abstrakty

EN

The Bodner-Partom elastic-visco-plastic constitutive eąuations [4] were used for numerical analysis of inelastic problems. This rate-dependent model makes it possible to describe elastic, plastic and viscous processes in metals, including temperaturę and continuum damage effects. The adaptive finite element method [9] was applied to approximate solution of the governing eąuations with two a posteriori error es-timates that control accuracy of time and space discretization of displacements and internal variables. The paper addresses a further development of the methodology proposed by the author in previous works [7, 8] and used in [6]. We present here certain additional theoretical background and propose a novel strategy of adaptation as well as verify the method of solution transfer.

Słowa kluczowe

EN

h-adaptive finite element method; error estimate; elastic-visco-plasticity

PL

metoda elementów skończonych; lepkoplastyczność; elastoplastyczność

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2006
• Tom: Vol. 13, No. 4
• Strony: 513--521
• Opis fizyczny: Bibliogr. 26 poz., rys.

Twórcy

autor

Cecot W.

• Cracow University of Technology, ul. Warszawska 2A, 31-155 Kraków, Poland

Bibliografia

• [1] M. Ainsworth, J.T. Oden. A Posteriori Error Estimation in Finite Element Analysis. J. Wiley & Sons, 2000.
• [2] I. Babuska, W.C. Rheinboldt. Error estimates for adaptive finite element computations. Int. J. Num. Meth. Engng., 12: 1597-1615, 1978.
• [3] J.M. Bass, J.T. Oden. Adaptive finite element methods for a class of evolution problems in viscoplasticity. Int. J. Engng. Sci., 25(623-653), 1987.
• [4] S.R. Bodner, Y. Partom. Constitutive equations elastic viscoplastic strain-hardening materials. J. Appl. Mech., 42: 385-389, 1975.
• [5] D. Braess. Finite Elements. Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, 1997.
• [6] W. Cecot. Analysis of selected in-elastic problems by h-adaptive finite element method. No. 323 in Mechanics. Cracow University of Technology Press, 2005.
• [7] W. Cecot. Application of h-adaptive FEM and Zarka's approach to analysis of shakedown problems. Int. J. Num. Meth. Engng., 61: 2139-2158, 2004.
• [8] W. Cecot, W. Rachowicz. Adaptive Solution of Problems Modeled by Unified State Variable Constitutive Equations. Comp. Assist. Mech. Engng. Sci., 7: 479-492, 2000.
• [9] L. Demkowicz, J.T. Oden, W. Rachowicz, O. Hardy. Toward a universal Zip-adaptive finite element strategy. Part 1: Constrained approximation and data structure. Comp. Meth. Appl. Mech. Engng., 77: 79-112, 1989.
• [10] L. Demkowicz, W. Rachowicz, K. Banas, J. Kucwaj. 2-D hp adaptive package. Technical Report 4/92, CracowUniversity of Technology, 1992.
• [11] M. Dyduch, A.M. Habraken, S. Cescotto. Automatic adaptive remeshing for numerical simulations of metalforming. Comp. Meth. Appl. Mech. Engng., 101: 283-298, 1992.
• [12] C. Johnson, P. Hansbo. Adaptive finite element methods in computational mechanics. Comp. Meth. Appl. Mech.Engng., 101: 143-181, 1992.
• [13] V. Kumar, M. Morjaria, S. Mukherjee. Numerical integration of some stiff constitutive models of inelasticdeformation. ASME J. Engng. Mater Technoi, 102: 92-96, 1980.
• [14] P. Ladeveze, N. Moes, B. Douchin. Constitutive relation error estimators for (visco)plastic analysis with softening. Comp. Meth. Appl. Mech. Engng., 176: 247-264, 1999.
• [15] P. Ladeveze, J.P. Pelle, P. Rougeot. Error estimate procedure in the finite element method and application.SIAM J. Numer. Anal, 20: 485-509, 1983.
• [16] P. Lancaster, K. Salkauskas. Surface generated by moving least squares methods. Mathematics of Computation, 155(37): 141-158, 1981.
• [17] T. Liszka, J. Orkisz. The finite difference method at arbitrary irregular grids and its applications in appliedmechanics. Comp. Struct., 11: 83-95, 1980.
• [18] J.B. Min, W.W. Tworzydlo, K.E. Xiques. Adaptive finite element methods for continuum damage modeling.Comp. Struct, 58: 887-900, 1995.
• [19] J.T. Oden, L. Demkowicz, W. Rachowicz, T.A. Westermann. Toward a universal hp-adaptive finite elementstrategy. Part 2: A posteriori error estimation. Comp. Meth. Appl. Mech. Engng., 77: 113-180, 1989.
• [20] S. Prudhomme, J.T. Oden. Computable error estimators and adaptive techniques for fluid flow problems. In:Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics, pp. 207-268. Springer, 2001.
• [21] W. Rachowicz, J.T. Oden, L. Demkowicz. Toward a universal Zip-adaptive finite element strategy. Part 3: Design of hp meshes. Comp. Meth. Appl. Mech. Engng., 77: 181-212, 1989.
• [22] S. Repin, L. Xanthis. A posteriori error estimation for elasto-plastic problems based on duality theory. Comp. Meth. Appl. Mech. Engng., 138: 317-339, 1996.
• [23] J.S. Sandhu, H. Liebowitz. Examples of adaptive FEA in plasticity. Engng. Fract. Mech., 50: 947-956, 1995.
• [24] J.C. Simo, T.J.R. Hughes. Computational Inelasticity. Springer-Verlag, 1998.
• [25] E. Stein, ed. Error-Controlled Adaptive Finite Elements in Solid Mechanics. J. Wiley & Sons, 2003.
• [26] O.C. Zienkiewicz, J.Z. Zhu. Superconvergence and the superconvergent patch recovery. Finite Elements in Analysis and Design, 19: 11-23, 1995.