Abstract
A mixed/hybrid FE formulation for the solution of elasto-viscoplastic problems is presented. The spatially semidiscretized system of ordinary differential equations is numerically integrated in time by means of a midpoint type algorithm. Stability considerations are discussed and conditions for its maintenance are established. Illustrative numerical examples demonstrate the ability of the proposed method to reproduce elasto-viscoplastic behaviour. Comparison with known results is also made.
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Atluri, S. N. (1975): On hybrid finite element models in solid mechanics. In: vichnevetsky, R. ed.: Advances in computer methods for partial differential equations. AICA, Rutgers University/University of Ghent, pp. 346–356
BenallalA. (1986): Structural analysis in quasi-static elasto-viscoplasticity. Eng. Comput. 3, 323–330
BenallalA. (1987): On the stability of some time-integration schemes in quasi-static hardening elasto-viscoplasticity. Eng. Anal. 4, No. 2, 95–99
BenallalA.; ChabrandP.; GhazouaneM.; ChaudonneretM.; CuliéJ. P.; ContestiE.; GamhaH.; GolinvalJ. C.; TurbatA. (1990): Validation of structural computation codes in elasto-viscoplasticity. Int. J. Numer. Meth. Eng. 29, 1109–1130
BenallalA.; MarquisD. (1987): Constitutive equations for nonproportional cyclic elasto-viscoplasticity. J. Eng. Mater. Techn., Trans ASME 109, 326–336
ChabocheJ. L.; RousselierG. (1983): On the plastic and viscoplastic constitutive equations—Part I: Rules developed with internal variable concept. J. Press. Vess. Techn., Trans ASME 105, 153–158
ChabocheJ. L.; RousselierG. (1983): On the plastic and viscoplastic constitutive equations—Part II: Application of internal variable concepts to the 316 stainless steel. J. Press. Vess. Techn., Trans ASME 105, 159–164
LinT. H. (1968) Theory of inelastic structures. New York: Wiley
OwenD. R. J.; DamjanicF. (1982): Viscoplastic analysis of solids: Stability considerations, Chapter 8 in: HintonE.; OwenD. R. J.; TaylorC. (eds) Recent Advances in Non-Linear Computational Mechanics. Swansea: Pineridge Press, pp. 225–253
PunchE. F.; AtluriS. N. (1984): Development and testing of stable, invariant, isoparametric curvilinear 2-and 3-D hybrid-stress elements. Comp. Meth. Appl. Mech. Eng. 47, 331–356
RubinsteinR.; PunchE. F.; AtluriS. N. (1983) An analysis of, and remedies for, kinematic modes in hybrid-stress finite elements: Selection of stable, invariant stress fields. Comp. Meth. Appl. Mech. Eng. 38, 63–92
XueW.-M.; KarlovitzL. A.; AtluriS. N. (1985) On the existence and stability conditions for mixed-hybrid element solutions based on Reissner's variational principle. Int. J. Solids Struct. 21, 97–116
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Communicated by S. N. Atluri, August 29, 1991
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Harbord, R., Knippers, J. & Gellert, M. A mixed/hybrid FE formulation for solution of elasto-viscoplastic problems. Computational Mechanics 9, 173–184 (1992). https://doi.org/10.1007/BF00350184
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DOI: https://doi.org/10.1007/BF00350184