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Finite element simulation of the rolling and extrusion of multi-phase materials. Application to the rolling of prepared sugar cane. (English) Zbl 0906.73068

Summary: We describe a general framework for the finite element simulation of the rolling and extrusion of multiphase materials. Emphasis is placed on the following aspects: the characterization of the coupling between the liquid and solid phases of the material; the modelling of the (highly nonlinear) behaviour of the solid skeleton; the adaptive mesh refinement strategy, required in view of the magnitude of the strains and complex deformations involved in the processes; the use of an efficient contact algorithm; and, the inverse identification of material parameters for the solid phase by means of ‘numerical experiments’. Practical application is made to simulate the process by which juice is extracted from prepared sugar cane by rolling.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
76S05 Flows in porous media; filtration; seepage
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
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[1] Biot, M. A., General theory of three-dimensional consolidation, J. Appl. Phys., 12, 155-164 (1941) · JFM 67.0837.01
[2] Biot, M. A.; Willis, P. G., The elastic coefficients of the theory of consolidation, J. Appl. Mech., 24, 594-601 (1957)
[3] Bishop, A. W., The principle of effective stress, Teknisk Ukeblad, 39, 859-863 (1959)
[4] Bishop, A. W., The measurement of pore pressure in the triaxial test, (Pore Pressure and Suction in Soils (1961), Butterworths: Butterworths London), 38-46
[5] Chan, A. H.C., A unified finite element solution to static and dynamic problems in geomechanics, (Ph.D. Thesis (1988), University College of Swansea), C/Ph/106/88
[6] Darcy, H., Les Fontaines Publiques de la Ville de Dijon (1856), Dalmont: Dalmont Paris
[7] Lewis, R. W.; Schrefler, B. A., The finite element mehtod in the deformation and consolidation of porous media (1987), Wiley: Wiley London
[8] Perić, D.; Hochard, Ch.; Dutko, M.; Owen, D. R.J., Transfer operators for evolving meshes in small strain elasto-plasticity, Comput. Methods Appl. Mech. Engrg., 137, 331-344 (1966) · Zbl 0884.73071
[9] Perić, D.; Owen, D. R.J., Computational model for 3-D contact problems with friction based on the penalty method, Int. J. Numer. Methods Engrg., 35, 1289-1309 (1992) · Zbl 0768.73100
[10] Perić, D.; Owen, D. R.J.; Honnor, M. E., A model for finite strain elasto-plasticity based on logarithmic strains: Computatioanl issues, Comput. Methods Appl. Mech Engrg., 94, 35-61 (1992) · Zbl 0747.73020
[11] Perić, D.; Yu, J.; Owen, D. R.J., On error estimates and adaptivity in elastoplastic solids: Application to the numerical simulation of strain localization in classical and cosserat continua, Int. J. Numer. Methods Engrg., 37, 1351-1379 (1994) · Zbl 0805.73066
[12] Simo, J. C.; Taylor, R. L., Consistent tangent operators for rate-independent elastoplasticity, Comput Methods Appl. Mech. Engrg., 48, 101-118 (1985) · Zbl 0535.73025
[13] Simo, J. C.; Hughes, T. R.J., General return mapping algorithms for rate-independent plasticity, (Desai, C. S.; etal., Constitutive Laws for Engineering Materials: Theory and Applications (1987), Elsevier), 221-231
[14] de Souza Neto, E. A.; Perić, D.; Dutko, M.; Owen, D. R.J., Finite strian implementation of an elasto-plastic model for crushable foam, (Proc. the European Workshop on Computational Mechanics. Proc. the European Workshop on Computational Mechanics, Göteborg Sweden (1995)), 174-188
[15] Terzaghi, K., Theoretical Soil Mechanics (1943), Wiley: Wiley New York
[16] Zienkiewicz, O. C., Basic formulation of static and dynamic behaviour of soil and other porous media, (Martins, J. B., Numerical Methods in Geomechanics (1982), D. Reidel Publishing Co), 39-57 · Zbl 0539.73127
[17] Zienkiewicz, O. C.; Mroz, Z., Generalized plasticity formulation and applications to geomechanics, (Desai, C. S.; Gallagher, R. H., Mechanics of Engineering Materials (1984), John Wiley and Sons Ltd), 655-679
[18] Zienkiewicz, O. C.; Shiomi, T., Dynamic behaviour of saturated porous media; the generalized biot formulation and its numerical solution, Int. J. Numer. Anal. Methods Geomech., 8, 71-96 (1984) · Zbl 0526.73099
[19] Zienkiewicz, O. C.; Taylor, R. L., The finite element method. Vol. 1: basic formulation and linear problems (1989), McGraw-Hill Ltd · Zbl 0979.74002
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