[en] In the present paper, a detailed description of the formulation of the new SSH3D solid-shell element is presented. This formulation is compared with the previously proposed RESS solid-shell element [1, 2]. Both elements were recently implemented within the LAGAMINE in-house research finite element code. These solid-shell elements possess eight nodes with only displacement nodal degrees of freedom (DOF). In order to overcome various locking pathologies, the SSH3D formulation employs the well known Enhanced Assumed Strain (EAS) concept originally introduced by Simo and Rifai [3] and based on the Hu-Veubeke-Washizu variational principle combined with the Assumed Natural Strain (ANS) technique based on the work of Dvorkin and Bathe [4]. For the RESS solid-shell element, on the other hand, only the EAS technique is used with a Reduced Integration (RI) Scheme. A particular characteristic of these elements is their special integration schemes, with an arbitrary number of integration points along the thickness direction, dedicated to analyze problems involving non-linear through-thickness distribution (i.e. metal forming applications) without requiring many element layers. The formulation of the SSH3D element is also particular, with regard to the solid-shell elements proposed in the literature, in the sense that it is characterized by an in-plane full integration and a large variety in terms of (i) enhancing parameters, (ii) the ANS version choice and (iii) the number of integration points through the thickness direction. The choice for these three parameters should be adapted to each problem so as to obtain accurate results and to keep the calculation time low.
<br />Numerous numerical examples are performed to investigate the performance of these elements. These examples illustrate the reliability and the efficiency of the proposed formulations in various cases including linear and non-linear problems. SSH3D element is more robust thanks to the various options proposed and its full in-plane integration scheme, while RESS element in more efficient from a computational point of view.
Alves De Sousa, R.J., Cardoso, R.P.R., Valente, R.A.F., Yoon, J.W., Gracio, J.J., Jorge, R.M.N., A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part i - Geometrically linear applications (2005) Int. J. Numer. Methods Eng., 62, pp. 952-977
Alves De Sousa, R.J., Cardoso, R.P.R., Valente, R.A.F., Yoon, J.W., Gracio, J.J., Jorge, R.M.N., A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness - Part II: Nonlinear applications (2006) Int. J. Numer. Methods Eng., 67, pp. 160-188
Simo, J.C., Rifai, M.S., A class of mixed assumed strain methods and the method of incompatible modes (1990) Int. J. Numer. Methods Eng., 29, pp. 1595-1638
Dvorkin, E.N., Bathe, K.J., A continuum mechanics based four-node shell element for general nonlinear analysis (1984) Eng. Comput., 1, pp. 77-88
Hauptmann, R., Schweizerhof, K., A systematic development of 'solid-shell' element formulations for linear and non-linear analyses employing only displacement degrees of freedom (1998) Int. J. Numer. Methods Eng., 42, pp. 49-69
Vu-Quoc, L., Tan, X.G., Optimal solid shells for non-linear analyses of multilayer composites I. Statics (2003) Comput Method Appl. Mech. Eng., 192, pp. 975-1016
Vu-Quoc, L., Tan, X.G., Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics (2003) Comput Method Appl. Mech. Eng., 192, pp. 1017-1059
Reese, S., A large deformation solid-shell concept based on reduced integration with hourglass stabilization (2007) Int. J. Numer. Methods Eng., 69, pp. 1671-1677
Schwarze, M., Reese, S., A reduced integration solid-shell finite element based on the EAS and the ANS concept-geometrically linear problems (2009) Int. J. Numer. Methods Eng., 80, pp. 1322-1355
Schwarze, M., Reese, S., A reduced integration solid-shell finite element based on the EAS and the ANS concept-Large deformation problems (2011) Int. J. Numer. Methods Eng., 85, pp. 289-329
Abed-Meraim, F., Combescure, A., An improved assumed strain solid-shell element formulation with physical stabilization for geometric non-linear applications and elastic-plastic stability analysisc (2009) Int. J. Numer. Methods Eng., 80, pp. 1640-1646
Rah, K., Paepegem, W.V., Habraken, A.M., Degrieck, J., De Sousa, R.J.A., Valente, R.A.F., Optimal low-order fully integrated solid-shell elements (2012) Comput. Mech., pp. 1-18
Vu-Quoc, L., Tan, X., Efficient hybrid-EAS solid element for accurate stress prediction in thick laminated beams, plates, and shells (2013) Comput. Method Appl. Mech. Eng., 253, pp. 337-355
Kaiping, L., Cescotto, S., An 8-node brick element with mixed formulation for large deformation analyses (1997) Comput. Method Appl. Mech. Eng., 141, pp. 157-204
Reese, S., On a physically stabilized one point finite element formulation for three-dimensional finite elasto-plasticity (2005) Comput. Method Appl. Mech. Eng., 194, p. 31
Miehe, C., A theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains (1998) Comput. Method Appl. Mech. Eng., 155, pp. 193-233
Hauptmann, R., Schweizerhof, K., Doll, S., Extension of the 'solid-shell' concept for application to large elastic and large elastoplastic deformations (2000) Int. J. Numer. Methods Eng., 49, pp. 1121-1141
Klinkel, S., Gruttmann, F., Wagner, W., A continuum based three-dimensional shell element for laminated structures (1999) Comput. Struct., 71, pp. 43-62
Sze, K.Y., Chan, W.K., Pian, T.H.H., An eight-node hybrid-stress solid-shell element for geometric non-linear analysis of elastic shells (2002) Int. J. Numer. Methods Eng., 55, pp. 853-878
Malkus, D.S., Hughes, T.J.R., Mixed finite element methods - Reduced and selective integration techniques: A unification of concepts (1978) Comput. Method Appl. Mech. Eng., 15, pp. 63-81
Hughes, T.J.R., Generalization of selective integration procedures to anisotropic and nonlinear media (1980) Int. J. Numer. Methods Eng., 15, pp. 1413-1418
Simo, J.C., Armero, F., Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes (1992) Int. J. Numer. Methods Eng., 33, pp. 1413-1449
Klinkel, S., Gruttmann, F., Wagner, W., A robust non-linear solid shell element based on a mixed variational formulation (2006) Comput. Method Appl. Mech. Eng., 195, pp. 179-201
Klinkel, S., Wagner, W., A geometrical non-linear brick element based on the EAS-method (1997) Int. J. Numer. Methods Eng., 40, pp. 4529-4545
Alves De Sousa, R.J., Jorge, R.M.N., Valente, R.A.F., César De Sa, J.M.A., A new volumetric and shear locking-free 3D enhanced strain element (2003) Eng. Comput., 20, pp. 896-925
Parente, M.P.L., Valente, R.A.F., Jorge, R.M.N., Cardoso, R.P.R., Alves De Sousa, R.J., Sheet metal forming simulation using EAS solid-shell finite elements (2006) Finite Elem. Anal. Des., 42, pp. 1137-1149
Schwarze, M., Vladimirov, N.I., Reese, S., On the implementation of the EAS and ANS concept into a reduced integration continuum shell element and applications to sheet forming (2009) Int. J. Mater. Form., 2, p. 4
Andelfinger, U., Ramm, E., EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements (1993) Int. J. Numer. Methods Eng., 36, pp. 1311-1337
Betsch, P., Gruttmann, F., Stein, E., A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains (1996) Comput. Method Appl. Mech. Eng., 130, pp. 57-79
Bathe, K.-J., Dvorkin, E.N., (1985) A Four-Node Plate Bending Element Based on Mindlin/Reissner Plate Theory and A Mixed Interpolation, , Wiley Chichester, United Kingdom
Bischoff, M., Ramm, E., Shear deformable shell elements for large strains and rotations (1997) Int. J. Numer Methods Eng., 40, pp. 4427-4449
Cardoso, R.P.R., Yoon, J.W., Mahardika, M., Choudhry, S., Alves De Sousa, R.J., Valente, R.A.F., Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods for one-point quadrature solid-shell elements (2008) Int. J. Numer. Methods Eng., 75, pp. 156-187
Norachan, P., Suthasupradit, S., Kim, K.D., A co-rotational 8-node degenerated thin-walled element with assumed natural strain and enhanced assumed strain (2012) Finite Elem. Anal. Des., 50, pp. 70-85
Cescotto, S., Grober, H., Calibration and Application of an elastic viscoplastic constitutive equation for steels in hot rolling conditions (1985) Eng. Comput., 2, pp. 101-106
Habraken, A.M., Cescotto, S., An automatic remeshing technique for finite element simulation of forging processes (1990) Int. J. Numer. Methods Eng., 30, pp. 1503-1525
Castagne, S., Pascon, F., Bles, G., Habraken, A.M., Developments in finite element simulations of continuous casting (2004) J. Phys. IV, 120, pp. 447-455
Duchêne, L., (2003) FEM Study of Metal Sheets with A Texture Based, Local Description of the Yield Locus, , University of Liège - Belgium Department of Architecture, Geology, Environment and Constructions
Henrard, C., (2008) Numerical Simulations of the Single Point Incremental Forming Process, , University of Liège - Belgium Department of Architecture, Geology, Environment and Constructions
Betsch, P., Stein, E., An assumed strain approach avoiding artificial thickness straining for a non-linear 4-node shell element (1995) Commun. Numer. Methods Eng., 11, pp. 899-909
Caseiro, J.F., AlvesdeSousa, R.J., Valente, R.A.F., A systematic development of EAS three-dimensional finite elements for the alleviation of locking phenomena (2013) Finite Elem. Anal. Des., 73, pp. 30-41
Alves De Sousa, R.J., Yoon, J.W., Cardoso, R.P.R., Valente, R.A.F., Gracio, J.J., On the use of a reduced enhanced solid-shell (RESS) element for sheet forming simulations (2007) Int. J. Plast., 23, pp. 490-515
Cardoso, R.P.R., Yoon, J.W., Gracio, J.J., Barlat, F., De Sa, J.M.A.C., Development of a one point quadrature shell element for nonlinear applications with contact and anisotropy (2002) Comput. Method Appl. Mech. Eng., 191, pp. 5177-5206
César De Sá, J.M.A., Jorge, R.M.N., Valente, R.A.F., Areias, P.M.A., Development of shear locking-free shell elements using an enhanced assumed strain formulation (2002) Int. J. Numer. Methods Eng., 53, pp. 1721-1727
Simo, J.C., Rifai, M.S., Fox, D.D., (1990) On A Stress Resultant Geometrically Exact Shell Model. IV, Variable Thickness Shells with Through-the Thickness Stretching, , Elsevier United Kingdom
Valente, R.A.F., Alves De Sousa, R.J., Jorge, R.M.N., An enhanced strain 3D element for large deformation elastoplastic thin-shell applications (2004) Comput. Mech., 34, pp. 38-52
Simo, J.C., Fox, D.D., Rifai, M.S., On a stress resultant geometrically exact shell model III (1990) Computational Aspects of the Nonlinear Theory, , Elsevier United Kingdom
Macneal, R.H., Harder, R.L., (1985) A Proposed Standard Set of Problems to Test Finite Element Accuracy, , Elsevier Amsterdam, Netherlands
Valente, R.A.F., Jorge, R.M.N., Cardoso, R.P.R., César De Sá, J.M.A., Grácio, J.J.A., On the use of an enhanced transverse shear strain shell element for problems involving large rotations (2003) Comput. Mech., 30, pp. 286-296
Gelin, J.C., Picart, P., NUMISHEET '99 (1999) Proceedings of the 4th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes: BURS
Yang, D.Y., NUMISHEET 2002 (2002) Proceedings of the 5th International Conference and Workshop on Numerical Simulation of 3D Shell Forming Processes -verification of Simulation with Experiment
Yoon, J.W., Pourboghrat, F., Chung, K., Yang, D.Y., Springback prediction for sheet metal forming process using a 3D hybrid membrane/shell method (2002) Int. J. Mech. Sci., 44, pp. 2133-2153
Salahouelhadj, A., Abed-Meraim, F., Chalal, H., Balan, T., Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elastic-plastic formulation (2012) Arch. Appl. Mech., 82, pp. 1269-1290
Xu, H.J., Liu, Y.Q., Zhong, W., Three-dimensional finite element simulation of medium thick plate metal forming and springback (2012) Finite Elem. Anal. Des., 51, pp. 49-58
Sá De César, J.M.A., Owen, D.R.J., The imposition of the incompressibility constraint in finite elements - A review of methods with a new insight to the locking phenomenoa (1986) Proceedings of the International Conference on Numerical Methods for Non-Linear Problems, , Pineridge Press Swansea, UK
César De Sa, J.M.A., Natal Jorge, R.M., New enhanced strain elements for incompressible problems (1999) Int. J. Numer. Methods Eng., 44, pp. 229-248
César De Sá, J.M.A., Areias, P.M.A., Natal Jorge, R.M., Quadrilateral elements for the solution of elasto-plastic finite strain problems (2001) Int. J. Numer. Methods Eng., 51, pp. 883-917