In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.
If the inline PDF is not rendering correctly, you can download the PDF file here.
 Che, F. X., and Pang, J. H. “Study on Board-Level Drop Impact Reliability of Sn–Ag–Cu Solder Joint by Considering Strain Rate Dependent Properties of Solder”, IEEE Transactions on Device and Materials Reliability, vol. 15, no. 2, pp. 181-190, 2015.
 de Souza Neto, E. A., Peric, D., & Owen, D. R., “Computational methods for plasticity: theory and applications”, John Wiley & Sons, 2011.
 Pope, G. G., “A discrete element method for the analysis of plane elasto-plastic stress problems”, The Aeronautical Quarterly, vol. 17, no. 1, pp. 83-104, 1966.
 Marcal, P. V., & King, I. P., “Elastic-plastic analysis of two-dimensional stress systems by the finite element method”, International Journal of Mechanical Sciences, vol. 9, no. 3, pp. 143-155, 1967.
 Yamada, Y., Yoshimura, N., & Sakurai, T., “Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method”, International Journal of Mechanical Sciences, vol. 10, no. 5, pp. 343-354, 1968.
 Oden, J. T., “Finite element applications in nonlinear structural analysis”, in Proceedings of the ASCE Symposium on Application of Finite Element Methods in Civil Engineering, Vanderbilt University, 1969, pp. 419-456.
 Yang, H. T., Saigal, S., Masud, A., & Kapania, R. K., “A survey of recent shell finite elements”, International Journal for numerical methods in engineering, vol. 47, no. 1-3, pp. 101-127, 2000.
 Wang, J., & Wagoner, R. H., “A practical large-strain solid finite element for sheet forming”, International journal for numerical methods in engineering, vol. 63, no. 4, pp. 473-501, 2005.
 Brank, B., Korelc, J., & Ibrahimbegović, A., “Nonlinear shell problem formulation accounting for through-the-thickness stretching and its finite element implementation”, Computers & structures, vol. 80, no. 9-10, pp. 699-717, 2002.
 Cardoso, R. P., & Yoon, J. W., “One point quadrature shell element with through-thickness stretch” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 9-11, pp. 1161-1199, 2005.
 Klinkel, S., Gruttmann, F., & Wagner, W., “A mixed shell formulation accounting for thickness strains and finite strain 3D material models”, International journal for numerical methods in engineering, vol. 74, no. 6, pp. 945-970, 2008.
 Legay, A., & Combescure, A., “Elastoplastic stability analysis of shells using the physically stabilized finite element SHB8PS”, International Journal for Numerical Methods in Engineering, vol. 57, no. 9, pp. 1299-1322, 2003.
 Abed-Meraim, F., and Combescure, A., “An improved assumed strain solid–shell element formulation with physical stabilization for geometric non-linear applications and elastic– plastic stability analysis”, International Journal for Numerical Methods in Engineering, vol. 80, no. 13, pp. 1640-1686, 2009.
 Schwarze, M., Vladimirov, I. N., & Reese, S., “Sheet metal forming and springback simulation by means of a new reduced integration solid-shell finite element technology”, Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 5-8, pp. 454-476, 2011.
 Wang, P., Chalal, H., & Abed-Meraim, F., “Quadratic solid–shell elements for nonlinear structural analysis and sheet metal forming simulation”, Computational Mechanics, vol. 59, no. 1, pp. 161-186, 2017.
 Mackerle, J., “Finite element linear and nonlinear, static and dynamic analysis of structural elements: a bibliography (1992-1995)”, Engineering Computations, vol. 14, no. 4, pp. 347-440, 1997.
 Mackerle, J., “Finite element linear and nonlinear, static and dynamic analysis of structural elements–an addendum–A bibliography (1996-1999)”, Engineering computations, vol. 17, no. 3, pp. 274-351, 2000.
 Mackerle, J., “Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendum: A bibliography (1999–2002)”, Engineering Computations, vol. 19, no. 5, pp. 520-594, 2002.
 May, I. M., & Al-Shaarbaf, I. A. S., “Elasto-plastic analysis of torsion using a three-dimensional finite element model”, Computers & structures, vol. 33, no. 3, pp. 667-678, 1989.
 Roehl, D., & Ramm, E., “Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain concept”, International Journal of Solids and Structures, vol. 33, no. 20-22, pp. 3215-3237, 1996.
 Liu, W. K., Guo, Y., Tang, S., & Belytschko, T., “A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis”, Computer Methods in Applied Mechanics and Engineering, vol. 154, no. 1-2, pp. 69-132, 1998.
 Cao, Y. P., Hu, N., Fukunaga, H., Lu, J., & Yao, Z. H., “A highly accurate brick element based on a three-field variational principle for elasto-plastic analysis”, Finite elements in analysis and design, vol. 39, no. 12, pp. 1155-1171, 2003.
 Artioli, E., Castellazzi, G., & Krysl, P., “Assumed strain nodally integrated hexahedral finite element formulation for elastoplastic applications”, International Journal for Numerical Methods in Engineering, vol. 99, no. 11, pp. 844-866, 2014.
 Krysl, P., & Zhu, B., “Locking-free continuum displacement finite elements with nodal integration”, International Journal for Numerical Methods in Engineering, vol. 76, no. 7, pp. 1020-1043, 2008.
 Ayad, R., “Contribution to the numerical modeling of solids and structures and the non-Newtonian fluids forming process: Application to packaging materials”, Habilitation to conduct researches, University of Reims, 2002.
 Ayad, R., Zouari, W., Meftah, K., Zineb, T. B., & Benjeddou, A., “Enrichment of linear hexahedral finite elements using rotations of a virtual space fiber”, International Journal for Numerical Methods in Engineering, vol. 95, no. 1, pp. 46-70, 2013.
 Meftah, K., Ayad, R., & Hecini, M., “A new 3D 6-node solid finite element based upon the Space Fibre Rotation concept”, European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, vol. 22, no. 1, pp. 1-29, 2013.
 Meftah, K., Sedira, L., Zouari, W., Ayad, R., & Hecini, M., “A multilayered 3D hexahedral finite element with rotational DOFs”, European Journal of Computational Mechanics, vol. 24, no. 3, pp. 107-128, 2015.
 Meftah, K., Zouari, W., Sedira, L., and Ayad, R., “Geometric non-linear hexahedral elements with rotational DOFs”, Computational Mechanics, vol. 57, no. 1, pp. 37-53, 2016.
 Simo, J. C., and Taylor, R. L., “Consistent tangent operators for rate-independent elastoplasticity”, Computer methods in applied mechanics and engineering, vol. 48, no. 1, pp. 101-118, 1985.
 Simo, J. C., and Taylor, R. L., “A return mapping algorithm for plane stress elastoplasticity”, International Journal for Numerical Methods in Engineering, vol. 22, no. 3, pp. 649-670, 1986.
 Nayak, G. C., & Zienkiewicz, O. C., “Elasto-plastic stress analysis. A generalization for various constitutive relations including strain softening”, International Journal for Numerical Methods in Engineering, vol. 5, no. 1, pp. 113-135, 1972.
 Peng, Q., and Chen, M. X., “An efficient return mapping algorithm for general isotropic elastoplasticity in principal space”, Computers & Structures, vol. 92, pp. 173-184, 2012.
 Owen, D. R. J., and Hinton, E., “Finite elements in plasticity”, Pineridge press, 1980.