An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

[1] 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, 2015.10.1109/TDMR.2015.2408327Search in Google Scholar

[2] de Souza Neto, E. A., Peric, D., & Owen, D. R., “Computational methods for plasticity: theory and applications”, John Wiley & Sons, 2011.Search in Google Scholar

[3] 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, 1966.10.1017/S0001925900003711Search in Google Scholar

[4] 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, 1967.10.1016/0020-7403(67)90004-5Search in Google Scholar

[5] 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, 1968.10.1016/0020-7403(68)90001-5Search in Google Scholar

[6] 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.Search in Google Scholar

[7] 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, 2000.10.1002/(SICI)1097-0207(20000110/30)47:1/3<101::AID-NME763>3.0.CO;2-CSearch in Google Scholar

[8] 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, 2005.10.1002/nme.1225Search in Google Scholar

[9] 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, 2002.10.1016/S0045-7949(02)00042-1Search in Google Scholar

[10] 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, 2005.10.1016/j.cma.2004.06.017Search in Google Scholar

[11] 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, 2008.10.1002/nme.2199Search in Google Scholar

[12] 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, 2003.10.1002/nme.728Search in Google Scholar

[13] 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, 2009.10.1002/nme.2676Search in Google Scholar

[14] 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, 2011.10.1016/j.cma.2010.07.020Search in Google Scholar

[15] 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, 2017.10.1007/s00466-016-1341-8Search in Google Scholar

[16] 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, 1997.10.1108/02644409710178494Search in Google Scholar

[17] 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, 2000.10.1108/02644400010324893Search in Google Scholar

[18] 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, 2002.10.1108/02644400210435843Search in Google Scholar

[19] 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, 1989.10.1016/0045-7949(89)90241-1Search in Google Scholar

[20] 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, 1996.10.1016/0020-7683(95)00246-4Search in Google Scholar

[21] 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, 1998.10.1016/S0045-7825(97)00106-0Search in Google Scholar

[22] 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, 2003.10.1016/S0168-874X(02)00162-2Search in Google Scholar

[23] 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, 2014.10.1002/nme.4723Search in Google Scholar

[24] 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, 2008.10.1002/nme.2354Search in Google Scholar

[25] 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.Search in Google Scholar

[26] 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, 2013.10.1002/nme.4500Search in Google Scholar

[27] 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, 2013.10.1080/17797179.2012.721502Search in Google Scholar

[28] 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, 2015.10.1080/17797179.2015.1089462Search in Google Scholar

[29] 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, 2016.10.1007/s00466-015-1220-8Search in Google Scholar

[30] 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, 1985.10.1016/0045-7825(85)90070-2Search in Google Scholar

[31] 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, 1986.10.1002/nme.1620220310Search in Google Scholar

[32] 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, 1972.10.1002/nme.1620050111Search in Google Scholar

[33] 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, 2012.10.1016/j.compstruc.2011.11.006Search in Google Scholar

[34] Owen, D. R. J., and Hinton, E., “Finite elements in plasticity”, Pineridge press, 1980.Search in Google Scholar