References
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, USA, 1991.
- O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method for Solid and Structural Mechanics, 6th ed., Elsevier Butterworth and Heinemann, Oxford, England, 2005.
- C. Kadapa, Mixed Galerkin and least-squares formulations for isogeometric analysis, PhD thesis, College of Engineering, Swansea University, 2014.
- C. Kadapa, W.G. Dettmer, and D. Perić, Subdivision based mixed methods for isogeometric analysis of linear and nonlinear nearly incompressible materials, Comput. Methods Appl. Mech. Eng., vol. 305, pp. 241–270, 2016. DOI: https://doi.org/10.1016/j.cma.2016.03.013.
- C. Kadapa, Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Extension to nearly incompressible implicit and explicit elastodynamics in finite strains, Int. J. Numer. Methods Eng., vol. 119, no. 2, pp. 75–104, 2019. DOI: https://doi.org/10.1002/nme.6042.
- E.A. de Souza Neto, D. Perić, M. Dutko, and D.R.J. Owen, Design of simple low order finite elements for large strain analysis of nearly incompressible solids, Int. J. Solids Struct., vol. 33, no. 20–22, pp. 3277–3296, 1996. DOI: https://doi.org/10.1016/0020-7683(95)00259-6.
- E.A. de Souza Neto, F.M. Andrade Pires, and D.R.J. Owen, F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: Formulation and benchmarking, Int. J. Numer. Meth. Eng., vol. 62, no. 3, pp. 353–383, 2005. DOI: https://doi.org/10.1002/nme.1187.
- J.C. Simo and T.J.R. Hughes, On the variational foundations of assumed strain methods, J. Appl. Mech., vol. 53, no. 1, pp. 51–54, 1986. DOI: https://doi.org/10.1115/1.3171737.
- J. Bonet and A.J. Burton, A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications, Commun. Numer. Methods Eng., vol. 14, no. 5, pp. 437–449, 1998. DOI: https://doi.org/10.1002/(SICI)1099-0887(199805)14:5<437::AID-CNM162>3.0.CO;2-W.
- F.M.A. Pires, E.A. de Souza Neto, and J.L. de la Cuesta Padilla. An, assessment of the average nodal volume formulation for the analysis of nearly incompressible solids under finite strains, Commun. Numer. Methods Eng., vol. 20, no. 7, pp. 569–583, 2004. DOI: https://doi.org/10.1002/cnm.697.
- D.P. Flanagan and T. Belytschko, A uniform strain hexahedron and quadrilateral with orthogonal hourglass control, Int. J. Numer. Methods Eng., vol. 17, no. 5, pp. 679–706, 1981. DOI: https://doi.org/10.1002/nme.1620170504.
- T. Belytschko, J.S. Ong, W.K. Liu, and J.M. Kennedy, Hourglass control in linear and nonlinear problems, Comput. Methods Appl. Mech. Eng., vol. 43, pp. 251–276, 1984. DOI: https://doi.org/10.1016/0045-7825(84)90067-7.
- P. Wriggers and J. Korelc, On enhanced strain methods for small and finite deformations, Comput. Mech., vol. 18, no. 6, pp. 413–428, 1996. DOI: https://doi.org/10.1007/s004660050159.
- J. Korelc, U. Šolinc, and P. Wriggers, An improved EAS brick element for finite deformation, Comput. Mech., vol. 46, no. 4, pp. 641–659, 2010. DOI: https://doi.org/10.1007/s00466-010-0506-0.
- J.S. Chen, W. Han, C.T. Wu, and W. Duan, On the perturbed Lagrangian formulation for nearly incompressible and incompressible hyperelasticity, Comput. Methods Appl. Mech. Eng., vol. 142, no. 3–4, pp. 335–351, 1997. DOI: https://doi.org/10.1016/S0045-7825(96)01139-5.
- J.C. Simo, R.L. Taylor, and K.S. Pister, Variational and projection methods for the volume constraint in finite deformation elasto-plasticity, Comput. Methods Appl. Mech. Eng., vol. 51, no. 1–3, pp. 177–208, 1985. DOI: https://doi.org/10.1016/0045-7825(85)90033-7.
- M. Chiumenti, Q. Valverde, C.A. de Saracibar, and M. Cervera, A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations, Comput. Methods Appl. Mech. Eng., vol. 191, no. 46, pp. 5253–5264, 2002. DOI: https://doi.org/10.1016/S0045-7825(02)00443-7.
- M. Cervera, M. Chiumenti, and R. Codina, Mixed stabilized finite element methods in nonlinear solid mechanics. Part I: Formulation, Comput. Methods Appl. Mech. Eng., vol. 199, no. 37–40, pp. 2559–2570, 2010. DOI: https://doi.org/10.1016/j.cma.2010.04.006.
- M. Cervera, M. Chiumenti, and R. Codina, Mixed stabilized finite element methods in nonlinear solid mechanics. Part II: Strain localization, Comput. Methods Appl. Mech. Eng., vol. 199, no. 37–40, pp. 2571–2589, 2010. DOI: https://doi.org/10.1016/j.cma.2010.04.005.
- G. Scovazzi, B. Carnes, X. Zeng, and S. Rossi, A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach, Int. J. Numer. Methods Eng., vol. 106, no. 10, pp. 799–839, 2016. DOI: https://doi.org/10.1002/nme.5138.
- G. Scovazzi, T. Song, and X. Zeng, A velocity/stress mixed stabilized nodal finite element for elastodynamics: Analysis and computations with strongly and weakly enforced boundary conditions, Comput. Methods Appl. Mech. Eng., vol. 325, pp. 532–576, 2017. DOI: https://doi.org/10.1016/j.cma.2017.07.018.
- N. Abboud and G. Scovazzi, Elastoplasticity with linear tetrahedral elements: A variational multiscale method, Int. J. Numer. Methods Eng., vol. 115, no. 8, pp. 913–955, 2018. DOI: https://doi.org/10.1002/nme.5831.
- L.P. Franca, T.J.R. Hughes, A.F.D. Loula, and I. Miranda, A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element formulation, Numer. Math., vol. 53, no. 1–2, pp. 123–141, 1988. DOI: https://doi.org/10.1007/BF01395881.
- O. Klaas, A. Maniatty, and M.S. Shephard, A stabilized mixed finite element method for finite elasticity. Formulation for linear displacement and pressure interpolation, Comput. Methods Appl. Mech. Eng., vol. 180, no. 1–2, pp. 65–79, 1999. DOI: https://doi.org/10.1016/S0045-7825(99)00059-6.
- A. Masud and K. Xia, A stabilized mixed finite element method for nearly incompressible elasticity, J. Appl. Mech., vol. 72, no. 5, pp. 711–720, 2005. DOI: https://doi.org/10.1115/1.1985433.
- A. Pakravan and P. Krysl, Mean-strain 10-node tetrahedron with energy-sampling stabilization for nonlinear deformation, Int. J. Numer. Methods Eng., vol. 111, no. 7, pp. 603–623, 2017. DOI: https://doi.org/10.1002/nme.5473.
- A. Bijalwan and B.P. Patel, A new 3D finite element for the finite deformation of nearly incompressible hyperelastic solids, IJMSI, vol. 13, no. 1/2/3, pp. 67–80, 2019. DOI: https://doi.org/10.1504/IJMSI.2019.10022238.
- C. Kadapa, W.G. Dettmer, and D. Perić, NURBS based least-squares finite element methods for fluid and solid mechanics, Int. J. Numer. Methods Eng., vol. 101, no. 7, pp. 521–539, 2015. DOI: https://doi.org/10.1002/nme.4765.
- T.A. Manteuffel, S.F. McCormick, J.G. Schmidt, and C.R. Westphal, First-order system least squares for geometrically nonlinear elasticity, SIAM J. Numer. Anal., vol. 44, no. 5, pp. 2057–2081, 2006. DOI: https://doi.org/10.1137/050628027.
- M. Majidi and G. Starke, Least-squares Galerkin methods for parabolic problems I: Semi-discretization in time, SIAM J. Numer. Anal., vol. 39, no. 4, pp. 1302–1323, 2001. DOI: https://doi.org/10.1137/S0036142900370125.
- M. Majidi and G. Starke, Least-squares Galerkin methods for parabolic problems II: The fully discrete case and adaptive algorithms, SIAM J. Numer. Anal., vol. 39, no. 5, pp. 1648–1666, 2002. DOI: https://doi.org/10.1137/S0036142900379461.
- T. Elguedj, Y. Bazilevs, V.M. Calo, and T.J.R. Hughes, B̄ and F̄ projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements, Comput. Methods Appl. Mech. Eng., vol. 197, no. 33–40, pp. 2732–2762, 2008. DOI: https://doi.org/10.1016/j.cma.2008.01.012.
- Z. Lei, E. Rougier, E.E. Knight, L. Frash, J.W. Carey, and H. Viswanathan, A non-locking composite tetrahedron element for the combined finite discrete element method, Eng. Comput., vol. 33, no. 7, pp. 1929–1956, 2016. DOI: https://doi.org/10.1108/EC-09-2015-0268.
- M. Mehnert, J.P. Pelteret, and P. Steinmann, Numerical modelling of nonlinear thermo-electro-elasticity, Math. Mech. Solids., vol. 22, no. 11, pp. 2196–2213, 2017. DOI: https://doi.org/10.1177/1081286517729867.
- S. Wulfinghoff, H.R. Bayat, A. Alipour, and S. Reese, A low-order locking-free hybrid discontinuous Galerkin element formulation for large deformations, Comput. Methods Appl. Mech. Eng., vol. 323, pp. 353–372, 2017. DOI: https://doi.org/10.1016/j.cma.2017.05.018.
- P. Wriggers, B.D. Reddy, W. Rust, and B. Hudobivnik, Efficient virtual element formulations for compressible and incompressible finite deformations, Comput. Mech., vol. 60, no. 2, pp. 253–268, 2017. DOI: https://doi.org/10.1007/s00466-017-1405-4.
- C. Jiang, X. Han, Z.-Q. Zhang, G.R. Liu, and G.-J. Gao, A locking-free face-based S-FEM via averaging nodal pressure using 4-nodes tetrahedrons for 3D explicit dynamics and quasi-statics, Int. J. Comput. Methods., vol. 15, no. 06, pp. 1850043, 2018. DOI: https://doi.org/10.1142/S0219876218500433.
- H.R. Bayat, S. Wulfinghoff, S. Kastian, and S. Reese, On the use of reduced integration in combination with discontinuous Galerkin discretization: Application to volumetric and shear locking problems, Adv. Model. Simul. Eng. Sci., vol. 5, pp. 10, 2018.
- H.R. Bayat, J. Krämer, L. Wunderlich, S. Wulfinghoff, S. Reese, B. Wohlmuth, and C. Wieners, Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics, Comput. Mech., vol. 62, no. 6, pp. 1413–1427, 2018. DOI: https://doi.org/10.1007/s00466-018-1571-z.
- W.M. Coombs, T.J. Charlton, M. Cortis, and C.E. Augarde, Overcoming volumetric locking in material point methods, Comput. Methods Appl. Mech. Eng., vol. 333, pp. 1–21, 2018. DOI: https://doi.org/10.1016/j.cma.2018.01.010.
- R. Sevilla, M. Giacomini, A. Karkoulias, and A. Huerta, A superconvergent hybridisable discontinuous Galerkin method for linear elasticity, Int. J. Numer. Methods Eng., vol. 116, no. 2, pp. 91–116, 2018. DOI: https://doi.org/10.1002/nme.5916.
- A. Taghipour, J. Parvizian, S. Heinze, and A. Düster, The finite cell method for nearly incompressible finite strain plasticity problems with complex geometries, Comput. Math. Appl., vol. 75, no. 9, pp. 3298–3316, 2018. DOI: https://doi.org/10.1016/j.camwa.2018.01.048.
- G. Moutsanidis, J.J. Koester, M.R. Tupek, J.-S. Chen, and Y. Bazilevs, Treatment of near-incompressibility in meshfree and immersed-particle methods, Comput. Part. Mech., vol. 7, no. 2, pp. 309–319, 2020. pages DOI: https://doi.org/10.1007/s40571-019-00238-z.
- H. Dal, A quasi incompressible and quasi inextensible element formulation for transversely isotropic materials, Int. J. Numer. Methods Eng., vol. 117, no. 1, pp. 118–140, 2019. DOI: https://doi.org/10.1002/nme.5950.
- Y. Onishi, R. Iida, and K. Amaya, F-bar aided edge-based smoothed finite element method using tetrahedral elements for finite deformation analysis of nearly incompressible solids, Int. J. Numer. Methods Eng., vol. 109, no. 11, pp. 1582–1606, 2017. DOI: https://doi.org/10.1002/nme.5337.
- Y. Onishi, F-bar aided edge-based smoothed finite element method with 4-node tetrahedral elements for static large deformation elastoplastic problems, Int. J. Comput. Methods, vol. 16, no. 05, pp. 1840010, 2019. DOI: https://doi.org/10.1142/S0219876218400108.
- R. Sevilla, M. Giacomini, and A. Huerta, A locking-free face-centred finite volume (FCFV) method for linear elastostatics, Comput. Struct., vol. 212, pp. 43–57, 2019. DOI: https://doi.org/10.1016/j.compstruc.2018.10.015.
- S.J. Connolly, D. Mackenzie, and Y. Gorash, Isotropic hyperelasticity in principal stretches: Explicit elasticity tensors and numerical implementation, Comput. Mech., vol. 64, no. 5, pp. 1273–1288, 2019. DOI: https://doi.org/10.1007/s00466-019-01707-1.
- S.J. Connolly, D. Mackenzie, and Y. Gorash, Higher-order and higher floating-point precision numerical approximations of finite strain elasticity moduli, Int. J. Numer. Methods Eng., vol. 120, no. 10, pp. 1184–1201, 2019. DOI: https://doi.org/10.1002/nme.6176.
- N. Viebahn, J. Schröder, and P. Wriggers, An extension of assumed stress finite elements to a general hyperelastic framework, Adv. Model. Simul. Eng. Sci., vol. 6, no. 1, pp. 9, 2019. DOI: https://doi.org/10.1186/s40323-019-0133-z.
- A. Rajagopal, M. Kraus, and P. Steinmann, Hyperelastic analysis based on a polygonal finite element method, Mech. Adv. Mater. Struct., vol. 25, no. 11, pp. 930–942, 2018. DOI: https://doi.org/10.1080/15376494.2017.1329463.
- J. Bonet and R.D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge, UK, 1997.
- J. Schröder, N. Viebahn, P. Wriggers, F. Auricchio, and K. Steeger, On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations, Comput. Mech., vol. 60, no. 3, pp. 479–492, 2017. DOI: https://doi.org/10.1007/s00466-017-1415-2.
- R. Ortigosa, A.J. Gil, and C.H. Lee, A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies, Comput. Methods Appl. Mech. Eng., vol. 310, pp. 297–334, 2016. DOI: https://doi.org/10.1016/j.cma.2016.06.025.
- D. Bishara and M. Jabareen, A reduced mixed finite-element formulation for modeling the viscoelastic response of electro-active polymers at finite deformation, Math. Mech. Solids, vol. 24, no. 5, pp. 1578–1610, 2019. DOI: https://doi.org/10.1177/1081286518802419.
- H. S. Park, Z. Suo, J. Zhou, and P. A. Klein, A dynamic finite element method for inhomogeneous deformation and electromechanical instability of dielectric elastomer transducers, Int. J. Solids Struct., vol. 49, no. 15–16, pp. 2187–2194, 2012. DOI: https://doi.org/10.1016/j.ijsolstr.2012.04.031.
- H.S. Park and T.D. Nguyen, Viscoelastic effects on electromechanical instabilities in dielectric elastomers, Soft Matter., vol. 9, no. 4, pp. 1031–1042, 2013. DOI: https://doi.org/10.1039/C2SM27375F.
- S. Seifi, K.C. Park, and H.S. Park, A staggered explicit-implicit finite element formulation for electroactive polymers, Comput. Methods Appl. Mech. Eng., vol. 337, pp. 150–164, 2018. DOI: https://doi.org/10.1016/j.cma.2018.03.028.
- A. Ask, A. Menzel, and M. Ristinmaa, Phenomenological modeling of viscous electrostrictive polymers, Int. J. NonLin Mech., vol. 47, no. 2, pp. 156–165, 2012. DOI: https://doi.org/10.1016/j.ijnonlinmec.2011.03.020.
- J. P. Pelteret, D. Davydov, A. McBride, D.K. Vu, and P. Steinmann, Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space, Int. J. Numer. Methods Eng., vol. 108, no. 11, pp. 1307–1342, 2016. DOI: https://doi.org/10.1002/nme.5254.
- M. Jabareen, On the modeling of electromechanical coupling in electro-active polymers using the mixed finite element formulation, Proc. IUTAM, vol. 12, pp. 105–115, 2015. DOI: https://doi.org/10.1016/j.piutam.2014.12.012.
- M. Mehnert, M. Hossain, and P. Steinmann, Numerical modeling of thermo-electro-viscoelasticity with field-dependent material parameters, Int. J. NonLin Mech., vol. 106, pp. 13–24, 2018. DOI: https://doi.org/10.1016/j.ijnonlinmec.2018.08.016.
- M. Mehnert, M. Hossain, and P. Steinmann, Experimental and numerical investigations of the electro-viscoelastic behavior of VHB 4905, Eur. J. Mech. A/Solids., vol. 77, pp. 103797, 2019. DOI: https://doi.org/10.1016/j.euromechsol.2019.103797.
- P. Steinmann, M. Hossain, and G. Possart, Hyperelastic models for rubber-like materials: Consistent tangent operators and suitability of Treloar’s data, Arch. Appl. Mech., vol. 82, no. 9, pp. 1183–1217, 2012. DOI: https://doi.org/10.1007/s00419-012-0610-z.
- M. Hossain and P. Steinmann, More hyperelastic models for rubber-like materials: Consistent tangent operator and comparative study, J. Mech. Behav. Mater., vol. 22, no. 1–2, pp. 27–50, 2013. DOI: https://doi.org/10.1515/jmbm-2012-0007.
- M. Hossain, N. Kabir, and A.F.M.S. Amin, Eight-chain and full-network models and their modified versions for rubber hyperelasticity: A comparative study, J. Mech. Behav. Mater., vol. 24, no. 1–2, pp. 11–24, 2015. DOI: https://doi.org/10.1515/jmbm-2015-0002.
- G. Marckmann and E. Verron, Comparison of hyperelastic models for rubber-like materials, Rubber Chem. Technol. Am. Chem. Soc., vol. 79, no. 5, pp. 835–858, 2006. DOI: https://doi.org/10.5254/1.3547969.
- S. Doll and K. Schweizerhof, On the development of volumetric strain energy functions, J. Appl. Mech., vol. 67, no. 1, pp. 17–21, 2000. DOI: https://doi.org/10.1115/1.321146.
- K.M. Moerman, B. Fereidoonnezhad, and P. McGarry, Novel Hyperelastic Models for Large Volumetric Deformations. Available from https://engrxiv.org/cfxdr, 2019
- M. Bercovier, Perturbation of mixed variational problems, RAIRO. Anal. Numér., vol. 12, no. 3, pp. 211–236, 1978. DOI: https://doi.org/10.1051/m2an/1978120302111.
- P. Wriggers, J. Schröder, and F. Auricchio, Finite element formulations for large strain anisotropic material with inextensible fibers, Adv. Model. Simul. Eng. Sci., vol. 3, no. 1, pp. 25, 2016. DOI: https://doi.org/10.1186/s40323-016-0079-3.
- O.C. Zienkiewicz, R.L. Taylor, and J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th ed., Elsevier Butterworth and Heinemann, Oxford, UK, 2005.
- J.C. Simo, P. Wriggers, and R.L. Taylor, A perturbed Lagrangian formulation for the finite element solution of contact problems, Comput. Methods Appl. Mech. Eng., vol. 50, no. 2, pp. 163–180, 1985. DOI: https://doi.org/10.1016/0045-7825(85)90088-X.
- M. Tur, J. Albelda, J.M. Navarro-Jimenez, and J. Rodenas, A modified perturbed Lagrangian formulation for contact problems, Comput. Mech., vol. 55, no. 4, pp. 737–754, 2015. DOI: https://doi.org/10.1007/s00466-015-1133-6.
- C. Kadapa, Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics, Int. J. Numer. Methods Eng., vol. 117, no. 5, pp. 543–573, 2019. DOI: https://doi.org/10.1002/nme.5967.
- I.S. Duff, A.M. Erisman, and J.K. Reid, Direct Methods for Sparse Matrices, 2d ed., Oxford Science Publications, Oxford, UK, 2017.
- N.I. Gould, J.A. Scott, and Y. Hu, A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations, ACM Trans. Math. Softw., vol. 33, no. 2, pp. 10, 2007. DOI: https://doi.org/10.1145/1236463.1236465.
- J. Dongarra, I.S. Duff, D.C. Sorensen, and H.A. van der Vorst, Numerical Linear Algebra for High-Performance Computers, SIAM, Philadelphia, USA, 1998.
- S. Pissanetzky, Sparse Matrix Technology, Academic Press, Florida, USA, 1984.
- Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., Vol. 82. SIAM, Philadelphia, USA, 2003.
- R. Barrett, M.W. Berry, T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, USA, 1994.
- N.M. Nachtigal, S.C. Reddy, and L.N. Trefethen, How fast are nonsymmetric matrix iterations? SIAM J. Matrix Anal. Appl., vol. 13, no. 3, pp. 778–795, 1992. DOI: https://doi.org/10.1137/0613049.
- D.S. Watkins, Fundamentals of Matrix Computations, 2nd ed., Wiley, New York, 2002.
- Abaqus theory manual. Available from https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/stm/default.htm?startat=ch03s02ath61.html.
- S. Hartmann and P. Neff, Polyconvexity of generalized polynomial type hyperelastic strain energy functions for near incompressibility, Int. J. Solids Struct., vol. 40, no. 11, pp. 2767–2791, 2003. DOI: https://doi.org/10.1016/S0020-7683(03)00086-6.
- Ansys Inc. ANSYS Theory Manual, 2000.
- J.C. Simo and R.L. Taylor, Quasi-incompressible finite elasticity in principal stretches. continuum basis and numerical algorithms, Comput. Methods Appl. Mech. Eng., vol. 85, no. 3, pp. 273–310, 1991. DOI: https://doi.org/10.1016/0045-7825(91)90100-K.
- J.C. Simo and R.L. Taylor, Penalty function formulations for incompressible nonlinear elastostatics, Comput. Methods Appl. Mech. Eng., vol. 35, no. 1, pp. 107–118, 1982. DOI: https://doi.org/10.1016/0045-7825(82)90035-4.
- C.H. Liu, G. Hofstetter, and H.A. Mang, 3D finite element analysis of rubber-like materials at finite strains, Eng. Comput., vol. 11, no. 2, pp. 111–128, 1994. DOI: https://doi.org/10.1108/02644409410799236.
- C. Meihe, Aspects of the formulation and finite element implementation of large strain isotropic elasticity, Int. J. Numer. Methods Eng., vol. 37, pp. 2004–1994, 1981.
- S. Reese, M. Kussner, and B.D. Reddy, A new stabilization technique for finite elements in non-linear elasticity, Int. J. Numer. Methods Eng., vol. 44, no. 11, pp. 1617–1652, 1999. DOI: https://doi.org/10.1002/(SICI)1097-0207(19990420)44:11<1617::AID-NME557>3.0.CO;2-X.
- P. Krysl, Mean-strain eight-node hexahedron with optimized energy-sampling stabilization for large-strain deformation, Int. J. Numer. Methods Eng., vol. 103, no. 9, pp. 650–670, 2015. DOI: https://doi.org/10.1002/nme.4907.