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Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 14, 1–137 (2005) Bercoff, J., Tanter, M., Fink, M.: Supersonic shear imaging: a new technique for soft tissue elasticity mapping. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 396–409 (2004) Bonet, J., Wood, R.D.: Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, Cambridge (1997) Brezzi, F., Bathe, K.J.: A discourse on the stability conditions for mixed finite element formulations. Comput. Methods Appl. Mech. Eng. 82, 27–57 (1990) Brezzi, F., Falk, R.S.: Stability of higher-order Hood–Taylor methods. SIAM J. Numer. Anal. 28, 581–590 (1991) Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer, New York (1991) Caforio, F., Imperiale, S.: A conservative penalisation strategy for the semi-implicit time discretisation of the incompressible elastodynamics equation. In: Advanced Modeling and Simulation in Engineering Sciences, vol. 5 (2018) Cervera, M., Chiumenti, M., Codina, R.: Mixed stabilized finite element methods in nonlinear solid mechanics. Part I: formulation. Comput. Methods Appl. Mech. Eng. 199, 2559–2570 (2010) Chiumenti, M., Valverde, Q., de Saracibar, C.A., Cervera, M.: A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations. Comput. Methods Appl. Mech. Eng. 191, 5253–5264 (2002) Chorin, A.J.: A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2(1), 12–26 (1967) Chorin, A.J.: Numerical solution of the Navier–Stokes equations. Math. Comput. 22, 745–762 (1968) Chung, J., Lee, J.M.: A new family of explicit time integration methods for linear and non-linear structural dynamics. Int. J. Numer. Methods Eng. 37, 3961–3976 (1994) Gao, C., Slesarenko, V., Boyce, M.C., Rudykh, S., Li, Y.: Instability-induced pattern transformation in soft metamaterial with hexagonal networks for tunable wave propagation. Sci. Rep. 8, 11834 (2018) Gil, A.J., Lee, C.H., Bonet, J., Aguirre, M.: A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible, and truly incompressible fast dynamics. Comput. Methods Appl. Mech. Eng. 276, 659–690 (2014) Guennebaud, G., Jacob, B., et al.: Eigen v3. http://eigen.tuxfamily.org (2010) Guermond, J.L., Minev, P., Shen, J.: An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng. 195, 6011–6045 (2006) Guermond, J.L., Quartapelle, L.: On the approximation of the unsteady Navier–Stokes equations by finite element projection methods. Numer. Math. 80, 207–238 (1998) Hartmann, S., Neff, P.: Polyconvexity of generalized polynomial type hyperelastic strain energy functions for near incompressibility. Int. J. Solids Struct. 40, 2767–2791 (2003) Hilber, H.M., Hughes, T.J.R.: Collocation dissipation and overshoot for time integration schemes in structural dynamics. Earthq. Eng. Struct. Dyn. 6, 99–118 (1978) Holzapfel, G.A.: Nonlinear Continuum Mechanics—A Continuum Approach for Engineering. Wiley, Hoboken (2000) Hossain, M., Steinmann, P.: More hyperelastic models for rubber-like materials: consistent tangent operator and comparative study. J. Mech. Behav. Mater. 22(1–2), 27–50 (2013) Hughes, T.J.R.: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications, Mineola (2000) Hussein, M.I., Leamy, M.J., Ruzzene, M.: Dynamics of phononic materials and structures: historical origins, recent progress, and future outlook. Appl. Mech. Rev. 66, 040802 (2014) Janz, A., Betsch, P., Franke, M.: Structure-preserving space-time discretization of a mixed formulation for quasi-incompressible large strain elasticity in principal stretches. Int. J. Numer. Methods Eng. 120(13), 1381–1410 (2019) Joly, P.: Numerical methods for elastic wave propagation. In: Kampanis, N.A., Dougalis, V.A., Ekaterinaris, J.A. (eds.) Effective Computational Methods for Wave Propagation. CRC Press, Boca Raton (2008) Kadapa, C.: Mixed Galerkin and least-squares formulations for isogeometric analysis. Ph.D. thesis, College of Engineering, Swansea University (2014) Kadapa, C.: 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. 117, 543–573 (2019) Kadapa, C.: 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. 119, 75–104 (2019) Kadapa, C., Dettmer, W.G., Perić, D.: Subdivision based mixed methods for isogeometric analysis of linear and nonlinear nearly incompressible materials. Comput. Methods Appl. Mech. Eng. 305, 241–270 (2016) Kadapa, C., Dettmer, W.G., Perić, D.: On the advantages of using the first-order generalised-alpha scheme for structural dynamic problems. Comput. Struct. 193, 226–238 (2017) Kadapa, C., Hossain, M.: A linearized consistent mixed displacement-pressure formulation for hyperelasticity. Mech. Adv. Mater. Struct. (2020). https://doi.org/10.1080/15376494.2020.1762952 Kadapa, C., Hossain, M.: A robust and computationally efficient finite element framework for coupled electromechanics. Comput. Methods Appl. Mech. Eng. 372, 113443 (2020) Kim, J., Moin, P.: Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323 (1985) Lahiri, S.K., Bonet, J., Peraire, J., Casals, L.: A variationally consistent fractional time-step integration method for incompressible and nearly incompressible Lagrangian dynamics. Int. J. Numer. Methods Eng. 63, 1371–1395 (2005) Li, G.Y., Cao, Y.: Mechanics of ultrasound elastography. Proc. R. Soc.A (2017). https://doi.org/10.1098/rspa.2016.0841 Liu, J., Marsden, A.L.: A unified continuum and variational multiscale formulation for fluids, solids, and fluid–structure interaction. Comput. Methods Appl. Mech. Eng. 337, 549–597 (2018) Liu, J., Marsden, A.L.: A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning. J. Comput. Phys. 383, 72–93 (2019) Lovrić, A., Dettmer, W.G., Kadapa, C., Perić, D.: A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping. Comput. Methods Appl. Mech. Eng. 339, 160–183 (2018) Malkus, D.S., Hughes, T.J.R.: Mixed finite element methods—reduced and selective integration techniques: a unification of concepts. Comput. Methods Appl. Mech. Eng. 15, 68–81 (1978) Maniatty, A.M., Liu, Y., Klaas, O., Shephard, M.S.: Higher order stabilized finite element method for hyperelastic finite deformation. Comput. Methods Appl. Mech. Eng. 191, 1491–1503 (2002) Marckmann, G., Verron, E.: Comparison of hyperelastic models for rubber-like materials. Rubber Chem. Technol. 79(5), 835–858 (2006) Masud, A., Truster, T.J.: A framework for residual-based stabilization of incompressible finite elasticity: stabilized formulations and methods for linear triangles and tetrahedra. Comput. Methods Appl. Mech. Eng. 267, 359–399 (2013) Masud, A., Xia, K.: A stabilized mixed finite element method for nearly incompressible elasticity. J. Appl. Mech. 72, 711–720 (2005) Mihai, L.A., Chin, L., Janmey, P.A., Goriely, A.: A comparison of hyperelastic constitutive models applicable to brain and fat tissues. J. R. Soc. Interface 12, 20150486 (2015) Olovsson, L., Simonsson, K., Unosson, M.: Selective mass scaling for explicit finite element analyses. Int. J. Numer. Methods Eng. 63, 1436–1445 (2005) Ophir, J., Alam, S.K., Garra, B., Kallel, F., Konofagou, E., Krouskop, T., Varghese, T.: Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues. Proc. Inst. Mech. Eng. Part H J. Eng. Med. 213, 203–233 (1999) Rossi, S., Abboud, N., Scovazzi, G.: Implicit finite incompressible elastodynamics with linear finite elements: a stabilized method in rate form. Comput. Methods Appl. Mech. Eng. 311, 208–249 (2016) Sarvazyan, A.P., Rudenko, O.V., Swanson, S.D., Fowlkes, J.B., Emelianov, S.Y.: Shear wave elasticity imaging: a new ultrasonic technology of medical diagnostics. Ultrasound Med. Biol. 24, 1419–1435 (1998) Scovazzi, G., Carnes, B., Zeng, X., Rossi, S.: 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. 106, 799–839 (2016) Scovazzi, G., Song, T., Zeng, X.: 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. 325, 532–576 (2017) Taylor, C., Hood, P.: A numerical solution of the Navier–Stokes equations using the finite element technique. Comput. Fluids 1, 73–100 (1973) Temam, R.: Navier–Stokes Equations: Theory and Numerical Analysis. North-Holland Publishing Company, New York (1977) Tkachuk, A., Bischoff, M.: Local and global strategies for optimal selective mass scaling. Comput. Mech. 53, 1197–1207 (2014) Wriggers, P.: Computational Contact Mechanics. Springer, Berlin (2006) Ye, W., Bel-Brunon, A., Catheline, S., Combescure, A., Rochette, M.: Simulation of nonlinear transient elastography: finite element model for the propagation of shear waves in homogeneous soft tissues. Int. J. Numer. Methods Biomed. Eng. 34, e2901 (2018). https://doi.org/10.1002/cnm.2901 Ye, W., Bel-Brunon, A., ad Catheline, S., Rochette, M., Combescure, A.: A selective mass scaling method for shear wave propagation analyses in nearly incompressible materials. Int. J. Numer. Methods Eng. 109, 155–173 (2017) Zeng, X., Scovazzi, G., Abboud, N., Colomés, O., Rossi, S.: A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements. Int. J. Numer. Methods Eng. 112, 1951–2003 (2017) Zhang, P., Parnell, W.J.: Soft phononic crystals with deformation-independent band gaps. Proc. R. Soc. A 473, 20160865 (2017) Zienkiewicz, O.C., Rojek, J., Taylor, R.L., Pastor, M.: Triangles and tetrahedra in explicit dynamic codes for solids. Int. J. Numer. Methods Eng. 43, 565–583 (1998) Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method. Volume 1: The Basics, 5th edn. Elsevier Butterworth and Heinemann, Oxford (2000) Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method for Solid and Structural Mechanics, 6th edn. Elsevier Butterworth and Heinemann, Oxford (2005)