A multiscale overlapped coupling formulation for large-deformation strain localization

Abellan Marie-Angèle, de Borst René (2006) Wave propagation and localisation in a softening two-phase medium. Comput Methods Appl Mech Eng 195(37):5011–5019 Aubertin P, Réthoré J, de Borst R (2009) Energy conservation of atomistic/continuum coupling. Int J Numer Methods Eng 78(11):1365–1386 Babus̆ka I (1973) The finite element method with lagrangian multipliers. Numerische Mathematik 20:179–192. ISSN 0029–599X Badia S, Parks M, Bochev P, Gunzburger M, Lehoucq R (2008) On atomistic-to-continuum coupling by blending. Multiscale Model Simul 7(1):381–406 Bathe K-J (2001) The inf-sup condition and its evaluation for mixed finite element methods. Comput Struct 79(2):243–252. ISSN 0045–7949 Bauman PT, Ben Dhia H, Elkhodja N, Oden J, Prudhomme S (2008) On the application of the arlequin method to the coupling of particle and continuum models. Comput Mech 42:511–530 Bauman PT, Oden JT, Prudhomme S (2009) Adaptive multiscale modeling of polymeric materials with arlequin coupling and goals algorithms. Comput Methods Appl Mech Eng 198(5):799– 818 Bažant ZP, Jirásek M (2002) Nonlocal integral formulations of plasticity and damage: survey of progress. J Eng Mech 128(11):1119–1149 Belytschko T, Fish J, Engelmann BE (1988) A finite element with embedded localization zones. Comput Methods Appl Mech Eng 70(1):59–89 Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, New York Belytschko T, Loehnert S, Song J-H (2008) Multiscale aggregating discontinuities: A method for circumventing loss of material stability. Int J Numer Methods Eng 73(6):869–894 Ben Dhia H (1998) Multiscale mechanical problems: the arlequin method. Compt Rendus de Acad des Sci Ser IIB 326(12):899– 904 Ben Dhia H (2008) Further insights by theoretical investigations of the multiscale arlequin metho. Int J Multiscale Comput Eng 6(3):215–232 Ben Dhia H, Rateau G (2005) The arlequin method as a flexible engineering design tool. Int J Numer Methods Eng 62(11):1442–1462 Borja RI (2000) A finite element model for strain localization analysis of strongly discontinuous fields based on standard galerkin approximation. Comput Methods Appl Mech Eng 190(11–12):1529–1549 Borja RI (2002) Finite element simulation of strain localization with large deformation: capturing strong discontinuity using a petrov-galerkin multiscale formulation. Comput Methods Appl Mech Eng 191(27–28):2949–2978 Brezzi F, Marini LD (2005) The three-field formulation for elasticity problems. GAMM Mitteilungen 28:124–153 Brezzi F, Douglas J, Marini LD (1985) Two families of mixed finite elements for second order elliptic problems. Numerische Mathematik 47:217–235 Chapelle D, Bathe KJ (1993) The inf-sup test. Comput Struct 47(4–5):537–545 Chen Yi-Chao (1991) On strong ellipticity and the legendre-hadamard condition. Arch Ration Mech Anal 113(2):165–175 Feyel F(2003) A multilevel finite element method (fe2) to describe the response of highly non-linear structures using generalized continua. Comput Methods Appl Mech Eng 192(28–30):3233–3244. Fleck NA, Hutchson JW (2001) A reformulation of strain gradient plasticity. J Mech Phys Solids 49(10):2245–2271 Guidault PA, Belytschko T (2007) On the l2 and the h1 couplings for an overlapping domain decomposition method using lagrange multipliers. Int J Numer Methods Eng 70(3):322–350 Han F, Lubineau G (2012) Coupling of nonlocal and local continuum models by the Arlequin approach. Int J Numer Methods Eng 89(6):671–685 Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, West Sussex Kouznetsova VG, Geers MGD, Brekelmans WAM (2004) Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. Comput Methods Appl Mech Eng 193(48–51):5525–5550 McAuliffe C, Waisman H (2013) Mesh insensitive formulation for initiation and growth of shear bands using mixed finite elements. Comput Mech 2:1–17 Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150 Mota A, Foulk JW, Ostien JT (2013) Variational nonlocal regularization in finite-deformation inelasticity. In: Proceedings of the 12th U.S. National Congress on Computational Mechanics, Raleigh, NC Prudhomme S, Ben Dhia H, Bauman PT, Elkhodja N, Oden JT (2008) Computational analysis of modeling error for the coupling of particle and continuum models by the arlequin method. Comput Methods Appl Mech Eng 197(41–42):3399–3409 Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23(6):371–394 Sun W, Andrade JE, Rudnicki JW (2011) Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability. Int J Numer Methods Eng 88(12):1260–1279 Sun W, Chen Q, Ostien JT (2013a) Modeling hydro-mechanical responses of strip and circular footings on saturated collapsible geomaterials. Acta Geotech 5:189–198. doi:10.1007/s11440-013-0276-x Sun W, Ostien JT, Salinger AG (2013b) A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain. Int J Numer Anal Methods Geomech 37(16):2755–2788 Toh K-C, Phoon K-K, Chan S-H (2004) Block preconditioners for symmetric indefinite linear systems. Int J N Methods Eng 60(8):1361–1381 White JA, Borja RI (2011) Block-preconditioned newton-krylov solvers for fully coupled flow and geomechanics. Comput Geosci 15:647–659. White JA, Borja RI, Fredrich JT (2006) Calculating the effective permeability of sandstone with multiscale lattice boltzmann/finite element simulations. Acta Geotechn 1:195–209 Yang Q, Mota A, Ortiz M (2005) A class of variational strain-localization finite elements. Int J Numer Methods Eng 62(8):1013–1037 Zhang HW, Schrefler BA, Wriggers P (2003) Interaction between different internal length scales for strain localisation analysis of single phase materials. Comput Mech 30(3):212–219