A non-intrusive global/local approach applied to phase-field modeling of brittle fracture
Tóm tắt
Từ khóa
Tài liệu tham khảo
Francfort GA, Marigo JJ. Revisiting brittle fractures as an energy minimization problem. J Mech Phys Solids. 1998;46:1319–42.
Bourdin B, Francfort GA, Marigo JJ. Numerical experiments in revisited brittle fracture. J Mech Phys Solids. 2000;48(4):797–826.
Bourdin B. Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces Free Bound. 2007;9:411–30.
Bourdin B. The variational formulation of brittle fracture: numerical implementation and extensions. In: Combescure R, Belytschko T, editors. Proceedings of the IUTAM symposium on discretization methods for evolving discontinuities. Berlin: Springer; 2007.
Bourdin B, Francfort GA, Marigo JJ. The variational approach to fracture. J Elast. 2008;91(1–3):5–148.
Gendre L, Allix O, Gosselet P, Comte F. Non-intrusive and exact global/local techniques for structural problems with local plasticity. Comput Mech. 2009;44(2):233–45.
Amor H, Marigo JJ, Maurini C. Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids. 2009;57:1209–29.
Miehe C, Welschinger F, Hofacker M. Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Intat J Numer Methods Eng. 2010;83:1273–311.
Miehe C, Hofacker M, Welschinger F. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng. 2010;199:2765–78.
Pham K, Amor H, Marigo JJ, Maurini C. Gradient damage models and their use to approximate brittle fracture. Int J Damage Mech. 2011;20(4):618–52.
Borden MJ, Hughes TJR, Landis CM, Verhoosel CV. A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework. Comput Methods Appl Mech Eng. 2014;273:100–18.
Mesgarnejad A, Bourdin B, Khonsari MM. Validation simulations for the variational approach to fracture. Comput Methods Appl Mech Eng. 2015;290:420–37.
Kuhn C, Schlüter A, Müller R. On degradation functions in phase field fracture models. Comput Mater Sci. 2015;108:374–84.
Ambati M, Gerasimov T, De Lorenzis L. A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech. 2015;55(2):383–405.
Wu T, Carpiuc-Prisacari A, Poncelet M, De Lorenzis L. Phase-field simulation of interactive mixed-mode fracture tests on cement mortar with full-field displacement boundary conditions. Eng Fract Mech. 2017;182:658–88.
Duda FP, Ciarbonetti A, Sanchez PJ, Huespe AE. A phase-field/gradient damage model for brittle fracture in elastic-plastic solids. Int J Plast. 2015;65:269–96.
Ambati M, Gerasimov T, De Lorenzis L. Phase-field modeling of ductile fracture. Comput Mech. 2015;55(5):1017–40.
Alessi R, Marigo JJ, Vidoli S. Gradient damage models coupled with plasticity: variational formulation and main properties. Mech Mater. 2015;80(Part B):351–67.
Borden MJ, Hughes TJR, Landis CM, Anvari A, Lee IJ. A phase-field formulation for fracture in ductile materials: finite deformation balance law derivation, plastic degradation, and stress triaxiality effects. Comput Methods Appl Mech Eng. 2016;312:130–66.
Miehe C, Aldakheel F, Raina A. Phase field modeling of ductile fracture at finite strains: a variational gradient-extended plasticity-damage theory. Int J Plast. 2016;84:1–32.
Alessi R, Ambati M, Gerasimov T, Vidoli S, De Lorenzis L. Comparison of phase-field models of fracture coupled with plasticity. In: Oñate E, et al., editors. Advances in computational plasticity, computational methods in applied sciences, vol. 46. Berlin: Springer; 2018. p. 1–21. https://doi.org/10.1007/978-3-319-60885-3-1 .
Wheeler MF, Wick T, Wollner W. An augmented-Lagangrian method for the phase-field approach for pressurized fractures. Comput Methods Appl Mech Eng. 2014;271:69–85.
Mikelić A, Wheeler MF, Wick T. A quasi-static phase-field approach to pressurized fractures. Nonlinearity. 2015;28:1371–99.
León-Baldelli AA, Babadjian JF, Bourdin B, Henao D, Maurini C. A variational model for fracture and debonding of thin films under in-plane loadings. J Mech Phys Solids. 2014;70:320–48.
Amiria F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theor Appl Fract Mech. 2014;69:102–9.
Ambati M, De Lorenzis L. Phase-field modeling of brittle and ductile fracture in shells with isogeometric NURBS-based solid-shell elements. Comput Methods Appl Mech Eng. 2016;312:351–73.
Kiendl J, Ambati M, De Lorenzis L, Gomez H, Reali A. Phase-field description of brittle fracture in plates and shells. Comput Methods Appl Mech Eng. 2016;312:374–94.
Bourdin B, Marigo JJ, Maurini C, Sicsic P. Morphogenesis and propagation of complex cracks induced by thermal shocks. Phys Rev Lett. 2014;112:014301.
Miehe C, Schänzel L, Ulmer H. Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids. Comput Methods Appl Mech Eng. 2015;294:449–85.
Miehe C, Hofacker M, Schänzel L. Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids. Comput Methods Appl Mech Eng. 2015;294:486–522.
Miehe C, Mauthe S. Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media. Comput Methods Appl Mech Eng. 2016;304:619–55.
Mikelić A, Wheeler MF, Wick T. A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium. SIAM Multiscale Model Simul. 2015;13:367–98.
Mikelić A, Wheeler MF, Wick T. Phase-field modeling of a fluid-driven fracture in a poroelastic medium. Comput Geosci. 2015;19:1171–95.
Wu T, De Lorenzis L. A phase-field approach to fracture coupled with diffusion. Comput Methods Appl Mech Eng. 2016;312:196–223.
Cajuhi T, Sanavia L, De Lorenzis L. Phase-field modeling of fracture in variably saturated porous media. Comput Mech. 2017;61:299–318. https://doi.org/10.1007/s00466-017-1459-3 .
Passieux JC, Rethore J, Gravouil A, Baietto MC. Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver. Comput Mech. 2013;52(6):1381–93.
Guguin G, Allix O, Gosselet P, Guinard S. On the computation of plate assemblies using realistic 3D joint model: a non-intrusive approach. Adv Model Simul Eng Sci. 2016;3:16.
Duval M, Passieux JC, Salaun M, Guinard S. Non-intrusive coupling: recent advances and scalable nonlinear domain decomposition. Arch Comput Methods Eng. 2014;23:17–38.
Bettinotti O, Allix O, Malherbe B. A coupling strategy for adaptive local refinement in space and time with a fixed global model in explicit dynamics. Comput Mech. 2014;53(4):561–74.
Bettinotti O, Allix O, Perego U, Oancea V, Malherbe B. A fast weakly intrusive multiscale method in explicit dynamics. Int J Numer Methods Eng. 2014;100(8):577–95.
Bettinotti O, Allix O, Perego U, Oancea V, Malherbe B. Simulation of delamination under impact using a global local method in explicit dynamics. Finite Elem Anal Des. 2017;125(8):1–13.
Plews J, Duarte CA, Eason T. An improved non-intrusive global-local approach for sharp thermal gradients in a standard FEA platform. Int J Numer Methods Eng. 2011;91(4):426–49.
Kim J, Duarte CA. A new generalized finite element method for two-scale simulations of propagating cohesive fractures in 3-D. Int J Numer Methods Eng. 2015;103(13):113–1172.
Heister T, Wheeler MF, Wick T. A primal-dual active active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach. Comput Methods Appl Mech Eng. 2015;290:466–95.
Gerasimov T, De Lorenzis L. A line search assisted monolithic approach for phase-field computing of brittle fracture. Comput Methods Appl Mech Eng. 2016;312:276–303.
Wick T. Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation. Comput Methods Appl Mech Eng. 2017;325:577–611.
Farrell PE, Maurini C. Linear and nonlinear solvers for variational phase-field models of brittle fracture. Int J Numer Methods Eng. 2017;109:648–67.
Kinderlehrer D, Stampacchia G. An introduction to variational inequalities and their applications. New York: Academic Press; 1980.
Glowinski R, Lions JL, Trémolières R. Numerical analysis of variational inequalities. Amsterdam: Elsevier; 1981.
Liu YJ, Sun Q, Fan XL. A non-intrusive global/local algorithm with non-matching interface: derivation and numerical validation. Comput Methods Appl Mech Eng. 2014;277:81–103.
Jara-Almonte CC, Knight CE. The specified boundary stiffness and force (SBSF) method for finite element subregion analysis. Int J Numer Methods Eng. 1988;26:1567–78.
Farhat C, Roux FX. A method of finite element tearing and interconnecting and its parallel solution algorithm. Int J Numer Methods Eng. 1991;32:1205–27.
Park KC, Felippa CA. A variational principle for the formulation of partitioned structural systems. Int J Numer Methods Eng. 2000;47:395–418.
Park KC, Felippa CA, Rebel G. A simple algorithm for localized construction of non-matching structural interfaces. Int J Numer Methods Eng. 2002;53:2117–42.
Song YU, Youn SK, Park KC. A gap element for treating non-matching discrete interfaces. Comput Mech. 2015;56:551–63.
Wohlmuth BI. A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J Numer Anal. 2000;38:989–1012.
Wohlmuth BI. A comparison of dual Lagrange multiplier spaces for mortar finite element discretizations. ESAIM Math Model Numer Anal. 2003;36:995–1012.
Küttler U, Wall WA. Fixed-point fluid-structure interaction solvers with dynamic relaxation. Comput Mech. 2008;43:61–72.
Erbts P, Düster A. Accelerated staggered coupling schemes for problems of thermoelasticity at finite strains. Comput Math Appl. 2012;64:2408–30.