Application of an enriched FEM technique in thermo-mechanical contact problems

Computational Mechanics - Tập 62 - Trang 1127-1154 - 2018
A. R. Khoei1, B. Bahmani1
1Department of Civil Engineering, Center of Excellence in Structures and Earthquake Engineering, Sharif University of Technology, Tehran, Iran

Tóm tắt

In this paper, an enriched FEM technique is employed for thermo-mechanical contact problem based on the extended finite element method. A fully coupled thermo-mechanical contact formulation is presented in the framework of X-FEM technique that takes into account the deformable continuum mechanics and the transient heat transfer analysis. The Coulomb frictional law is applied for the mechanical contact problem and a pressure dependent thermal contact model is employed through an explicit formulation in the weak form of X-FEM method. The equilibrium equations are discretized by the Newmark time splitting method and the final set of non-linear equations are solved based on the Newton–Raphson method using a staggered algorithm. Finally, in order to illustrate the capability of the proposed computational model several numerical examples are solved and the results are compared with those reported in literature.

Tài liệu tham khảo

Khoei AR, Shamloo A, Azami AR (2006) Extended finite element method in plasticity forming of powder compaction with contact friction. Int J Solids Struct 43:5421–5448 Khoei AR, Mohammadnejad T (2011) Numerical modeling of multiphase fluid flow in deforming porous media: a comparison between two- and three-phase models for seismic analysis of earth and rockfill dams. Comp Geotech 38:142–166 Khoei AR, Hirmand M, Vahab M, Bazargan M (2015) An enriched FEM technique for modeling hydraulically-driven cohesive fracture propagation in impermeable media with frictional natural faults; Numerical and experimental investigations. Int J Numer Methods Eng 104:439–468 Khoei AR, Vahab M, Hirmand M (2016) Modeling the interaction between fluid-driven fracture and natural fault using an enriched-FEM technique. Int J Fract 197:1–24 Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45:601–620 Belytschko T, Moës N, Usui S, Parimi C (2001) Arbitrary discontinuities in finite elements. Int J Numer Methods Eng 50:993–1013 Chessa J, Belytschko T (2003) An extended finite element method for two-phase fluids. J Appl Mech 70:10–17 Khoei AR, Haghighat E (2011) Extended finite element modeling of deformable porous media with arbitrary interfaces. Appl Math Model 35:5426–5441 Dolbow JE, Moës N, Belytschko T (2001) An extended finite element method for modeling crack growth with frictional contact. Comput Methods Appl Mech Eng 190:6825–6846 Khoei AR, Nikbakht M (2007) An enriched finite element algorithm for numerical computation of contact friction problems. Int J Mech Sci 49:183–199 Liu F, Borja RI (2008) A contact algorithm for frictional crack propagation with the extended finite element method. Int J Numer Meth Eng 76:1489–1512 Khoei AR, Vahab M (2014) A numerical contact algorithm in saturated porous media with the extended finite element method. Comput Mech 54:1089–1110 Béchet E, Moës N, Wohlmuth B (2009) A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. Int J Numer Methods Eng 78:931–954 Hautefeuille M, Annavarapu C, Dolbow JE (2012) Robust imposition of Dirichlet boundary conditions on embedded surfaces. Int J Numer Methods Eng 90:40–64 Annavarapu C, Hautefeuille M, Dolbow JE (2014) A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: single interface. Comp Methods Appl Mech Eng 268:417–436 Hirmand M, Vahab M, Khoei AR (2015) An augmented Lagrangian contact formulation for frictional discontinuities with the extended finite element method. Finite Elem Anal Des 107:28–43 Duflot M (2008) The extended finite element method in thermoelastic fracture mechanics. Int J Numer Methods Eng 74:827–847 Zamani A, Eslami MR (2010) Implementation of the extended finite element method for dynamic thermoelastic fracture initiation. Int J Solids Struct 47:1392–1404 Khoei AR, Moallemi S, Haghighat E (2012) Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique. Eng Fract Mech 96:701–723 Shao Q, Bouhala L, Younes A, Núñez P, Makradi A, Belouettar S (2014) An XFEM model for cracked porous media: effects of fluid flow and heat transfer. Int J Fract 185:155–169 Gill P, Davey K (2014) A thermomechanical finite element tool for Leak-before-Break analysis. Int J Numer Methods Eng 98:678–702 Yvonnet J, He QC, Toulemonde C (2008) Numerical modelling of the effective conductivities of composites with arbitrarily shaped inclusions and highly conducting interface. Compos Sci Technol 68:2818–2825 Yvonnet J, He QC, Zhu QZ, Shao JF (2011) A general and efficient computational procedure for modelling the Kapitza thermal resistance based on XFEM. Comput Mat Sci 50:1220–1224 Gu ST, Monteiro E, He QC (2011) Coordinate-free derivation and weak formulation of a general imperfect interface model for thermal conduction in composites. Compos Sci Technol 71:1209–1216 Liu JT, Gu ST, Monteiro E, He QC (2014) A versatile interface model for thermal conduction phenomena and its numerical implementation by XFEM. Comput Mech 53:825–843 Javili A, McBride A, Steinmann P (2012) Numerical modelling of thermomechanical solids with mechanically energetic (generalised) Kapitza interfaces. Comput Mat Sci 65:542–551 Javili A, Kaessmair S, Steinmann P (2014) General imperfect interfaces. Comp Methods Appl Mech Eng 275:76–97 Jain A, Tamma KK (2010) Parabolic heat conduction specialized applications involving imperfect contact surfaces: local discontinuous Galerkin finite element method—Part 2. J Therm Stresses 33:344–355 Gu ST, Liu JT, He QC (2014) The strong and weak forms of a general imperfect interface model for linear coupled multifield phenomena. Int J Eng Sci 85:31–46 Curnier AR, Taylor RL (1982) A thermomechanical formulation and solution of lubricated contacts between deformable solids. J Lubrication Technol 104:109–117 Zavarise G, Wriggers P, Stein E, Schrefler BA (1992) Real contact mechanisms and finite element formulation–a coupled thermomechanical approach. Int J Numer Methods Eng 35:767–785 Wriggers P, Miehe C (1994) Contact constraints within coupled thermomechanical analysis—a finite element model. Comp Methods Appl Mech Eng 113:301–319 Zavarise G, Wriggers P, Schrefler B (1995) On augmented Lagrangian algorithms for thermomechanical contact problems with friction. Int J Numer Methods Eng 38:2929–2949 Pantuso D, Bathe KJ, Bouzinov PA (2000) A finite element procedure for the analysis of thermo-mechanical solids in contact. Comput Struct 75:551–573 Rieger A, Wriggers P (2004) Adaptive methods for thermomechanical coupled contact problems. Int J Numer Methods Eng 59:871–894 Zavarise G, Bacchetto A, Gänser HP (2005) Frictional heating in contact mechanics—a methodology to deal with high temperature gradients. Comput Mech 35:418–429 Hansen G (2011) A Jacobian-free Newton Krylov method for mortar-discretized thermo-mechanical contact problems. J Comput Phys 230:6546–6562 Hesch C, Franke M, Dittmann M, Temizer I (2016) Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact prblems. Comp Methods Appl Mech Eng 301:242–258 Belghith S, Mezlini S, Belhadjsalah H, Ligier JL (2013) Thermo-mechanical modelling of the contact between rough surfaces using homogenisation technique. Mech Res Commun 53:57–62 Dittmann M, Franke M, Temizer I, Hesch C (2014) Isogeometric analysis and thermomechanical Mortar contact problems. Comp Methods Appl Mech Eng 274:192–212 Murashov MV, Panin SD (2015) Numerical modelling of contact heat transfer problem with work hardened rough surfaces. Int J Heat Mass Trans 90:72–80 Grisvard P (2011) Elliptic problems in nonsmooth domains. Vol 69: classics in applied mathematics. SIAM, Philadelphia Khoei AR (2015) Extended finite element method: theory and applications. Wiley, New York Le-Quang H, Bonnet G, He QC (2010) Size-dependent Eshelby tensor fields and effective conductivity of composites made of anisotropic phases with highly conducting imperfect interfaces. Phys Rev B 81:064203 Benveniste Y, Miloh T (1986) The effective conductivity of composites with imperfect thermal contact at constituent interfaces. Int J Eng Sci 24:1537–1552 Lipton R, Vernescu B (1996) Composites with imperfect interface. Proc R Soc Lond A Math Phys Eng Sci. https://doi.org/10.1098/rspa.1996.0018 Hashin Z (2001) Thin interphase/imperfect interface in conduction. J Appl Phys 89:2261–2267 Benveniste Y, Miloh T (1999) Neutral inhomogeneities in conduction phenomena. J Mech Phys Solids 47:1873–1892 Madhusudana CV, Fletcher LS (1986) Contact heat transfer—the last decade. AIAA J 24:510–523 Grosch KA (1963) The relation between the friction and visco-elastic properties of rubber. Proc R Soc Lond A 274:21–39 Mase CW, Smith L (1987) Effect of frictional heating on the thermal, hydrologic, and mechanical response of a fault. J Geophys Res 92:6249–6272 Braun OM, Steenwyk B, Warhadpande A, Persson BNJ (2016) On the dependency of friction on load: theory and experiment. Europhys Lett 113:56002 Farhat C, Park KC, Yves DP (1991) An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems. Comput Methods Appl Mech Eng 85:349–365 Turska E, Schrefler BA (1993) On convergence conditions of partitioned solution procedures for consolidation problems. Comput Methods Appl Mech Eng 106:51–63 Danowski C, Gravemeier V, Yoshihara L, Wall WA (2013) A monolithic computational approach to thermo-structure interaction. Int J Numer Methods Eng 95:1053–1078 Nguyen MN, Bui TQ, Nguyen NT, Truong TT, Lich LV (2017) Simulation of dynamic and static thermoelastic fracture problems by extended nodal gradient finite elements. Int J Mech Sci 134:370–386 Zienkiewicz OC, Chan AHC, Pastor M, Schrefler BA, Shiomi T (1999) Computational geomechanics with special reference to earthquake engineering. Wiley, New York