Spline-based smooth beam-to-beam contact model
Tóm tắt
The contact between bodies is a complex phenomenon that involves mechanical interaction, frictional sliding and heat transfer, among others. A common (and convenient) approach for the mechanical interaction in a finite element framework is to directly use the geometry of the elements to formulate the contact. The main drawback lies in the sharp corners that occur when straight finite elements are connected leading eventually to contact singularities. To circumvent this issue, particularly in the context of beam-to-beam contact, the present work proposes a pointwise contact formulation based on smooth C1 continuous spline contact elements. The proposed spline-based formulation, which can be directly attached to any quadratic beam finite element formulation, guarantees a smooth description for the whole set of elements, where contact takes place. A specific nonlinear normal contact interaction law and a rheological model for friction, both with elastic and viscous damping contributions, are developed increasing robustness in practical applications. To demonstrate this robustness, specific examples are considered including comparisons with a similar surface-to-surface formulation and an alternative smooth contact scheme, smooth contact with finite elements having sharp corners, modeling of a knot tightening with self-contact, and a simulation involving multiple pointwise contacts.
Tài liệu tham khảo
Jin S, Sohn D, Im S (2016) Node-to-node scheme for three-dimensional contact mechanics using polyhedral type variable-node elements. Comput Methods Appl Mech Eng 304:217–242. https://doi.org/10.1016/j.cma.2016.02.019
Xing W, Zhang J, Song C, Tin-Loi F (2019) A node-to-node scheme for three-dimensional contact problems using the scaled boundary finite element method. Comput Methods Appl Mech Eng 347:928–956. https://doi.org/10.1016/j.cma.2019.01.015
Wriggers P, Rust WT (2019) A virtual element method for frictional contact including large deformations. Eng Comput (Swansea, Wales) 36:2133–2161. https://doi.org/10.1108/EC-02-2019-0043
Paggi M, Wriggers P (2016) Node-to-segment and node-to-surface interface finite elements for fracture mechanics. Comput Methods Appl Mech Eng 300:540–560. https://doi.org/10.1016/j.cma.2015.11.023
Khoei AR, Biabanaki SOR, Parvaneh SM (2013) 3D dynamic modeling of powder forming processes via a simple and efficient node-to-surface contact algorithm. Appl Math Model 37:443–462. https://doi.org/10.1016/j.apm.2012.03.010
Crisfield MA (2000) Re-visiting the contact patch test. Int J Numer Methods Eng 48:435–449. https://doi.org/10.1002/(SICI)1097-0207(20000530)48:3%3c435::AID-NME891%3e3.0.CO;2-V
De Lorenzis L, Wriggers P, Hughes TJR (2014) Isogeometric contact: a review. GAMM Mitteilungen 37:85–123. https://doi.org/10.1002/gamm.201410005
Heinstein MW, Laursen TA (2003) A three-dimensional surface-to-surface projection algorithm for non-coincident domains. Commun Numer Methods Eng 19:421–432. https://doi.org/10.1002/cnm.601
Zimmerman BK, Ateshian GA (2018) A surface-to-surface finite element algorithm for large deformation frictional contact in febio. J Biomech Eng 140. https://doi.org/10.1115/1.4040497
Wriggers P, Zavarise G (1997) On contact between three-dimensional beams undergoing large deflections. Commun Numer Methods Eng 13:429–438. https://doi.org/10.1002/(SICI)1099-0887(199706)13:6%3c429::AID-CNM70%3e3.0.CO;2-X
Litewka P, Wriggers P (2001) Frictional contact between 3D beams. Comput Mech 28:26–39. https://doi.org/10.1007/s004660100266
Pietrzak G, Curnier A (1999) Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment. Comput Methods Appl Mech Eng 177:351–381. https://doi.org/10.1016/S0045-7825(98)00388-0
Padmanabhan V, Laursen TA (2001) A framework for development of surface smoothing procedures in large deformation frictional contact analysis. Finite Elem Anal Des 37:173–198. https://doi.org/10.1016/S0168-874X(00)00029-9
Magliulo M, Zilian A, Beex LAA (2020) Contact between shear-deformable beams with elliptical cross sections. Acta Mech 231:273–291. https://doi.org/10.1007/s00707-019-02520-w
Tasora A, Benatti S, Mangoni D, Garziera R (2020) A geometrically exact isogeometric beam for large displacements and contacts. Comput Methods Appl Mech Eng 358:112635. https://doi.org/10.1016/j.cma.2019.112635
Wriggers P, Krstulovic-Opara L, Korelc J (2001) Smooth C1-interpolations for two-dimensional frictional contact problems. Int J Numer Methods Eng 51:1469–1495. https://doi.org/10.1002/nme.227
Krstulović-Opara L, Wriggers P, Korelc J (2002) A C1-continuous formulation for 3D finite deformation frictional contact. Comput Mech 29:27–42. https://doi.org/10.1007/s00466-002-0317-z
Al-Dojayli M, Meguid SA (2002) Accurate modeling of contact using cubic splines. Finite Elem Anal Des 38:337–352. https://doi.org/10.1016/S0168-874X(01)00088-9
Litewka P (2007) Hermite polynomial smoothing in beam-to-beam frictional contact. Comput Mech 40:815–826. https://doi.org/10.1007/s00466-006-0143-9
Durville D (2010) Simulation of the mechanical behaviour of woven fabrics at the scale of fibers. Int J Mater Form 3:1241–1251. https://doi.org/10.1007/s12289-009-0674-7
Durville D (2012) Contact-friction modeling within elastic beam assemblies: an application to knot tightening. Comput Mech 49:687–707. https://doi.org/10.1007/s00466-012-0683-0
Konyukhov A, Schweizerhof K (2010) Geometrically exact covariant approach for contact between curves. Comput Methods Appl Mech Eng 199:2510–2531. https://doi.org/10.1016/j.cma.2010.04.012
Lu J (2011) Isogeometric contact analysis: geometric basis and formulation for frictionless contact. Comput Methods Appl Mech Eng 200:726–741. https://doi.org/10.1016/j.cma.2010.10.001
Temizer I, Wriggers P, Hughes TJR (2012) Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 209–212:115–128. https://doi.org/10.1016/j.cma.2011.10.014
Meier C, Grill MJ, Wall WA, Popp A (2018) Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures. Int J Solids Struct 154:124–146. https://doi.org/10.1016/j.ijsolstr.2017.07.020
Nishi S, Terada K, Temizer I (2019) Isogeometric analysis for numerical plate testing of dry woven fabrics involving frictional contact at meso-scale. Comput Mech 64:211–229. https://doi.org/10.1007/s00466-018-1666-6
de Boor C (1972) On calculating with B-splines. J Approx Theory 6:50–62. https://doi.org/10.1016/0021-9045(72)90080-9
Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Chichester
Piegl L, Tiller W (1997) The NURBS book. Springer, Berlin
Belytschko T, Neal MO (1991) Contact-impact by the pinball algorithm with penalty and Lagrangian methods. Int J Numer Methods Eng 31:547–572. https://doi.org/10.1002/nme.1620310309
Gay Neto A, Wriggers P (2020) Numerical method for solution of pointwise contact between surfaces. Comput Methods Appl Mech Eng 365:112971. https://doi.org/10.1016/j.cma.2020.112971
Gay Neto A, Wriggers P (2019) Computing pointwise contact between bodies: a class of formulations based on master–master approach. Comput Mech 64:585–609. https://doi.org/10.1007/s00466-019-01680-9
Gay Neto A, Pimenta PM, Wriggers P (2016) A master-surface to master-surface formulation for beam to beam contact. Part I: frictionless interaction. Comput Methods Appl Mech Eng 303:400–429. https://doi.org/10.1016/j.cma.2016.02.005
Gay Neto A, Pimenta PM, Wriggers P (2017) A master-surface to master-surface formulation for beam to beam contact. Part II: frictional interaction. Comput Methods Appl Mech Eng 319:146–174. https://doi.org/10.1016/j.cma.2017.01.038
Neto AG, Wriggers P (2022) Discrete element model for general polyhedra. Comput Part Mech 9:353–380. https://doi.org/10.1007/s40571-021-00415-z
Gay Neto A, Wriggers P (2020) Master-master frictional contact and applications for beam-shell interaction. Comput Mech 66:1213–1235. https://doi.org/10.1007/s00466-020-01890-6
Hertz H (1882) Ueber die Berührung fester elastischer Körper. J fur die Reine und Angew Math 1882:156–171. https://doi.org/10.1515/crll.1882.92.156
Boisse P, Gasser A, Hivet G (2001) Analyses of fabric tensile behaviour: determination of the biaxial tension-strain surfaces and their use in forming simulations. Compos - Part A Appl Sci Manuf 32:1395–1414. https://doi.org/10.1016/S1359-835X(01)00039-2
Wriggers P (2006) Computational contact mechanics. Springer, Berlin
Simo JC (1985) A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Comput Methods Appl Mech Eng 49:55–70. https://doi.org/10.1016/0045-7825(85)90050-7
Simo JC, Vu-Quoc L (1986) A three-dimensional finite-strain rod model. part II: computational aspects. Comput Methods Appl Mech Eng 58:79–116. https://doi.org/10.1016/0045-7825(86)90079-4
Simo JC, Vu-Quoc L (1991) A geometrically-exact rod model incorporating shear and torsion-warping deformation. Int J Solids Struct 27:371–393. https://doi.org/10.1016/0020-7683(91)90089-X
Gay Neto A (2020) Giraffe User’s Manual v. 2.0.0
Gay Neto A, Pimenta PM, Wriggers P (2015) Self-contact modeling on beams experiencing loop formation. Comput Mech 55:193–208. https://doi.org/10.1007/s00466-014-1092-3
Ota NSN, Wilson L, Gay Neto A et al (2016) Nonlinear dynamic analysis of creased shells. Finite Elem Anal Des 121:64–74. https://doi.org/10.1016/j.finel.2016.07.008
Faccio Júnior CJ, Cardozo ACP, Monteiro Júnior V, Gay Neto A (2019) Modeling wind turbine blades by geometrically-exact beam and shell elements: a comparative approach. Eng Struct 180:357–378. https://doi.org/10.1016/j.engstruct.2018.09.032
Craveiro MV, Gay Neto A (2018) Upheaval buckling of pipelines due to internal pressure: a geometrically nonlinear finite element analysis. Eng Struct 158:136–154. https://doi.org/10.1016/j.engstruct.2017.12.010
Craveiro MV, Gay Neto A (2019) Lateral buckling of pipelines due to internal pressure: a geometrically nonlinear finite element analysis. Eng Struct 200:109505. https://doi.org/10.1016/j.engstruct.2019.109505
Gay Neto A, Martins C de A (2013) Structural stability of flexible lines in catenary configuration under torsion. Mar Struct 34:16–40. https://doi.org/10.1016/j.marstruc.2013.07.002
Neto AG, Martins CA, Pimenta PM (2014) Static analysis of offshore risers with a geometrically-exact 3D beam model subjected to unilateral contact. Comput Mech 53:125–145. https://doi.org/10.1007/s00466-013-0897-9
Gay Neto A, Ribeiro Malta E, de Mattos PP (2015) Catenary riser sliding and rolling on seabed during induced lateral movement. Mar Struct 41:223–243. https://doi.org/10.1016/j.marstruc.2015.02.001
Gay Neto A (2016) Dynamics of offshore risers using a geometrically-exact beam model with hydrodynamic loads and contact with the seabed. Eng Struct 125:438–454. https://doi.org/10.1016/j.engstruct.2016.07.005
Faccio Júnior CJ, Gay Neto A (2021) Challenges in representing the biaxial mechanical behavior of woven fabrics modeled by beam finite elements with contact. Compos Struct 257:113330. https://doi.org/10.1016/j.compstruct.2020.113330
Pimenta PM, Yojo T (1993) Geometrically exact analysis of spatial frames. Appl Mech Rev 46:S118–S128. https://doi.org/10.1115/1.3122626
Pimenta PM, Campello EMB (2001) Geometrically nonlinear analysis of thin-walled space frames. In: Proceedings of the Second European conference on computational mechanics, II ECCM
da Costa e Silva C, Maassen SF, Pimenta PM, Schröder J (2020) A simple finite element for the geometrically exact analysis of Bernoulli–Euler rods. Comput Mech 65:905–923. https://doi.org/10.1007/s00466-019-01800-5
Zavarise G, Wriggers P (2000) Contact with friction between beams in 3-D space. Int J Numer Methods Eng 49:977–1006. https://doi.org/10.1002/1097-0207(20001120)49:8%3c977::AID-NME986%3e3.0.CO;2-C
Ibrahimbegović A, Mamouri S (2000) On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3D geometrically exact beam model. Comput Methods Appl Mech Eng 188:805–831. https://doi.org/10.1016/S0045-7825(99)00363-1
Gay Neto A (2017) Simulation of mechanisms modeled by geometrically-exact beams using Rodrigues rotation parameters. Comput Mech 59:459–481. https://doi.org/10.1007/s00466-016-1355-2
Cao J, Akkerman R, Boisse P et al (2008) Characterization of mechanical behavior of woven fabrics: experimental methods and benchmark results. Compos Part A Appl Sci Manuf 39:1037–1053. https://doi.org/10.1016/j.compositesa.2008.02.016
Refachinho de Campos PR, Gay Neto A (2018) Rigid body formulation in a finite element context with contact interaction. Comput Mech 62:1369–1398. https://doi.org/10.1007/s00466-018-1569-6