Stability of 3D Textile Composite Reinforcement Simulations: Solutions to Spurious Transverse Modes
Source abstract
Abstract
The simulation of thick 3D composite reinforcement forming brings to light new modeling challenges. The specific anisotropic material behavior due to the possible slippage between fibers induces, among other phenomena, the development of spurious transverse modes in bending-dominated 3D simulations. To obtain coherent finite element responses, two solutions are proposed. The first one uses a simple assumed strain formulation usually prescribed to prevent volumetric locking. This solution avoids spurious transverse modes by stiffening of the hourglass modes. Nevertheless the deformation obtained by this approach still suffers from the inability of the standard continuum mechanics of Cauchy to describe fibrous material deformation. The second proposed approach is based on the introduction of a bending stiffness which both avoids the spurious transverse modes and also improves the global behavior of the element formulation by enriching the underlying continuum. To emphasize the differences between different formulations, element stiffnesses are explicitly calculated and compared.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Mechanical Behavior of Composites · Structural Analysis and Optimization · Composite Structure Analysis and Optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (43)
Show source-provided references
1. Lomov, S.V., Perie, G., Ivanov, D.S., Verpoest, I., Marsal, D.: Modeling three-dimensional fabrics and three-dimensional reinforced composites: challenges and solutions. Text. Res. J. 81(1), 28–41 (2011)10.1177/0040517510385169 ↗
2. Rudd, C.D., Long, A.: Liquid Molding Technologies. Woodhead Publishing Limited, Cambridge (1997)10.1533/9781845695446 ↗
3. Potter, K.D.: The early history of the resin transfer moulding process for aerospace applications. Compos. A: Appl. Sci. Manuf. 30(5), 619–621 (1999)10.1016/S1359-835X(98)00179-1 ↗
4. Allaoui, S., Hivet, G., Soulat, D., Wendling, A., Ouagne, P., Chatel, S.: Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement. Int. J. Mater. Form. 7, 155–165 (2014)10.1007/s12289-012-1116-5 ↗
5. Peng, X.Q., Cao, J.: A continuum mechanics-based non-orthogonal constitutive model for woven composite fabrics. Compos. A: Appl. Sci. Manuf. 36(6), 859–874 (2005)10.1016/j.compositesa.2004.08.008 ↗
6. Yu, W., Harrison, P., Long, A.: Finite element forming simulation for non-crimp fabrics using a non-orthogonal constitutive equation. Compos. A: Appl. Sci. Manuf. 36, 1079–1093 (2005)10.1016/j.compositesa.2005.01.007 ↗
7. Badel, P., Vidal-Sallé, E., Boisse, P.: Large deformation analysis of fibrous materials using rate constitutive equations. Comput. Struct. 86, 1164–1175 (2008)10.1016/j.compstruc.2008.01.009 ↗
8. Spencer, A.J.M.: Deformations of Fibre Reinforced Materials. Oxford University Press, London (1972)
9. ten Thije, R.H.W., Akkerman, R., Huétink, J.: Large deformation simulation of anisotropic material using an updated Lagrangian finite element method. Comput. Methods Appl. Mech. Eng. 196, 3141–3150 (2007)10.1016/j.cma.2007.02.010 ↗
10. Aimene, Y., Vidal-Sallé, E., Hagège, B., Sidoroff, F., Boisse, P.: A hyperelastic approach for composite reinforcement large deformation analysis. J. Compos. Mater. 44(1), 5–26 (2009)10.1177/0021998309345348 ↗
11. de Luycker, E., Morestin, F., Boisse, P., Marsal, D.: Simulation of 3D interlock composite preforming. Compos. Struct. 88(4), 615–623 (2009)10.1016/j.compstruct.2008.06.005 ↗
12. Charmetant, A., Orliac, J.G., Vidal-Sallé, E., Boisse, P.: Hyperelastic model for large deformation analyses of 3D interlock composite preforms. Compos. Sci. Technol. 72, 1352–1360 (2012)10.1016/j.compscitech.2012.05.006 ↗
13. ten Thije, R.H.W., Akkerman, R.: Solutions to intra-ply shear locking in finite element analyses of fibre reinforced materials. Compos. Part A 39, 1167–1176 (2008)10.1016/j.compositesa.2008.03.014 ↗
14. Hamila, N., Boisse, P.: Locking in simulation of composite reinforcement deformations. Analysis and treatment. Compos. Part A 53, 109–117 (2013)10.1016/j.compositesa.2013.06.001 ↗
15. Boehler, J.P.: Lois de comportement anisotrope des milieux continus. J. Méc. 17, 153–170 (1978)
16. Quanshui, Z., Boehler, J.P.: Tensor function representations as applied to formulating constitutive laws for clinotropic materials. Acta Mech. Sinica 10, 336–348 (1994)10.1007/BF02486676 ↗
17. Itskov, M.: On the theory of fourth-order tensors and their applications in computational mechanics. Comput. Methods Appl. Mech. Eng. 189, 419–438 (2000)10.1016/S0045-7825(99)00472-7 ↗
18. Mathieu, S.: Mechanical behavior modeling of CMC interlocks through the forming and pyrolysis proceses. PhD thesis INSA Lyon (2014)
19. Belytschko, T., Bachrach, W.E.: Efficient implementation of quadrilaterals with high coarse-mesh accuracy. Comput. Methods Appl. Mech. Eng. 54, 279–301 (1986)10.1016/0045-7825(86)90107-6 ↗
20. Koh, B.C., Kikuchi, N.: New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity. Comput. Methods Appl. Mech. Eng. 65, 1–46 (1987)10.1016/0045-7825(87)90181-2 ↗
21. Simo, J.C., Armero, F., Taylor, R.L.: Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems. Comput. Methods Appl. Mech. Eng. 110, 359–386 (1993)10.1016/0045-7825(93)90215-J ↗
22. Belytschko, T., Bindeman, L.P.: Assumed strain stabilization of the eight node hexahedral element. Comput. Methods Appl. Mech. Eng. 105, 225–260 (1993)10.1016/0045-7825(93)90124-G ↗
23. Nagtegaal, J.C., Parks, D.M., Rice, J.R.: On numerically accurate finite element solutions in the fully plastic range. Comput. Methods Appl. Mech. Eng. 4, 153–177 (1974)10.1016/0045-7825(74)90032-2 ↗
24. Hughes, T.J.R.: Generalization of selective integration procedures to anisotropic and nonlinear media. Int. J. Numer. Methods Eng. 15, 1413–1418 (1980)10.1002/nme.1620150914 ↗
25. Hughes, T.J.R.: Generalization of selective integration procedure to anisotropic and nonlinear media. J. Appl. Mech. 15, 1413–1418 (1977)
26. Hughes, T.J.R.: Equivalence of finite elements for nearly incompressible elasticity. J. Appl. Mech. 44, 181–183 (1977)10.1115/1.3423994 ↗
27. 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, 63–81 (1978)10.1016/0045-7825(78)90005-1 ↗
28. Hughes, T.J.R., Taylor, R.L., Sackman, J.L.: Finite element formulation and solution of contact-impact problems in continuum mechanics-III. SESM Report 75–3, Department of Civil Engineering, The University of California, Berkeley (1975).
29. Simo, J.C., Taylor, R.L., Pister, K.S.: Variational and projection methods for the volume contraint in finite deformation elasto-plasticity. Comput. Methods Appl. Mech. Eng. 51, 177–208 (1985)10.1016/0045-7825(85)90033-7 ↗
30. de Souza Neto, E.A., Peric, D., Dutko, M., Owen, D.R.J.: Design of simple low order finite elements for large strain analysis of nearly incompressible solids. Int. J. Solids Struct. 33, 20–22 (1996)
31. de Souza Neto, E.A., Pires, F.M.A., Owen, D.R.J.: F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking. Int. J. Numer. Methods Eng. 62, 353–383 (2005)10.1002/nme.1187 ↗
32. Flory, R.J.: Thermodynamic relations for highly elastic materials. Trans. Faraday Soc. 57, 829–838 (1969)10.1039/tf9615700829 ↗
33. Simo, J.C., Taylor, R.L.: Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithm. Comput. Methods Appl. Mech. Eng. 85, 273–310 (1991)10.1016/0045-7825(91)90100-K ↗
34. Ferretti, M., Madeo, A., dell’Isola, F., Boisse, P.: Modeling the onset of shear boundary layers in fibrous composite reinforcements by second-gradient theory. Z. Angew. Math. Phys. 65, 587–612 (2014)10.1007/s00033-013-0347-8 ↗
35. d’Agostino, M.V., Giorgio, I., Greco, L., Madeo, A., Boisse, P.: Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements. Int. J. Solids Struct. 59, 1–17 (2015)10.1016/j.ijsolstr.2014.12.014 ↗
36. Madeo, A., Ferretti, M., dell’Isola, F., Boisse, P.: Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks. Z. Angew. Math. Phys. 66, 2041–2060 (2015)10.1007/s00033-015-0496-z ↗
37. Onate, E., Cervera, M.: Derivation of thin plate bending element with one degree of freedom per node : a simple three node triangle. Eng. Comput. 10, 543–561 (1993)10.1108/eb023924 ↗
38. Sabourin, F., Brunet, M.: Analyses of plates and shells with a simplified 3 node triangular element. Thin-Walled Struct. 21, 238–251 (1995)10.1016/0263-8231(94)00001-G ↗
39. Onate, E., Zarate, F.: Rotation-free triangular plate and shell elements. Int. J. Numer. Methods Eng. 47, 557–603 (2000)10.1002/(SICI)1097-0207(20000110/30)47:1/3<557::AID-NME784>3.0.CO;2-9 ↗
40. Brunet, M., Sabourin, F.: Analysis of a rotation-free 4-node shell element. Int. J. Numer. Methods Eng. 66, 1483–1510 (2006)10.1002/nme.1608 ↗
41. Hamila, N., Boisse, P., Sabourin, F., Brunet, M.: A semi-discrete shell finite element for textile composite reinforcement forming simulation. Int. J. Numer. Methods Eng. 79, 1443–1466 (2009)10.1002/nme.2625 ↗
42. Schnur, D.S., Zabaras, N.: An inverse method for determining elastic material properties and a material interface. Int. J. Numer. Methods Eng. 33, 2039–2057 (1992)10.1002/nme.1620331004 ↗
43. Liang, B., Hamila, N., Peillon, M., Boisse, P.: Analysis of thermoplastic prepreg bending stiffness during manufacturing and of its influence on wrinkling simulations. Compos. Part A 67, 111–122 (2014)10.1016/j.compositesa.2014.08.020 ↗