Does the Weaving and Knitting Pattern of a Fabric Determine its Relaxation Time?

Quarterly Journal of Mechanics and Applied Mathematics

Volumn 70, Issue 4, 2017, Pages 337-361

  Orlik, J ^a   Andra H ^a   Argatov, I ^a   Staub, S ^a  

^a FRAUNHOFER INSTITUTE FOR INDUSTRIAL MATHEMATICS ITWM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPOSITE MATERIALS; DEFORMATION; HOMOGENIZATION METHOD;

ASYMPTOTIC HOMOGENIZATION; HOMOGENIZATION SCHEME; PERIODIC MICROSTRUCTURE; QUASI-STATIC DEFORMATION; TORSIONAL DEFORMATIONS; TWO SCALE CONVERGENCE; VISCOELASTIC COMPOSITE MATERIALS; VISCOELASTIC PROPERTIES;

VISCOELASTICITY;

EID: 85040117445     PISSN: 00335614     EISSN: 14643855     Source Type: Journal    
DOI: 10.1093/qjmam/hbx011     Document Type: Article

References (39)

1. J. J. F. Knapton, F. J. Ahrens, W. W. Ingenthron and W. Fong, The dimensional properties of knitted wool fabrics. Part I: The plain-knitted structure, Textile Res. J. 38 (1968) 999-1012.
2. X. Zhang, Y. Li, K. W. Yeung and M. Yao, Mathematical simulation of fabric bagging, Textile Res. J. 70 (2000) 18-28.
3. M. I. Okereke, A. I. Akpoyomare and M. S. Bingley, Virtual testing of advanced composites, cellular materials and biomaterials: a review, Compos. B 60 (2014) 637-662.
4. F. Stig and S. Hallström, A modelling framework for composites containing 3D reinforcement, Compos. Struct. 94 (2012) 2895-2901.
5. G. Haasemann and V. Ulbricht, Numerical evaluation of the viscoelastic and viscoplastic behavior of composites, Technische Mechanik 30 (2010) 122-135.
6. Y. Cai and H. Sun, Prediction on viscoelastic properties of three-dimensionally braided composites by multi-scale model, J. Mater. Sci. 48 (2013) 6499-6508.
7. T. Hui and C. Oskay, Laplace-domain, high-order homogenization for transient dynamic response of viscoelastic composites, Int. J. Numer. Meth. Eng. 103 (2015) 937-957.
8. P. Upadhyaya and C. S. Upadhyay, A three-dimensional micromechanical model to predict the viscoelastic behavior of woven composites, Compos. Struct. 93 (2011) 2733-2739.
9. N. Lahellec and P. Suquet, Effective behavior of linear viscoelastic composites: a timeintegration approach, Int. J. Solids Struct. 44 (2007) 507-529.
10. A. El Mourid, R. Ganesan and M. Lévesque, Comparison between analytical and numerical predictions for the linearly viscoelastic behavior of textile composites,Mech. Mater. 58 (2013), 69-83.
11. Y. Xu, P. Zhang and W. Zhang, Two-scale micromechanical modeling of the time dependent relaxation modulus of plain weave polymer matrix composites, Compos. Struct. 123 (2015) 35-44.
12. H. Reda,Y. Rahali, J. F. Ganghoffer and H. Lakiss,Wave propagation in 3D viscoelastic auxetic and textile materials by homogenized continuum micropolar models, Compos. Struct. 141 (2016) 328-345.
13. S. Staub, H. Andrä and M. Kabel, Fast FFT based solver for rate-dependent deformations of composites and nonwovens, Int. J. Solids Struct. (2016)
14. L. Tartar, The General Theory of Homogenization. A Personalized Introduction (Springer, Berlin 2009).
15. G. Panasenko, Multi-Scale Modelling for Structures and Composites (Springer, Dordrecht 2005).
16. G. P. Panasenko, Asymptotic solutions of the system of elasticity theory for rod and frame structures, Sbornik Math. 75 (1993) 85-110.
17. S. Pastukhova, Homogenization of problems of elasticity theory on periodic box and rod frames of critical thickness, J. Math. Sci. 130 (2005) 4954-5004.
18. V. V. Zhikov, S. E. Pastukhova, Homogenization for elasticity problems on periodic networks of critical thickness, Sbornik Math. 194 (2003) 61-95.
19. G. Griso, A. Migunova and J. Orlik, Asymptotic analysis for domains separated by a thin layer made of periodic vertical beams, J. Elast (2017). doi:10.1007/s10659-017-9628-3.
20. A. Damlamian, D. Cioranescu and J. Orlik, Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymp. Anal. 82 (2013) 201-232.
21. N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods (SIAM, Philadelphia 1988).
22. C. Eck and J. Jaru?sek, Existence results for the static contact problem with Coulomb friction, Math. Model. Meth. Appl. Sci. 8 (1998) 445-468.
23. P. Alart and F. Lebon, Numerical study of a stratified composite coupling homogenization and frictional contact, Math. Comp. Model. 28 (1998) 273-286.
24. Z. Bare, J. Orlik and G. Panasenko, Asymptotic dimension reduction of a Robin type elasticity boundary value problem in thin beams, Appl. Anal. 93 (2014) 1217-1238.
25. J. Orlik, Existence and stability estimate for the solution of the ageing hereditary linear viscoelasticity problem, Abstract Appl. Anal. 2009 (2009) Article ID 828315, 19 p.
26. J. Orlik and A. Ostrovska, Space-time finite element approximation and numerical solution of hereditary linear viscoelastic problems, Comp. Appl. Math. 27 (2008) 1-28.
27. M. Kaliske and H. Rothert, Formulation and implementation of three-dimensional viscoelasticity at small and finite strains, Comp. Mech. 19 (1997) 228-239.
28. M.Walloth, Formulation of quasistatic viscoelastic contact problem, Report ITWM (2008).
29. Yu. N. Rabotnov, Creep Problems in Structural Members (Amsterdam, North-Holland Publishing Company 1969).
30. Y. A. Rossikhin and M. V. Shitikova, Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl. Mech. Rev. 50 (1997) 15-67.
31. S. Sukigara, R. Dhingra, R. Postle and X. Tao, Physical ageing and annealing in fibers and textile materials. Pt. V Master stress relaxation curves for annealed textile materials, Textile Res. J. 56 (1988) 543-551.
32. J. Orlik,G. Panasenko andV. Shiryaev, Optimization of textile-like materials via homogenization and Beam approximations, SIAM J. Multiscale Model. Simul. 14 (2016) 637-667.
33. B.E. Pobedrya, Mechanics of Composite Materials, (Moscow State University Publishers, Moscow 1984).
34. G. Griso, Asymptotic behaviour of curved rods by the unfolding method, Math. Meth. Appl. Sci. 27 (2004) 2081-2110.
35. R. Rodríguez-Ramos, R. Guinovart-Díaz, J. C. López-Realpozo, J. Bravo-Castillero, J.A. Otero, F. J. Sabina and F. Lebon, Effective properties of periodic fibrous electro-elastic composites with mechanic imperfect contact condition, Int. J. Mech. Sci. 73 (2013) 1-13.
36. R. Rodríguez-Ramos, R. de Medeiros, R. Guinovart-Díaz, J. Bravo-Castillero, J. A. Otero and V. Tita, Different approaches for calculating the effective elastic properties in composite materials under imperfect contact adherence, Compos. Struct. 99 (2013) 264-275.
37. F.J. Sabina, R. Guinovart-Díaz, R. Rodriguez-Ramos, J. C. López-Realpozo, J. Bravo-Castillero, Overall properties in fibrous elastic composite with imperfect contact condition, Int. J. Eng. Sci. 61 (2012) 142-155.
38. G. R. Liu and S. S. Quek, The Finite Element Method, A Practical Course (Elsevier, Oxford, Second edition, Butterworth-Heinemann, 2003).
39. L. Trabucho, J. M. Viaño, Mathematical Modelling of Rods, Handbook of Numerical Analysis, Vol. IV, (ed. P. G. Ciarlet and J.-L. Lions, North-Holland, 1996).