Modeling failure of heterogeneous viscoelastic solids under dynamic/impact loading due to multiple evolving cracks using a two-way coupled multiscale model
Tóm tắt
This paper presents a model for predicting damage evolution in heterogeneous viscoelastic solids under dynamic/impact loading. Some theoretical developments associated with the model have been previously reported. These are reviewed briefly, with the main focus of this paper on new developments and applications. A two-way coupled multiscale approach is employed and damage is considered in the form of multiple cracks evolving in the local (micro) scale. The objective of such a model is to develop the ability to consider energy dissipation due to both bulk dissipation and the development of multiple cracks occurring on multiple length and time scales. While predictions of these events may seem extraordinarily costly and complex, there are multiple structural applications where effective models would save considerable expense. In some applications, such as protective devices, viscoelastic materials may be preferred because of the considerable amount of energy dissipated in the bulk as well as in the fracture process. In such applications, experimentally based design methodologies are extremely costly, therefore suggesting the need for improved models. In this paper, the authors focus on the application of the newly developed multiscale model to the solution of some example problems involving dynamic and impact loading of viscoelastic heterogeneous materials with growing cracks at the local scale.
Tài liệu tham khảo
Allen, D.H.: Damage evolution in laminates. In: Talreja, R. (ed.) Damage Mechanics of Composite Materials. Composite Materials Series, vol. 9, pp. 79–114. Elsevier, Amsterdam (1994)
Allen, D.H.: Homogenization principles and their application to continuum damage mechanics. Compos. Sci. Technol. 61(15), 2223–2230 (2001). doi:10.1016/S0266-3538(01)00116-6
Allen, D.H., Searcy, C.R.: Numerical aspects of a micromechanical model of a cohesive zone. J. Rein. Plast. Compos. 19(3), 240–248 (2000). doi:10.1177/073168440001900304
Allen, D.H., Searcy, C.R.: A micromechanical model for a viscoelastic cohesive zone. Int. J. Fract. 107(2), 159–176 (2001a). doi:10.1023/A:1007693116116
Allen, D.H., Searcy, C.R.: A micromechanically-based model for predicting dynamic damage evolution in ductile polymers. Mech. Mater. 33(3), 177–184 (2001b). doi:10.1016/S0167-6636(00)00069-7
Allen, D.H., Searcy, C.R.: A model for predicting the evolution of multiple cracks on multiple length scales in viscoelastic composites. J. Mater. Sci. 41(20), 6510–6519 (2006). doi:10.1007/s10853-006-0185-6
Allen, D.H., Yoon, C.: Homogenization techniques for thermoviscoelastic solids containing cracks. Int. J. Solids Struct. 35(31–32), 4035–4053 (1998). doi:10.1016/S0020-7683(97)00299-0
Barenblatt, G.I.: The mathematical theory of equilibrium cracks in brittle fracture. In: Dryden, H.L., von Kármán, T., Kuerti, G., van den Dungen, F.H., Howarth, L. (eds.) Advances in Applied Mechanics, vol. 7, pp. 55–129. Elsevier, Amsterdam (1962). doi:10.1016/S0065-2156(08)70121-2
Camacho, G.T., Ortiz, M.: Computational modelling of impact damage in brittle materials. Int. J. Solids Struct. 33(20–22), 2899–2938 (1996). doi:10.1016/0020-7683(95)00255-3
Cauchy, A.L.: Recherches sur l’équilibre et le mouvement intérieur des corps solides ou fluides, élastiques ou non élastiques. Bull. Soc. Philomat. 9–13 (1823)
Christensen, R.M.: A rate-dependent criterion for crack growth. Int. J. Fract. 15(1), 3–21 (1979). doi:10.1007/BF00115904
Chudnovsky, A., Moet, A.: A theory for crack layer propagation in polymers. J. Elastomers Plast. 18(1), 50–55 (1986). doi:10.1177/009524438601800107
Costanzo, F., Allen, D.H.: A continuum mechanics approach to some problems in subcritical crack propagation. Int. J. Fract. 63(1), 27–57 (1993). doi:10.1007/BF00053315
Costanzo, F., Allen, D.H.: A continuum thermodynamic analysis of cohesive zone models. Int. J. Eng. Sci. 33(15), 2197–2219 (1995). doi:10.1016/0020-7225(95)00066-7. The Edelen Symposium
Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proceedings of the 1969 24th National Conference, pp. 157–172. ACM, New York (1969). http://doi.acm.org/10.1145/800195.805928
Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8(2), 100–104 (1960). doi:10.1016/0022-5096(60)90013-2
Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 241(1226), 376–396 (1957). doi:10.1098/rspa.1957.0133
Feyel, F.: Multiscale FE2 elastoviscoplastic analysis of composite structures. Comput. Mater. Sci. 16(1–4), 344–354 (1999). doi:10.1016/S0927-0256(99)00077-4
Feyel, F., Chaboche, J.L.: FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. Comput. Methods Appl. Mech. Eng. 183(3–4), 309–330 (2000). doi:10.1016/S0045-7825(99)00224-8
Fish, J., Shek, K.: Multiscale analysis of composite materials and structures. Compos. Sci. Technol. 60(12-13), 2547–2556 (2000). doi:10.1016/S0266-3538(00)00048-8
Fish, J., Yuan, Z.: Multiscale enrichment based on partition of unity. Int. J. Numer. Methods Eng. 62(10), 1341–1359 (2005). doi:10.1002/nme.1230
Fish, J., Shek, K., Pandheeradi, M., Shephard, M.S.: Computational plasticity for composite structures based on mathematical homogenization: Theory and practice. Comput. Methods Appl. Mech. Eng. 148(1–2), 53–73 (1997). doi:10.1016/S0045-7825(97)00030-3
Foulk, J.W., Allen, D.H., Helms, K.L.E.: Formulation of a three-dimensional cohesive zone model for application to a finite element algorithm. Comput. Methods Appl. Mech. Eng. 183(1–2), 51–66 (2000). doi:10.1016/S0045-7825(99)00211-X
Hashin, Z.: Theory of mechanical behavior of heterogeneous media. Appl. Mech. Rev. 17(1), 1–9 (1964)
Hill, R.: Elastic properties of reinforced solids: Some theoretical principles. J. Mech. Phys. Solids 11(5), 357–372 (1963). doi:10.1016/0022-5096(63)90036-X
Hill, R.: Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13(2), 89–101 (1965a). doi:10.1016/0022-5096(65)90023-2
Hill, R.: A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13(4), 213–222 (1965b). doi:10.1016/0022-5096(65)90010-4
Kambouchev, N., Noels, L., Radovitzky, R.: Numerical simulation of the fluid-structure interaction between air blast waves and free-standing plates. Comput. Struct. 85(11–14), 923–931 (2007). doi:10.1016/j.compstruc.2006.11.005. Fourth MIT Conference on Computational Fluid and Solid Mechanics
Knauss, W.G.: Delayed failure—the Griffith problem for linearly viscoelastic materials. Int. J. Fract. 6(1), 7–20 (1970). doi:10.1007/BF00183655
Knauss, W.G.: On the steady propagation of a crack in viscoelastic sheet: experiments and analysis. In: Kausch, H.H., Hassel, J.A., Jaffee, R.I. (eds.) Deformation and Fracture of High Polymers, pp. 501–540. Plenum, New York (1972)
Kouznetsova, V.G.: Computational homogenization for the multi-scale analysis of multi-phase materials. Ph.D. dissertation, Technische Universiteit Eindhoven (2002)
Lu, Y., Wang, Z.: Characterization of structural effects from above-ground explosion using coupled numerical simulation. Comput. Struct. 84(28), 1729–1742 (2006). doi:10.1016/j.compstruc.2006.05.002
Moës, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46(1), 131–150 (1999). doi:10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
Nemat-Nasser, S., Hori, M.: Micromechanics: Overall Properties of Heterogeneous Materials, 2nd edn. North-Holland, Amsterdam (1999)
Schapery, R.A.: A theory of crack initiation and growth in viscoelastic media—I. Theoretical development. Int. J. Fract. 11(1), 141–159 (1975a). doi:10.1007/BF00034721
Schapery, R.A.: A theory of crack initiation and growth in viscoelastic media—II. Approximate methods of analysis. Int. J. Fract. 11(3), 369–388 (1975b). doi:10.1007/BF00033526
Schapery, R.A.: A theory of crack initiation and growth in viscoelastic media—III. Analysis of continuous growth. Int. J. Fract. 11(4), 549–562 (1975c). doi:10.1007/BF00116363
Seidel, G.D.: A model for predicting the evolution of damage in the plastic bonded explosive LX17. M.Sc. thesis, Texas A&M University (2002)
Souza, F.V.: Modelo multi-escala para análise estrutural de compósitos viscoelásticos susceptíveis a dano. M.Sc. thesis, Universidade Federal do Ceará (2005). In Portuguese
Souza, F.V.: Multiscale modeling of impact on heterogeneous viscoelastic solids with evolving microcracks. Ph.D. dissertation, University of Nebraska–Lincoln (2009)
Souza, F.V., Allen, D.H.: Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks. Int. J. Numer. Methods Eng. (2009, to appear)
Souza, F.V., Allen, D.H., Kim, Y.R.: Multiscale model for predicting damage evolution in composites due to impact loading. Compos. Sci. Technol. 68(13), 2624–2634 (2008). doi:10.1016/j.compscitech.2008.04.043. Directions in Damage and Durability of Composite Materials, with regular papers
Subramaniam, K.V., Nian, W., Andreopoulos, Y.: Blast response simulation of an elastic structure: Evaluation of the fluid-structure interaction effect. Int. J. Impact Eng. 36(7), 965–974 (2009). doi:10.1016/j.ijimpeng.2009.01.001
Talreja, R.: Multi-scale modeling in damage mechanics of composite materials. J. Mater. Sci. 41(20), 6800–6812 (2006). doi:10.1007/s10853-006-0210-9
Tekalur, S.A., Bogdanovich, A.E., Shukla, A.: Shock loading response of sandwich panels with 3-D woven E-glass composite skins and stitched foam core. Compos. Sci. Technol. 69(6), 736–753 (2008). doi:10.1016/j.compscitech.2008.03.017, ISSN 0266-3538
Wei, J., Dharani, L.R.: Fracture mechanics of laminated glass subjected to blast loading. Theor. Appl. Fract. Mech. 44(2), 157–167 (2005). doi:10.1016/j.tafmec.2005.06.004
Yoon, C., Allen, D.H.: Damage dependent constitutive behavior and energy release rate for a cohesive zone in a thermoviscoelastic solid. Int. J. Fract. 96(1), 55–74 (1999). doi:10.1023/A:1018601004565
Zocher, M.A., Groves, S.E., Allen, D.H.: A three-dimensional finite element formulation for thermoviscoelastic orthotropic media. Int. J. Numer. Methods Eng. 40(12), 2267–2288 (1997). doi:10.1002/(SICI)1097-0207(19970630)40:12<2267::AID-NME156>3.0.CO;2-P