Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2013005506
pages 543-563

A TWO-SCALE STRONG DISCONTINUITY APPROACH FOR EVOLUTION OF SHEAR BANDS UNDER DYNAMIC IMPACT LOADS

Alireza Tabarraei
Department of Mechanical Engineering, University of North Carolina at Charlotte, 9201 University City Blvd., Charlotte, North Carolina 28223-0001, USA
Jeong-Hoon Song
University of Colorado Boulder
Haim Waisman
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA

ABSTRACT

A micro-macro two-scale method for modeling adiabatic shear bands in rate-dependent materials is presented. The phantom node method, which is a variant of the extended finite element method is used to model the shear band at the macroscale. The key contribution is the development of a micromodel which allows the extraction of tangential and normal traction-separation laws, i.e., cohesive laws. These extracted rate-dependent cohesive laws are then injected back into the macro scale to accurately model the postlocalization behavior. The results show good accuracy as compared to very fine finite element meshes but are orders of magnitude faster. Hence the scheme is attractive when tracking of shear bands is of greater importance than microscopic behavior.

REFERENCES

  1. Anand, L., Kim, K. H., and Shawki, T. G., Onset of shear localization in viscoplastic solids. DOI: 10.1016/0022-5096(87)90045-7

  2. Areias, P. M. A. and Belytschko, T., Two-scale shear band evolution by local partition of unity. DOI: 10.1002/nme.1589

  3. Areias, P. M. A. and Belytschko, T., Two-scale method for shear bands: Thermal effects and variable bandwidth. DOI: 10.1002/nme.2028

  4. Armero, F. and Garikipati, K., An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. DOI: 10.1016/0020-7683(95)00257-X

  5. Bai, Y. L., Thermo-plastic instability in simple shear. DOI: 10.1016/0022-5096(82)90029-1

  6. Batra, R. C. and Ko, K. I., An adaptive mesh refinement technique for the analysis of shear bands in plane strain compression of a thermoviscoplastic solid. DOI: 10.1007/BF00363993

  7. Bayliss, A., Belytschko, T., Kulkarni, M., and Lott-Crumpler, D. A., On the dynamics and the role of imperfections for localization in thermo-viscoplastic materials. DOI: 10.1088/0965-0393/2/5/001

  8. Bazant, Z. P., Belytschko, T. B., and Chang, T.-P., Continuum theory for strain-softening. DOI: 10.1061/(ASCE)0733-9399(1984)110:12(1666)

  9. Belytschko, T. and Black, T., Elastic crack growth in finite elements with minimal remeshing. DOI: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S

  10. Belytschko, T. and Fish, J., Numerical studies of two-dimensional shear bands with the spectral overlay on finite elements.

  11. Belytschko, T., Fish, J., and Engelman, B. E., A finite element with embedded localization zones. DOI: 10.1016/0045-7825(88)90180-6

  12. Belytschko, T., Fish, J., and Bayliss, A., The spectral overlay on the finite element solutions with high gradients.

  13. Belytschko, T., Moran, B., and Kulkarni, M., On the crutial role of imperfections in quasi-static viscoplastic solutions. DOI: 10.1115/1.2897246

  14. Belytschko, T., Liu, W. K., and Moran, B., Nonlinear Finite Elements for Continua and Structures.

  15. Belytschko, T., Chen, H., Xu, J., and Zi, G., Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. DOI: 10.1002/nme.941

  16. Coleman, B. D. and Hodgdon, M. L., On shear bands in ductile materials. DOI: 10.1007/BF00251732

  17. de Borst, R. and Sluys, L. J., Localisation in a cosserat continuum under static and dynamic loading conditions. DOI: 10.1016/0045-7825(91)90185-9

  18. Guduru, P. R., Ravichandran, G., and Rosakis, A. J., Observations of transient high temperature vortical microstructures in solids during adiabatic shear banding.

  19. Hansbo, A., and Hansbo, P., A finite element method for the simulation of strong and weak discontinuities in solid mechanics. DOI: 10.1016/j.cma.2003.12.041

  20. Hartley, K. A., Duffy, J., and Hawley, R. H., Measurement of the temperature profile during shear band formation in steels deforming at high strain rates. DOI: 10.1016/0022-5096(87)90009-3

  21. Jun, S. and Im, S., Multiple-scale meshfree adaptivity for simulation of adiabatic shear band formation. DOI: 10.1007/s004660050474

  22. Khoei, A. R., Tabarraei, A., and Gharehbaghi, S. A., H-adaptive mesh refinement for shear band localization in elasto-plasticity cosserat continuum. DOI: 10.1016/S1007-5704(03)00126-6

  23. Lemonds, J. and Needleman, A., Finite element analysis of shear localization in rate and temperature dependent solids. DOI: 10.1016/0167-6636(86)90039-6

  24. Li, S., Liu, W. K., Qian, D., Guduru, P. R., and Rosakis, A. J., Adiabatic shear band propagation and micro-structure of adiabatic shear band.

  25. Li, S., Liu, W. K., Rosakis, A. R., Belytschko, T., and Hao, W., Mesh-free galerkin simulations of dynamic shear band propagation and failure mode transition. DOI: 10.1016/S0020-7683(01)00188-3

  26. Menouillard, T., R&#233;thor&#233;, J., Combescure, A., and Bung, H., Efficient explicit time stepping for the extended finite element method (x-fem). DOI: 10.1002/nme.1718

  27. Mo&#235;s, N., Dolbow, J., and Belytschko, T., A finite element method for crack growth without remeshing. DOI: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J

  28. Needleman, A., Material rate dependence and mesh sensitivity in localization problems. DOI: 10.1016/0045-7825(88)90069-2

  29. Needleman, A. and Tvergaard, V., Finite element analysis of localization in plasticity.

  30. Oliver, J., Modelling strong discontinuities in solid mechanics via strain softening constituitive equations, Part 1: fundamentals. DOI: 10.1002/(SICI)1097-0207(19961115)39:21<3575::AID-NME65>3.0.CO;2-E

  31. Oliver, J., Modelling strong discontinuities in solid mechanics via strain softening constituitive equations, Part 2: Numerical simulation. DOI: 10.1002/(SICI)1097-0207(19961115)39:21<3601::AID-NME64>3.0.CO;2-4

  32. Ortiz, M., Leroy, Y., and Needleman, A., A finite element method for localized failure analysis. DOI: 10.1016/0045-7825(87)90004-1

  33. Ortiz, M. and Pandolfi, A., Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. DOI: 10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7

  34. Peirce, D., Shih, C. F., and Needleman, A., A tangent modulus method for rate dependent solids. DOI: 10.1016/0045-7949(84)90033-6

  35. Rabczuk, T., Areias, P. M. A., and Belytschko, T., A simplified mesh-free method for shear bands with cohesive surfaces. DOI: 10.1002/nme.1797

  36. Samaniego, E. and Belytschko, T., Continuum discontinuum modelling of shear bands. DOI: 10.1002/nme.1256

  37. Simo, J. C., Oliver, J., and Armero, F., An analysis of strong discontinuities induced by strain-softening in rateindependent inelastic solids. DOI: 10.1007/BF00372173

  38. Song, J.-H., Areias, P. M. A., and Belytschko, T., A method for dynamic crack and shear band propagation with phantom nodes. DOI: 10.1002/nme.1652

  39. Teng, X., Wierzbicki, T., and Couque, H., On the transition from adiabatic shear banding to fracture. DOI: 10.1016/j.mechmat.2006.03.001

  40. Thomas, T. Y., Plastic Flow and Fracture of Solids.

  41. Timothy, S. P. and Hutchings, I. M., Initiation and growth of microfractures along adiabatic shear bands in ti6al4v.

  42. Tvergaard, V., Needleman, A., and Lo, K. K., Flow localization in the plane strain tensile test. DOI: 10.1016/0022-5096(81)90019-3

  43. Wright, T. W., The Physics and Mathematics of Adiabatic Shear Bands.

  44. Zhang, Z. and Clifton, R. J., Shear band propagation from a crack tip subjected to mode ii shear wave loading. DOI: 10.1016/j.ijsolstr.2006.09.030

  45. Zhou, M., Ravichandran, G., and Rosakis, A. J., Dynamically propagating shear bands in numerical impact-loaded prenotched plates-II numerical simulations.


Articles with similar content:

FREQUENCY SHIFTS INDUCED BY LARGE DEFORMATIONS IN PLANAR PANTOGRAPHIC CONTINUA
Nanoscience and Technology: An International Journal, Vol.6, 2015, issue 2
Dionisio Del Vescovo, Antonio Battista, Nicola Luigi Rizzi, Christian Cardillo, Emilio Turco
A MULTISCALE COMPUTATIONAL METHOD FOR 2D ELASTOPLASTIC DYNAMIC ANALYSIS OF HETEROGENEOUS MATERIALS
International Journal for Multiscale Computational Engineering, Vol.12, 2014, issue 2
Hongwu Zhang, Hui Liu
AN XFEM BASED MULTISCALE APPROACH TO FRACTURE OF HETEROGENEOUS MEDIA
International Journal for Multiscale Computational Engineering, Vol.11, 2013, issue 6
Mirmohammadreza Kabiri, Franck J. Vernerey
NUMERICAL CALCULATION OF ACOUSTIC PROPERTIES OF LINERS
TsAGI Science Journal, Vol.43, 2012, issue 4
Aleksandr Aleksandrovich Siner, S. Myakotnikova
AN ADAPTIVE DOMAIN DECOMPOSITION PRECONDITIONER FOR CRACK PROPAGATION PROBLEMS MODELED BY XFEM
International Journal for Multiscale Computational Engineering, Vol.11, 2013, issue 6
Haim Waisman, Luc Berger-Vergiat