The paper is focused on the multi-scale modeling of shear banding in two-pha se linear elastic period-ically layered strip with damaging interfaces.A two-dimensional layered strip is considered subjected to transverse shear and is assumed to have afinitethickness along the direction of the layers and an infinite extension along the direction perpendicular to layering.The strip is analyzed as asecond-gradi ent continuum resulting from asecond-order homogenization procedure developed by the Authors,here specialized to the case of layered materials.This analysis is also aimed to understand the influence on the strain localization and post-peak structural response of the displacement boun dary conditions prescribed at the strip edges. To this end,afirstmodel representative of the strip with warping allowed at the edges is analyzed in which the strain localization process is obtained as aresults of abifurc ation in analogy to the approach by Chambon et al. (1998). A second model is analyzed in which the warping of the edge is inhibited and the damage propagates from the center of the specimen without exhibiting bifurcation phenomena. For this latter case the effects of apossible interactio nbetween the shear band and the boundary shear layer are considered,which are influencedmainly by the characteristic lengths of the model and the strip length.For realistic values of the relevan tparameters it is shown that the boundary conditions have a small effe cts on the elastic response and on the overall strength of the model.Conversely, the boundary conditions have asignificanteffe ct on the shear band location,the post- peak response and the structural brittleness.Since the model parameters directly depend on the material microstructure as a result of the homogenization process,both the extensio nof the shear band and the occurrence of snap-back in the post-peak phase may be controlled in terms of the constitutive parameters and of the geometry of the phases.
Multi-scale strain-localization analysis of a layered strip with debonding interfaces
Bacigalupo A.;GAMBAROTTA, LUIGI
2013-01-01
Abstract
The paper is focused on the multi-scale modeling of shear banding in two-pha se linear elastic period-ically layered strip with damaging interfaces.A two-dimensional layered strip is considered subjected to transverse shear and is assumed to have afinitethickness along the direction of the layers and an infinite extension along the direction perpendicular to layering.The strip is analyzed as asecond-gradi ent continuum resulting from asecond-order homogenization procedure developed by the Authors,here specialized to the case of layered materials.This analysis is also aimed to understand the influence on the strain localization and post-peak structural response of the displacement boun dary conditions prescribed at the strip edges. To this end,afirstmodel representative of the strip with warping allowed at the edges is analyzed in which the strain localization process is obtained as aresults of abifurc ation in analogy to the approach by Chambon et al. (1998). A second model is analyzed in which the warping of the edge is inhibited and the damage propagates from the center of the specimen without exhibiting bifurcation phenomena. For this latter case the effects of apossible interactio nbetween the shear band and the boundary shear layer are considered,which are influencedmainly by the characteristic lengths of the model and the strip length.For realistic values of the relevan tparameters it is shown that the boundary conditions have a small effe cts on the elastic response and on the overall strength of the model.Conversely, the boundary conditions have asignificanteffe ct on the shear band location,the post- peak response and the structural brittleness.Since the model parameters directly depend on the material microstructure as a result of the homogenization process,both the extensio nof the shear band and the occurrence of snap-back in the post-peak phase may be controlled in terms of the constitutive parameters and of the geometry of the phases.
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