1. Date of download: 10/16/2017
Copyright © ASME. All rights reserved.
From: Using Damage Delocalization to Model Localization Phenomena in Bammann-Chiesa-Johnson Metals
J. Eng. Mater. Technol. 2012;134(4): doi: /
Figure Legend:
Two dimensional scheme of nonlocal interaction between material points within a vicinity of length l

2. Date of download: 10/16/2017
Copyright © ASME. All rights reserved.
From: Using Damage Delocalization to Model Localization Phenomena in Bammann-Chiesa-Johnson Metals
J. Eng. Mater. Technol. 2012;134(4): doi: /
Figure Legend:
Discontinuity surface S toward a finite body

3. Date of download: 10/16/2017
Copyright © ASME. All rights reserved.
From: Using Damage Delocalization to Model Localization Phenomena in Bammann-Chiesa-Johnson Metals
J. Eng. Mater. Technol. 2012;134(4): doi: /
Figure Legend:
Deformed mesh for the strain in the vertical direction (displacement magnification factor: 50) for the local BCJ model. Note the presence of two different shear bands due to the presence of the imperfection and oriented at 45 deg with respect to the loading axis. One of them ends on the lateral traction-free surface on both sides, while the other one ends on a free surface on one side and on upper surface subject to the prescribed displacement on the other side. In fact, we choose a rectangular mesh rather than a square one to force one of the shear bands to end on free surfaces on both sides contrary to the other one, in order to generate a dissymmetry between the two shear bands.

4. Date of download: 10/16/2017
Copyright © ASME. All rights reserved.
From: Using Damage Delocalization to Model Localization Phenomena in Bammann-Chiesa-Johnson Metals
J. Eng. Mater. Technol. 2012;134(4): doi: /
Figure Legend:
Representation of the strain on the deformed mesh in the vertical direction for both the local (top) and nonlocal (bottom) models, respectively. Note the influence of the damage delocalization on the width of the shear bands: the shear bands in the nonlocal BCJ material are notably larger and are extended over several elements. Also remarkable from this figure is the predominance of one shear band over the other one. It is except that the system will choose one shear band during the subsequent loading and that the other one will cease developing.

5. Date of download: 10/16/2017
Copyright © ASME. All rights reserved.
From: Using Damage Delocalization to Model Localization Phenomena in Bammann-Chiesa-Johnson Metals
J. Eng. Mater. Technol. 2012;134(4): doi: /
Figure Legend:
Damage distribution in the early stage of the loading for both the local (top) and nonlocal (bottom) BCJ models, respectively. Contrary to the strain, the distribution of the damage is substantially affected by the damage nonlocality. However, the width of the shear band is less than that of two elements (of the size of the characteristic length scale); this leads to the conclusion that the damage process in the body considered may begin by the appearance of shear bands which govern void growth from the larger inhomogeneity.

6. Date of download: 10/16/2017
Copyright © ASME. All rights reserved.
From: Using Damage Delocalization to Model Localization Phenomena in Bammann-Chiesa-Johnson Metals
J. Eng. Mater. Technol. 2012;134(4): doi: /
Figure Legend:
Damage distribution in the later time of the loading for both the local (top) and nonlocal (bottom) BCJ models. Note the dramatic influence of damage delocalization on the localization of the damage in the two shear bands: the damage is now concentrated in much narrower zones and its maximum value is higher in local the BCJ material than in nonlocal one. Also remarkable from this figure is the predominance of one shear band over the other one. The width of the band is extended over almost four elements; thus, the shear band width is proportional to the length scale, which is of the size of two elements in this problem.