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Research Papers

A New Class of Damage Variables in Continuum Damage Mechanics

[+] Author and Article Information
George Z. Voyiadjis

 Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USA; Adjunct Professor Department of Civil and Environmental Engineering,  Hanyang University, World Class University Project, Seoul, Republic of Koreavoyiadjis@eng.lsu.edu

Peter I. Kattan

 Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USApkattan@tedata.net.jo

J. Eng. Mater. Technol 134(2), 021016 (Mar 27, 2012) (10 pages) doi:10.1115/1.4004422 History: Received March 07, 2010; Revised May 27, 2011; Published March 27, 2012; Online March 27, 2012

In this work various new proposed damage variables are introduced, examined and compared. Only the scalar case pertaining to isotropic damage is investigated here. Several types of new damage variables are proposed as follows: (1) damage variables that are defined in terms of cross-sectional area, (2) damage variables that are defined in terms of the elastic modulus or stiffness, and (3) composite damage variables that are defined in terms of two parameters relating to both cross-sectional area and stiffness. However, the generalization to tensors and general states of deformation and damage may be a straightforward process but is beyond the scope of this work. The damage variables introduced in this work can be applied to elastic materials including homogeneous materials like metals and heterogeneous materials like composite laminates. In the second part of this work, higher-order strain energy forms are proposed. It is seen that a specific nonlinear stress-strain relationship is associated with each higher-order strain energy form. These higher order strain energy forms along with some of the proposed damage variables are used in trying to lay the theoretical groundwork for the design of undamageable materials, i.e., materials that cannot be damaged where the value of the damage variable remains zero throughout the deformation process.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Damaged and effective undamaged configurations

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Figure 2

Relation between the damage variable and M.

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Figure 3

Damaged and effective moduli of elasticity

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Figure 4

Relation between the two damage variables in the case of elastic strain equivalence

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Figure 5

Relation between the two damage variables for the case of elastic energy equivalence

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Figure 6

Relation between the two damage variables in the case of elastic strain equivalence

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Figure 7

Relation between the two damage variables in the case of elastic strain equivalence

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Figure 8

Relation between the two damage variables in the case of elastic strain equivalence

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Figure 9

Relation between the two damage variables in the case of elastic energy equivalence

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Figure 10

Relation between the two damage variables in the case of elastic energy equivalence

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Figure 11

Relation between the two damage variables in the case of elastic energy equivalence

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Figure 12

Relation between l1 and the ratio of the stresses M

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Figure 13

Relation between l2 and the ratio of the stresses M

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