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TECHNICAL PAPERS

A Method to Generate Damage Functions for Quasi-Brittle Solids

[+] Author and Article Information
D. Cope

Departmemt of Mathematics,  North Dakota State University, Fargo, ND 58105davis.cope@ndsu.edu

S. Yazdani1

Department of Civil Engineering and Construction,  North Dakota State University, Fargo, ND 58105frank.yazdani@ndsu.edu

J. W. Ju

Department of Civil and Environmental Engineering,  University of California, Los Angeles, CA 90095juj@ucla.edu

1

To whom all correspondence should be addressed.

J. Appl. Mech 72(4), 553-557 (Oct 13, 2004) (5 pages) doi:10.1115/1.1935524 History: Received May 07, 2004; Revised October 13, 2004

In continuum damage mechanics theories, damage functions are identified based on experimental records. These functions also serve as strain hardening-softening functions similar to the conventional plasticity formulations. In a class of damage theories described in this paper it will be shown that if care is not taken, internal contradictions will arise as manifested by a snapback in the strain–stress space. This paper establishes a formal method by which different damage functions can consistently be developed leading to no snap-back in the solution.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Normalized damage function t(k)∕ft vs normalized k∕k* for logarithmic and bilinear damage functions

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Figure 2

Stress–strain curves for logarithmic and bilinear damage functions for η=0.08, 0.10 (E0εu∕ft=e)

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Figure 3

Schematic representation of Eq. 14

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Figure 4

Normalized stress–strain curves in uniaxial tension from Example 1. Initial slopes EN=E0εu∕ft=1.1, 1.25, 1.5, 2.0, 2.718 (Ortiz), and 4.0.

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Figure 5

Normalized stress–strain curves in uniaxial tension from Example 2. Model function ln(1+xp) with p=1 (Ortiz), 1.5, 2, 4, 8.

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Figure 6

Normalized stress–strain curves in uniaxial tension from Example 2. Model function (ln(1+x))q with q=1 (Ortiz), 2, 4, 8.

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