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Technical Briefs

An Analytical Study on the Post-Peak Structural Response

[+] Author and Article Information
Hui-Hui Dai1

Department of Mathematics, and Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, 83 TatChee Avenue, Kowloon Tong, Hong Kong SARmahhdai@cityu.edu.hk

Xiaowu Zhu

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R. China; Department of Mathematics, City University of Hong Kong, 83 TatChee Avenue, Kowloon Tong, Hong Kong SAR

Zhen Chen1

Department of Civil and Environmental Engineering, University of Missouri, Columbia, MO 65211-2200; Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, P.R. China.chenzh@missouri.edu

See http://arxiv.org/PS%5fcache/arxiv/pdf/1007/1007.5113v1.pdf

1

Corresponding authors.

J. Appl. Mech 78(4), 044501 (Apr 14, 2011) (4 pages) doi:10.1115/1.4003740 History: Received August 05, 2010; Posted March 02, 2011; Revised March 02, 2011; Published April 14, 2011; Online April 14, 2011

An analytical study is taken to investigate the relationship between material softening and structural softening through the use of a model problem in one dimension. General nonlinear constitutive relations are used. Compared with the bilinear assumptions in previous literature, we find that the nonlinear assumptions herein capture more details in the post-peak structural response. We manage to derive necessary and sufficient conditions for the occurrence of four important post-peak cases, which are often observed in experiments. In particular, our analysis reveals that the mechanism of the snap-through phenomenon is due to the convexity change in the constitutive curve of the softening part.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) One-dimensional model. (b) Stress-strain relations.

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Figure 2

Four cases of the post-peak engineering stress-strain curves

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Figure 3

(a) The constitutive curves. (b) The engineering stress-strain curves for different n.

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