A state space method is proposed for analyzing surface instability of elastic layers with elastic properties varying in the thickness direction. By assuming linear elasticity with nonlinear kinematics, the governing equations for the incremental stress field from a fundamental state are derived for arbitrarily graded elastic layers subject to plane-strain compression, which lead to an eigenvalue problem. By discretizing the elastic properties into piecewise constant functions with homogeneous sublayers, a state space method is developed to solve the eigenvalue problem and predict the critical condition for onset of surface instability. Results are presented for homogeneous layers, bilayers, and continuously graded elastic layers. The state space solutions for elastic bilayers are in close agreement with the analytical solution for thin film wrinkling within the limit of linear elasticity. Numerical solutions for continuously graded elastic layers are compared to finite element results in a previous study (Lee et al., 2008, J. Mech. Phys. Solids, 56, pp. 858–868). As a semi-analytical approach, the state space method is computationally efficient for graded elastic layers, especially for laminated multilayers.
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August 2014
Research-Article
A State Space Method for Surface Instability of Elastic Layers With Material Properties Varying in Thickness Direction
Zhigen Wu,
Zhigen Wu
1
School of Civil Engineering,
e-mail: zhigenwu@hfut.edu.cn
Hefei University of Technology
,Hefei, Anhui 230009
, China
e-mail: zhigenwu@hfut.edu.cn
1Corresponding author.
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Jixiang Meng,
Jixiang Meng
School of Civil Engineering,
Hefei University of Technology
,Hefei, Anhui 230009
, China
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Yihua Liu,
Yihua Liu
School of Civil Engineering,
Hefei University of Technology
,Hefei, Anhui 230009
, China
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Hao Li,
Hao Li
School of Civil Engineering,
Hefei University of Technology
,Hefei, Anhui 230009
, China
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Rui Huang
Rui Huang
1
Department of Aerospace Engineering
and Engineering Mechanics,
e-mail: ruihuang@mail.utexas.edu
and Engineering Mechanics,
University of Texas
,Austin, TX 78712
e-mail: ruihuang@mail.utexas.edu
1Corresponding author.
Search for other works by this author on:
Zhigen Wu
School of Civil Engineering,
e-mail: zhigenwu@hfut.edu.cn
Hefei University of Technology
,Hefei, Anhui 230009
, China
e-mail: zhigenwu@hfut.edu.cn
Jixiang Meng
School of Civil Engineering,
Hefei University of Technology
,Hefei, Anhui 230009
, China
Yihua Liu
School of Civil Engineering,
Hefei University of Technology
,Hefei, Anhui 230009
, China
Hao Li
School of Civil Engineering,
Hefei University of Technology
,Hefei, Anhui 230009
, China
Rui Huang
Department of Aerospace Engineering
and Engineering Mechanics,
e-mail: ruihuang@mail.utexas.edu
and Engineering Mechanics,
University of Texas
,Austin, TX 78712
e-mail: ruihuang@mail.utexas.edu
1Corresponding author.
Manuscript received March 24, 2014; final manuscript received April 17, 2014; accepted manuscript posted April 22, 2014; published online May 5, 2014. Editor: Yonggang Huang.
J. Appl. Mech. Aug 2014, 81(8): 081003 (10 pages)
Published Online: May 5, 2014
Article history
Received:
March 24, 2014
Revision Received:
April 17, 2014
Accepted:
April 22, 2014
Citation
Wu, Z., Meng, J., Liu, Y., Li, H., and Huang, R. (May 5, 2014). "A State Space Method for Surface Instability of Elastic Layers With Material Properties Varying in Thickness Direction." ASME. J. Appl. Mech. August 2014; 81(8): 081003. https://doi.org/10.1115/1.4027464
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