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Theoretical and experimental validation of nonlinear deflection and stress responses of an internally debonded layer structure using different higher-order theories

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Abstract

In this article, two types of higher-order kinematic theories are adopted to evaluate the nonlinear bending and the stress values of the internally damaged layered composite flat panel structure numerically including the thickness stretching effect. The structural distortion is modeled by Green–Lagrange strain kinematics including all of the nonlinear higher-order strain terms to maintain the required generality. Additionally, the internal debonding between the adjacent layers is introduced via two sub-laminate approaches by maintaining the intermittent link as a priori by the continuity condition. Subsequently, the static equilibrium equations of the debonded structure under the influence of uniform mechanical loading are obtained using a variational principle and solved iteratively in association with the isoparametric finite element steps. Further, the accuracy of the derived model is established by comparing the deflection and stress values with available published results including own experimental data (three-point bend test on artificially debonded layered composite). Finally, a suitable number of numerical examples is solved using the derived higher-order nonlinear models to reveal the operational strength and effect of the debonding (size, position, and location) on the nonlinear static deflection values of the debonded structure.

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Abbreviations

\(X_1, X_2, X_3\) :

Three mutually perpendicular axes in Cartesian coordinate system

\(\bar{{u}},\bar{{v}},\bar{{w}}\) :

Displacement along the \(X_1, X_2, X_3\) coordinates

\(u_0, v_0, w_0\) :

Mid-plane displacement along \(X_1, X_2, \hbox { and } X_3\) direction

a, b, h :

Length, width, and thickness of the plate structure

\(\phi _1, \phi _{2}\) :

Rotations with respect to \(X_{2}\) and \(X_{1}\)-direction, respectively

\(\psi _1, \psi _2, \theta _1 \hbox { and } \theta _2\) :

Higher-order terms of Taylor series expansion

\(E_{X_1 }, E_{X_2}, E_{X_3 }\) :

Young’s modulus in \(X_1, X_2 \hbox { and } X_3\) direction, respectively

\(G_{X_1 X_2 }, G_{X_2 X_3 }, G_{X_1 X_3 }\) :

Shear modulus

\(\upsilon _{X_1 X_2 } =\upsilon _{X_2 X_3 } =\upsilon _{X_1 X_3}\) :

Poisson’s ratios

U :

Total strain energy

W :

Work done

\({[}k_\mathrm{l} {]}\) :

Linear elemental stiffness matrix

\({[}k_{\mathrm{nl}} {]}\) :

Nonlinear elemental stiffness matrix

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology, Rourkela, Odisha, 769008, India

    Chetan K. Hirwani & Subrata K. Panda

  2. Department of Mechanical Engineering, CVR College of Engineering, Hyderabad, India

    B. K. Patle

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  1. Chetan K. Hirwani
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Correspondence to Subrata K. Panda.

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Hirwani, C.K., Panda, S.K. & Patle, B.K. Theoretical and experimental validation of nonlinear deflection and stress responses of an internally debonded layer structure using different higher-order theories. Acta Mech 229, 3453–3473 (2018). https://doi.org/10.1007/s00707-018-2173-8

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