# Antiplane-inplane shear mode delamination between two second-order shear deformable composite plates

Research output: Contribution to journalArticle

11 Citations (Scopus)

### Abstract

The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton's principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.

Original language English 259-282 24 Mathematics and Mechanics of Solids 22 3 https://doi.org/10.1177/1081286515581871 Published - Mar 1 2017

### Fingerprint

Anti-plane Shear
Composite Plates
Delamination
Plate Theory
Composite materials
J-integral
Elasticity
Kinematics
Hamilton's Principle
Laminated Plates
Linear Elasticity
State-space Model
Thin Layer
Governing equation
Finite Element
Formulation

### Keywords

• energy release rate
• J -integral
• Lévy plate formulation
• mixed-mode II/III
• second-order plate
• unsymmetric delamination

### ASJC Scopus subject areas

• Mathematics(all)
• Materials Science(all)
• Mechanics of Materials

### Cite this

In: Mathematics and Mechanics of Solids, Vol. 22, No. 3, 01.03.2017, p. 259-282.

Research output: Contribution to journalArticle

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abstract = "The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton's principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using L{\'e}vy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.",
keywords = "energy release rate, J -integral, L{\'e}vy plate formulation, mixed-mode II/III, second-order plate, unsymmetric delamination",
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AU - Szekrényes, A.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton's principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.

AB - The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton's principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.

KW - energy release rate

KW - J -integral

KW - Lévy plate formulation

KW - mixed-mode II/III

KW - second-order plate

KW - unsymmetric delamination

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