# Semi-layerwise analysis of laminated plates with nonsingular delamination-The theorem of autocontinuity

Research output: Contribution to journalArticle

37 Citations (Scopus)

### Abstract

The proposed semi-layerwise approach captures the mechanical behavior of delaminated composite plates using four equivalent single layers independently of the lay-up. Two equivalent single layers are applied for both the top and bottom parts of a delaminated plate. The updated version of the system of exact kinematic conditions formulates the continuity of the in-plane displacements between the neighboring layers, the location of the global reference plane of the plate and - as important additions compared to previous papers - the continuity of shear strains, their derivatives and curvatures, respectively. The method is demonstrated using the first-, second- and third-order plate theories. As examples, simply supported delaminated plates are considered.The continuity between the delaminated and undelaminated plate regions is established through the theorem of autocontinuity. The J-integral is calculated along the straight delamination front and compared to the results of the virtual crack closure technique. The results indicate that the first- and third-order plate theories provide the best solutions, and give good approximation even in those cases when the previous models failed, i.e., when the delamination is asymmetrically placed between two layers and it is close to the free surface of the plate.

Original language English 1344-1371 28 Applied Mathematical Modelling 40 2 https://doi.org/10.1016/j.apm.2015.06.037 Published - Jan 15 2016

### Fingerprint

Laminated Plates
Delamination
Crack closure
Shear strain
Theorem
Plate Theory
Kinematics
Derivatives
Composite materials
Crack Closure
J-integral
Composite Plates
Mechanical Behavior
Free Surface
Straight
Curvature
First-order
Derivative
Approximation

### Keywords

• Delamination
• Energy release rate
• Mixed mode II/III fracture
• Theoreom of autocontinuity
• Third-order plate theory

### ASJC Scopus subject areas

• Applied Mathematics
• Modelling and Simulation

### Cite this

In: Applied Mathematical Modelling, Vol. 40, No. 2, 15.01.2016, p. 1344-1371.

Research output: Contribution to journalArticle

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