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

Abstract

Available online xxxKeywords: Delamination Mixed mode II/III fracture Energy release rate Third-order plate theory Theoreom of autocontinuity a b s t r a c tThe 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 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.

Linear and Nonlinear Dynamic Analyses of Sandwich Panels with Face Sheet‐to‐Core Debonding

“…As found, it is a reason of parametrically induced vibration of delaminated beams and plates [35][36][37]. Other studies confirmed the efficiency of the LW-based finite element models compared to those using the ESL approach [38,39] and showed that such models provide a stress recovery for localized effects [40].…”

Analytical solution of some delamination scenarios in thick structural sandwich plates

“…However, the stress continuity results in a locking (over-constraining) problem in delaminated plates [105,106]. For the TSDT theory, one more set of conditions is reasonable to introduce.…”

“…Figure 1(a) shows the deformation of the cross sections in the vicinity of the delamination tip in the X -Z plane for the core failure scenario (Scenario I). In the Y -Z plane, the deformation is similar [105,106]. The top and bottom facesheets are captured by an ESL and two ESLs are applied to the core.…”

“…Previously, similar models have already been developed and applied to delaminated composite plates by the author using the Classical Laminated Plate Theory (CLPT) [98], the First-(FSDT) [99], the Second-(SSDT) [100,101] and Third-Order Shear Deformation Theories (TSDT) [102] as well as Reddy third-order theory [103,104]. The first attempts involved the application of two equivalent single layers (ESL) over the thickness, later refined models have been created by using four ESLs [105,106] leading to more accurate results for plates, wherein the delamination is close to the free boundary surface. The mechanical model developed previously is applied to create a model for delaminated sandwich plates.…”

Analyses of Delamination in Functionally Graded Multilayered Beams

“…Functionally graded materials are novel composites whose composition changes continuously within the solid. In this way, concentrations of stresses between different constituent materials are avoided in contrast to layered composites [7], [8], [9]. By variation of their properties with specific gradients along spatial coordinates, functionally graded materials can be designed to satisfy different requirements in different parts of a member.…”