Free Edge Problem for Bonded Orthotropic Elastic Layers

2009 ◽  
pp. 156-156-21
Author(s):  
S Kadioglu ◽  
F Erdogan
Keyword(s):  
Free Edge ◽  
Edge Problem ◽  
Elastic Layers

Interfacial Thermal Stresses in Layered Structures: The Stepped Edge Problem

1995 ◽  
Vol 117 (2) ◽  
pp. 153-158 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Stress Field ◽  
Elastic Layer ◽  
Thermal Stresses ◽  
Free Edge ◽  
Multilayered Structure ◽  
Local Geometry ◽  
Temperature Load ◽  
Edge Problem ◽  
Stress Functions ◽  
Multilayer Substrate

The intense, localized stress field produced by a temperature load in a multilayered structure may be significantly affected by the local geometry of the free edge. We examine here the stepped edge problem associated with bonding an elastic layer (silicon chip) to a single or multilayer substrate with a slightly larger length. Stress functions are introduced in various rectangular regions and the continuity of tractions are enforced across all inter-region boundaries. Furthermore, continuity of displacements is enforced across the junction of the two segments of the base laminate. The analysis results indicate that even a minute protrusion of the edge of the base laminate relative to the attached chip may cause significant changes in the peeling and shearing stresses in the end region of the interface.

Intersection of Interface Crack Front with Free Edge

2014 ◽  
Vol 627 ◽  
pp. 225-228 ◽  
Author(s):  
Alex Møberg ◽  
Michal K. Budzik ◽  
Henrik M. Jensen
Keyword(s):  
Interface Crack ◽  
Crack Front ◽  
Fracture Criterion ◽  
Free Edge ◽  
Interface Fracture ◽  
Special Focus ◽  
Type Specimens ◽  
Elastic Mismatch ◽  
Beam Type ◽  
Elastic Layers

Delamination in layered materials is analyzed in a fracture mechanical framework. The work deals with quasi-static propagation of crack fronts along planar interfaces between different isotropic, elastic layers. Special focus is here on local effects at the sides of the layers which are assumed to be stress free. The interface crack front meets the free sides of the specimen at an angle which depends on the elastic mismatch in the system. Finite element calculations allowing the shape of the crack front to be arbitrary are carried out for double cantilever beam type specimens. An iterative procedure is formulated which adjusts the shape of the crack front so that an interface fracture criterion is satisfied locally along the front. Apart from the overall shape of the crack front, the angle of intersection with the free sides is in particular determined numerically by this procedure. Comparisons with analytical formulations and experimental results are performed.

Nonlinear Theory for Flexural Motions of Thin Elastic Plate, Part 3: Numerical Evaluation of Boundary Layer Solutions

1982 ◽  
Vol 49 (2) ◽  
pp. 409-416
Author(s):  
N. Sugimoto
Keyword(s):  
Boundary Layer ◽  
Stress Singularity ◽  
Free Edge ◽  
Thin Elastic Plate ◽  
Normal Stresses ◽  
Interior Region ◽  
First Order ◽  
Plausible Values ◽  
Bending Stresses ◽  
Order Stress

The boundary layer solutions previoulsy obtained in Part 2 of this series for the cases of the built-in edge and the free edge are evaluated numerically. For the built-in edge, a characteristic penetration depth of the boundary layer toward the interior region is given by 0.13 εh, εh being the normalized thickness of the plate, while for the free edge, it is given by 0.32 εh. Thus the boundary layer for the free edge penetrates more deeply toward the interior region than that for the built-in edge. The first-order stress distribution in each boundary layer is displayed. For the built-in edge, the stress singularity appears on the edge. It is shown that, in the boundary layer, the shearing and normal stresses become comparable with the bending stresses. Similarly for the free edge, the shearing stress also becomes comparable with the twisting stress. It should be remarked that, in the boundary layer, the shearing or the normal stress plays a primarily important role as the bending or the twisting stress. But the former decays toward the interior region and remains higher order than the latter. Finally owing to these numerical results, the coefficients involved in the “reduced” boundary conditions for the built-in edge are evaluated for the various plausible values of Poisson’s ratio.

scholarly journals Micro-mechanical investigation of railway ballast behavior under cyclic loading in a box test using DEM: effects of elastic layers and ballast types

2019 ◽  
Vol 21 (4) ◽  
Author(s):  
Nishant Kumar ◽  
Bettina Suhr ◽  
Stefan Marschnig ◽  
Peter Dietmaier ◽  
Christof Marte ◽  
...  
Keyword(s):  
Cyclic Loading ◽  
Early Stage ◽  
Damage Model ◽  
Simulation Models ◽  
Railway Track ◽  
Maintenance Cost ◽  
Particle Movement ◽  
Railway Ballast ◽  
Elastic Layers ◽  
The Impact

Abstract Ballasted tracks are the commonly used railway track systems with constant demands for reducing maintenance cost and improved performance. Elastic layers are increasingly used for improving ballasted tracks. In order to better understand the effects of elastic layers, physical understanding at the ballast particle level is crucial. Here, discrete element method (DEM) is used to investigate the effects of elastic layers – under sleeper pad ($$\text {USP}$$USP) at the sleeper/ballast interface and under ballast mat ($$\text {UBM}$$UBM) at the ballast/bottom interface – on micro-mechanical behavior of railway ballast. In the DEM model, the Conical Damage Model (CDM) is used for contact modelling. This model was calibrated in Suhr et al. (Granul Matter 20(4):70, 2018) for the simulation of two different types of ballast. The CDM model accounts for particle edge breakage, which is an important phenomenon especially at the early stage of a tamping cycle, and thus essential, when investigating the impact of elastic layers in the ballast bed. DEM results confirm that during cyclic loading, $$\text {USP}$$USP reduces the edge breakage at the sleeper/ballast interface. On the other hand, $$\text {UBM}$$UBM shows higher particle movement throughout the ballast bed. Both the edge breakage and particle movement in the ballast bed are found to influence the sleeper settlement. Micro-mechanical investigations show that the force chain in deeper regions of the ballast bed is less affected by $$\text {USP}$$USP for the two types of ballast. Conversely, dense lateral forces near to the box bottom were seen with $$\text {UBM}$$UBM. The findings are in good (qualitative) agreement with the experimental observations. Thus, DEM simulations can aid to better understand the micro-macro phenomena for railway ballast. This can help to improve the track components and track design based on simulation models taking into account the physical behavior of ballast. Graphical Abstract

Reduction of Free-Edge Stress Concentration

1985 ◽  
Vol 52 (4) ◽  
pp. 801-805 ◽  
Author(s):  
P. R. Heyliger ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Finite Element Model ◽  
Three Dimensional ◽  
Element Model ◽  
Free Edge ◽  
Shear Stresses ◽  
Normal Stresses ◽  
Interlaminar Shear ◽  
Three Dimensional Elasticity

A quasi-three dimensional elasticity formulation and associated finite element model for the stress analysis of symmetric laminates with free-edge cap reinforcement are described. Numerical results are presented to show the effect of the reinforcement on the reduction of free-edge stresses. It is observed that the interlaminar normal stresses are reduced considerably more than the interlaminar shear stresses due to the free-edge reinforcement.

Bounds on the Maximum Contact Stress of an Indented Elastic Layer

1971 ◽  
Vol 38 (3) ◽  
pp. 608-614 ◽  
Author(s):  
Y. C. Pao ◽  
Ting-Shu Wu ◽  
Y. P. Chiu
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Elastic Layer ◽  
Theory Of Elasticity ◽  
Contact Conditions ◽  
Practical Applications ◽  
Method Of Solution ◽  
Elastic Layers ◽  
Maximum Contact ◽  
Contact Stress Distribution

This paper is concerned with the plane-strain problem of an elastic layer supported on a half-space foundation and indented by a cylinder. A study is presented of the effect of the contact condition at the layer-foundation interface on the contact stresses of the indented layer. For the general problem of elastic indenter or elastic foundation, the integral equations governing the contact stress distribution of the indented layer derived on the basis of two-dimensional theory of elasticity are given and a numerical method of solution is formulated. The limiting contact conditions at the layer-foundation interface are then investigated by considering two extreme cases, one with the indented layer in frictionless contact with the half space and the other with the indented layer rigidly adhered to the half space. Graphs of the bounds on the maximum normal stress occurring in indented elastic layers for the cases of rigid cylindrical indenter and rigid half-space foundation are obtained for possible practical applications. Some results of the elastic indenter problem are also presented and discussed.

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