scholarly journals A Traction-Free Model for the Tensile Stiffness and Bending Stiffness of Laminated Ribbons of Flexible Electronics

2019 ◽  
Vol 86 (5) ◽  
Author(s):  
Shizhen Yin ◽  
Yewang Su
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Flexible Electronics ◽  
Mechanical Analysis ◽  
Bending Stiffness ◽  
Stress Model ◽  
Tensile Stiffness ◽  
Free Model ◽  
Strain Model ◽  
Plane Strain Model

Laminated ribbons have been widely adopted for structures of flexible electronics to simultaneously achieve the electronic functions and mechanical performances. Their effective tensile stiffness and bending stiffness, which are extensively used as fundamental parameters in the mechanical analysis, are usually obtained by the plane-strain hypothesis for simplicity. However, it is found that the practical condition is usually closer to the traction free, even for the cases with a relatively large width. Here, a traction-free model is proposed to analytically obtain the effective tensile stiffness and bending stiffness of laminated ribbons, which can be used directly in the mechanical analysis of flexible electronics. The prediction of the traction-free model agrees very well with the precise result obtained by 3D finite element analysis (FEA) for the cases that are in the range of structure designs of flexible electronics. It is found that the tensile/bending stiffness of traction-free model is between the plane-stress model and plane-strain model, but is closer to the plane-stress model. The use of the plane-strain model sometimes may yield a considerable error in the mechanical analysis of flexible electronics. The parameter study shows that this model is very important for the problems with advanced materials, such as metamaterials with negative Poisson's ratio. This work provides a theoretical basis for the mechanical analysis of flexible electronics.

A New Embedded-Zone Method on Computation of the Transverse Elastic Properties of Fiber-Reinforced Composites

2005 ◽  
Author(s):  
Xiaochun Wang
Keyword(s):  
Plane Strain ◽  
Elastic Properties ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Zone Method ◽  
Two Dimension ◽  
The Matrix ◽  
Strain Model ◽  
Plane Strain Model

There are many methods on computation of transverse elastic properties of unidirectional fiber-reinforced composites when using the finite element method, such as three-dimension model, two-dimension plane strain model, unit cell model, etc[1]. But unit cell models could be used only when the fibers are arrayed regularly. The computations of three- and two-dimension plane strain models are tremendous when many fine fibers are spread randomly in the matrix so that the properties of block of composite must be computed. The paper proposes a new embedded-zone method to compute the transverse elastic properties for a block of fiber-reinforced composites containing a great amount of fibers embedded in the matrix stochastically while using very little computational work compared with three- and two-dimension plane strain model. The transverse elastic modulus and shear modulus of unidirectional fiber-reinforced composites are computed.

Thermal Stresses in Layered Electrical Assemblies Bonded With Solder

1991 ◽  
Vol 113 (4) ◽  
pp. 350-354 ◽  
Author(s):  
H. S. Morgan
Keyword(s):  
Residual Stresses ◽  
Plane Strain ◽  
3D Model ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Creep Models ◽  
Strain Model ◽  
Maximum Stresses ◽  
Generalized Plane Strain ◽  
Plane Strain Model

Thermal stresses in a layered electrical assembly joined with solder are computed with plane strain, generalized plane strain, and three-dimensional (3D) finite element models to assess the accuracy of the two-dimensional (2D) modeling assumptions. Cases in which the solder is treated as an elastic and as a creeping material are considered. Comparison of the various solutions shows that, away from the corners, the generalized plane strain model produces residual stresses that are identical to those computed with the 3D model. Although the generalized plane strain model cannot capture corner stresses, the maximum stresses computed with this 2D model are, for the mesh discretization used, within 12 percent of the corner stresses computed with the 3D model when the solder is modeled elastically and within 5 percent when the solder is modeled as a creeping material. Plane strain is not a valid assumption for predicting thermal stresses, especially when creep of the solder is modeled. The effect of cooling rate on the residual stresses computed with creep models is illustrated.

Three-dimensional thermo-mechanical analysis of continuous casting and comparison with two-dimensional models

2018 ◽  
Vol 53 (6) ◽  
pp. 421-434
Author(s):  
Reza Vaghefi ◽  
MR Hematiyan ◽  
Ali Nayebi
Keyword(s):  
Continuous Casting ◽  
Phase Change ◽  
Galerkin Method ◽  
Plane Strain ◽  
Plane Stress ◽  
Three Dimensional ◽  
Casting Process ◽  
Mechanical Analysis ◽  
Two Dimensional ◽  
Generalized Plane Strain

In this study, a three-dimensional thermo-elasto-plastic model is developed for simulating a continuous casting process. The obtained results are compared with those from different two-dimensional analyses, which are based on plane stress, plane strain, and generalized plane strain assumptions. All analyses are carried out using the meshless local Petrov–Galerkin method. The effective heat capacity method is employed to simulate the phase change process. The von Mises yield criterion and elastic–perfectly-plastic model are used to simulate the stress state during the casting process; while, material parameters are assumed to be temperature-dependent. Based on the three-dimensional and two-dimensional models, numerical results are provided to determine the stress, displacement, and temperature fields induced in the cast material. It is observed that the present meshless local Petrov–Galerkin method is accurate in three-dimensional thermo-mechanical analysis of highly nonlinear phase change problems. Reasonable agreements are observed between the results obtained from the three-dimensional analysis with those retrieved by the generalized plane strain assumption. However, it is observed that the results obtained under plane stress/strain conditions have some significant differences with the results obtained from three-dimensional modeling of continuous casting.

Multiple Diffractions of Elastic Waves by a Rigid Rectangular Foundation: Plane-Strain Model

1976 ◽  
Vol 43 (2) ◽  
pp. 291-294 ◽  
Author(s):  
M. Dravinski ◽  
S. A. Thau
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Elastic Waves ◽  
Equation Of Motion ◽  
Elastic Half Space ◽  
Strain Type ◽  
Time Required ◽  
Strain Model ◽  
Rectangular Foundation ◽  
Plane Strain Model

A rigid rectangular foundation embedded in an elastic half space moves in a direction perpendicular to the surface of the half space, Fig. 1. The model under consideration is of the plane-strain type. By application of the Laplace, Fourier, and Kontorovich-Lebedev (K-L) transforms, the equation of motion for the foundation is derived. The transient response of the foundation is exact during the period of time required for a longitudinal wave to traverse the base of the foundation twice. Thus the process of multiple diffractions at the corners of the foundation is taken into account.

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