• Structural Engineering and Mechanics
• /
• v.58 no.4
• /
• pp.641-659
• /
• 2016

This paper deals with the pure bending of incompressible elastic perfectly plastic two-layer sheets under plane strain conditions at large strains. Each layer is classified by its yield stress, shear modulus of elasticity and its initial percentage thickness in relation to the whole sheet. The solution found is semi-analytic. In particular, a numerical technique is only necessary to solve transcendental equations. The general solution is cumbersome because different analytic expressions for the radial and circumferential stresses should be adopted in different regions of the whole sheet. In particular, there are several alternative ways a plastic region (or plastic regions) can propagate. However, for any given set of material and process parameters the solution to the problem consists of a sequence of rather simple analytic expressions connected by transcendental equations. The general solution is illustrated by a simple example.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.4 no.6
• /
• pp.27-38
• /
• 1996

A two-dimensional FEM program, which considers bending effects in the membrane fromulation, was developed under plane strain assumption for analyzing forming processes of an arbitrarily shaped draw-die of automotive panels. For the evaluation of bending effects with membrane elements, the bending equivalent forces and stiffnesses are calculated from the bending moment computed using the changes in curvature of the formed shape of two membrane ones. The curves depicted with 3 nodes are described by a circle, a quadratic equation, and a cubic equation, respectively, and in the simulation of the stretch/draw sections of an automotive inner panel, three different description results are compared each other. Also, the bending results are compared with membrane results and measurements in order to verify the validity of the developed program.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.22 no.3
• /
• pp.493-503
• /
• 1998

The sectional forming analysis considering bending effects from the geometrically deformed shape of two linear membrane finite elements(called super element) was performed under plane strain assumption for analyzing forming processes of an arbitrarily shaped draw-die. For the evaluation of bending effects, the bending equivalent forces are calculated from the bending moment computed using the changes in the interior angle at the middle node of super element, and are agumented to the membrane stretch forces. In order to verify the validity of the bending formulation, the simulation results for the stretch, draw, and bend sections were compared with membrane analysis results and measurements.

• Advances in nano research
• /
• v.8 no.4
• /
• pp.265-276
• /
• 2020

A study that primarily focuses on nonlocal strain gradient plate model for the sole purpose of vibration examination, for graphene sheets under linearly variable in-plane mechanical loads. To study a better or more precise examination on graphene sheets, a new advance model was conducted which carries two scale parameters that happen to be related to the nonlocal as well as the strain gradient influences. Through the usage of two-variable shear deformation plate approach, that does not require the inclusion of shear correction factors, the graphene sheet is designed. Based on Hamilton's principle, fundamental expressions in regard to a nonlocal strain gradient graphene sheet on elastic half-space is originated. A Galerkin's technique is applied to resolve the fundamental expressions for distinct boundary conditions. Influence of distinct factors which can be in-plane loading, length scale parameter, load factor, elastic foundation, boundary conditions, and nonlocal parameter on vibration properties of the graphene sheets then undergo investigation.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.2 no.1
• /
• pp.73-83
• /
• 1994

Press formabilities of aluminum sheets for automobile body were investigated. Plane strain stretching test (called RIST-PSST), cupping test and U bending test were performed to assess the press formability of aluminum sheets respectively. The results showed that aluminum sheets are generally inferior to cold-rolled steel sheet of deep drawing quality (CSP3N) in press formability. The limiting punch height (LPH) and limiting plane strain (FLCo) of aluminum sheets are 50%-70% level compared to that of CSP3N. Moreover, the limiting drawing ratios(LDR) of aluminum sheets are ranged between 1.95 and 2.1. The poor press formability of aluminum sheets is responsible for low values of total elongation and plastic anisotropy parameter in tensile characteristic. The shape fixability of aluminum sheets evaluated in U bending test is very poor due to its low elastic modulus compared to CSP3N.

• Coupled systems mechanics
• /
• v.12 no.4
• /
• pp.297-313
• /
• 2023

This paper deals with delamination analysis of non-linear viscoelastic multilayered beam subjected to bending in the plane of the layers. For this purpose, first, a non-linear viscoelastic model is presented. In order to take into account the non-linear viscoelastic behaviour, a non-linear spring and a non-linear dashpot are assembled in series with a linear spring connected in parallel to a linear dashpot. The behaviours of the non-linear spring and dashpot are described by applying non-linear stress-strain and stress-rate of strain relationships, respectively. The constitutive law of the model is derived. Due to the non-linear spring and dashpot, the constitutive law is non-linear. This law is used for describing the time-dependent mechanical behaviour of the beam under consideration. The material properties involved in the constitutive law vary along the beam length due to the continuous material inhomogeneity of the layers. Solution of the strain energy release rate for the delamination is obtained by analyzing the balance of the energy with considering of the non-linear viscoelastic behaviour. The strain energy release rate is found also by using the complementary strain energy for verification. A parametric study is carried-out by using the solution obtained. The solutions derived and the results obtained help to understand the time-dependent delamination of non-linear viscoelastic beams under loading in the plane of layers.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.11
• /
• pp.2871-2882
• /
• 1994

Two kinds of 4-node plane stress/strain finite elements are presented in this work. They are derived from the modified Hellinger-Reissner variational principle so as to employ the internal incompatible displacement and independent stress fields, or the incompatible displacement and strain fields. The introduced incompatible functions are selected to satisfy the constant strain condition. The elements are evaluated on several problems of bending and material incompressibility with regular and distorted elements. The results show that the new elements perform excellently in the calculation of deformation and stresses.

• Progress in Superconductivity and Cryogenics
• /
• v.4 no.1
• /
• pp.40-44
• /
• 2002

Influences of bending strain on the critical current (Ic) were investigated in Bi-2223 superconducting tapes at 77K. The effect of bending mode on the Ic degradation behavior was discussed in viewpoints of test procedure, n-value and damage morphology Especially, in this paper, we reported the Ic behavior in Ag alloy/Bi-2223 multifilamentary superconducting tapes under bending occurred within a width plane of the tape which was called as a hard bending. The Ic degradation under hard bending appeared significantly as compared with that under easy bending. The n-value decreased slightly with the increase in bending strain under the hard bending.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.11a
• /
• pp.727-730
• /
• 2005

Cellulose based Electro-Active Papers (EAPap) is very promising material due to its merits in terms of large bending deformation, low actuation voltage, ultra-lightweight, and biodegradability. These advantages make it possible to utilize applications, such as artificial muscles and achieving flapping wings, micro-insect robots and smart wall papers. This paper investigates the in-plane strains of EAPap under electric fields, which are useful for a contractile actuator application The preparation of EAPap samples and the in-plane strain measurement system are explained, and the test results are shown in terms of electric field, frequency and the oriental ions of the samples. The power consumption and the strain energy of EAPap samples are discussed. Although there are still unknown facts in EAPap material, this in-plane strain may be useful for artificial muscle applications.

• Restorative Dentistry and Endodontics
• /
• v.15 no.2
• /
• pp.17-33
• /
• 1990

The purpose of this study was to evaluate the fracture toughness of dental composite resins and to investigate the filler factor affecting the fracture behaviour on which the degree of fracture toughness depends. Six kinds of commercially available composite resin;, including two of each macrofilled, microfilled, and hybrid type were used for this study, The plane strain fracture toughness ($K_{10}$) was determined by three-point bending test using the single edge notch specimen according to the ASTM-E399. The specimens were fabricated with visible light curing or self curing of each composite resin previously inserted into a metal mold, and three-point bending test was conducted with cross-head speed of 0.1mm/min following a day's storage of the specimens in $37^{\circ}C$ distilled water. The filler volume fractions were determined by the standard ashing test according to the ISO-4049. Acoustic Emission(AE), a nondestructive testing method detecting the elastic wave released from the localized sources In material under a certain stress, was detected during three-point bending test and its analyzed data was compared with, canning electron fractographs of each specimen. The results were as follows : 1. The filler content of composite resin material was found to be highest in the hybrid type followed by the macrofilled type, and the microfilled type. 2. It was found that the value of plane strain fracture toughness of composite resin material was in the range from 0.69 MPa$\sqrt{m}$ to 1 46 MPa$\sqrt{m}$ and highest In the macrofilled type followed by the hybrid type, and the microfilled type. 3. The consequence of Acoustic Emission analysis revealed that the plane strain fracture toughness increased according as the count of Acoustic Emission events increased. 4. The higher the plane strain fracture toughness became, the higher degree of surface roughness and irregularity the fractographs demonstrated.