scholarly journals Applicability of the interface spring model for micromechanical analyses with interfacial imperfections to predict the modified exterior Eshelby tensor and effective modulus

2019 ◽  
Vol 24 (9) ◽  
pp. 2944-2960 ◽  
Author(s):  
Sangryun Lee ◽  
Youngsoo Kim ◽  
Jinyeop Lee ◽  
Seunghwa Ryu
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Eshelby Tensor ◽  
Effective Moduli ◽  
Spring Model ◽  
Interfacial Damage ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
The Matrix ◽  
Linear Spring

Closed-form solutions for the modified exterior Eshelby tensor, strain concentration tensor, and effective moduli of particle-reinforced composites are presented when the interfacial damage is modeled as a linear-spring layer of vanishing thickness; the solutions are validated against finite element analyses. Based on the closed-form solutions, the applicability of the interface spring model is tested by calculating those quantities using finite element analysis augmented with a matrix–inhomogeneity non-overlapping condition. The results indicate that the interface spring model reasonably captures the characteristics of the stress distribution and effective moduli of composites, despite its well-known problem of unphysical overlapping between the matrix and inhomogeneity.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

Modified Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals

2000 ◽  
Vol 123 (4) ◽  
pp. 409-416 ◽  
Author(s):  
W. Y. Chien ◽  
J. Pan ◽  
S. C. Tang
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Matrix Material ◽  
Plastic Behavior ◽  
Computational Results ◽  
Sheet Metals ◽  
Element Analysis ◽  
The Matrix

The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The matrix material is first assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion suggested in Liao et al. 1997, “Approximate Yield Criteria for Anisotropic Porous Ductile Sheet Metals,” Mech. Mater., pp. 213–226. Three fitting parameters are suggested for the closed-form yield criterion to fit the results based on the modified yield criterion to those of finite element computations. When the strain hardening of the matrix is considered, the computational results of the macroscopic stress-strain behavior are in agreement with those based on the modified anisotropic Gurson’s yield criterion under uniaxial and equal biaxial tensile loading conditions.

An Algorithm for Reducing the Size of Finite Element Closed-Form Source Code Files

2009 ◽  
Author(s):  
Sara McCaslin ◽  
Kent Lawrence
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Source Code ◽  
Simple Algorithm ◽  
Higher Order ◽  
Error Estimator ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Large Source

Closed-form solutions, as opposed to numerically integrated solutions, can now be obtained for many problems in engineering. In the area of finite element analysis, researchers have been able to demonstrate the efficiency of closed-form solutions when compared to numerical integration for elements such as straight-sided triangular [1] and tetrahedral elements [2, 3]. With higher order elements, however, the length of the resulting expressions is excessive. When these expressions are to be implemented in finite element applications as source code files, large source code files can be generated, resulting in line length/ line continuation limit issues with the compiler. This paper discusses a simple algorithm for the reduction of large source code files in which duplicate terms are replaced through the use of an adaptive dictionary. The importance of this algorithm lies in its ability to produce manageable source code files that can be used to improve efficiency in the element generation step of higher order finite element analysis. The algorithm is applied to Fortran files developed for the implementation of closed-form element stiffness and error estimator expressions for straight-sided tetrahedral finite elements through the fourth order. Reductions in individual source code file size by as much as 83% are demonstrated.

scholarly journals Modified Eshelby tensor for an anisotropic matrix with interfacial damage

2018 ◽  
Vol 24 (6) ◽  
pp. 1749-1762 ◽  
Author(s):  
Sangryun Lee ◽  
Jinyeop Lee ◽  
Seunghwa Ryu
Keyword(s):  
Spherical Inclusion ◽  
Elastic Stiffness ◽  
Eshelby Tensor ◽  
Algebraic Expression ◽  
Stiffness Tensor ◽  
Interfacial Damage ◽  
Element Analysis ◽  
Linear Spring ◽  
Elastic Stiffness Tensor ◽  
Order Identity

We derive a simple tensor algebraic expression of the modified Eshelby tensor for a spherical inclusion embedded in an arbitrarily anisotropic matrix in terms of three tensor quantities (the fourth-order identity tensor, the elastic stiffness tensor, and the Eshelby tensor) and two scalar quantities (the inclusion radius and interfacial spring constant), when the interfacial damage is modelled as a linear-spring layer of vanishing thickness. We validate the expression for a triclinic crystal involving 21 independent elastic constants against finite element analysis.

Modeling of Plastic Behavior of Anisotropic Sheet Metals With Voids

2000 ◽  
Author(s):  
W. Y. Chien ◽  
J. Pan ◽  
S. C. Tang
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Matrix Material ◽  
Three Dimensional ◽  
Plastic Behavior ◽  
Element Analysis ◽  
Normal Anisotropy ◽  
The Matrix

Abstract The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The matrix material is assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion suggested in Liao et al. (Mechanics of Materials, 1997, pp. 213-226). Three fitting parameters are suggested in the closed-form yield criterion to fit the results based on the modified yield criterion to those of finite element computations.

Determination of Pipe Whip Restraint Location to Prevent Plastic Hinge Formation in High Energy Piping Systems

2011 ◽  
Author(s):  
Sivadol Vongmongkol ◽  
Asgar Faal-Amiri ◽  
Hari M. Srivastava
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Power Plants ◽  
Plastic Hinge ◽  
Bending Moment ◽  
High Energy ◽  
Piping System ◽  
Secondary Effects ◽  
Element Analysis ◽  
Closed Form Solutions

The purpose of this study is to determine the Pipe Whip Restraint (PWR) location that would prevent the formation of a plastic hinge due to secondary effects of a postulated pipe break load in a high energy line(1). The prevention of a plastic hinge formation at the PWR location is important since its secondary effects could lead to additional interactions with safety related equipment, structure, and component that are essential to safely shutdown the nuclear power plants. The proper location of the PWR can be found by using the relationship between bending moment-carrying capacity of the pipe and the applied thrust force. Several closed-form solutions obtained from several literatures were studied and used to calculate bending moment-carrying capacities of a piping system and ultimately used to determine a plastic hinge length. The plastic hinge formation is also determined analytically by using the Finite Element Analysis (FEA) method. ANSYS LS-DYNA® [8] Explicit Finite Element code is used in modeling the pipe whip models, which includes the piping system and pipe whip restraint. Comparisons are made between the analytical (FEA) results and the results from several closed-form solutions.

scholarly journals Closed-form solutions of hole distortion for use in deep-hole drilling measurements of residual stress in orthotropic plates

2016 ◽  
Vol 52 (2) ◽  
pp. 77-82 ◽  
Author(s):  
Carlos Garza ◽  
Anton Shterenlikht ◽  
Martyn J Pavier ◽  
David J Smith
Keyword(s):  
Residual Stress ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Hole Drilling ◽  
Shear Stresses ◽  
Deep Hole ◽  
Element Analysis ◽  
Deep Hole Drilling ◽  
Closed Form Solutions

The measurement of residual stress using the deep-hole drilling method relies on the evaluation of the distortion of a hole in a plate under the action of far-field direct and shear stresses. While closed-form solutions exist for the isotropic materials, in previous work for orthotropic materials, finite element analysis has been used to find the distortion. In this technical note, Lekhnitskii’s analysis is used to find closed-form solutions for the distortion of a circular hole in an orthotropic plate. The results are compared with those of finite element analysis for a range of material properties with excellent agreement.

scholarly journals Research on a 3-DOF Motion Device Based on the Flexible Mechanism Driven by the Piezoelectric Actuators

Micromachines ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 578 ◽  
Author(s):  
Bingrui Lv ◽  
Guilian Wang ◽  
Bin Li ◽  
Haibo Zhou ◽  
Yahui Hu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Machining Process ◽  
Element Analysis ◽  
3D Motion ◽  
Compliance Modeling ◽  
The Matrix ◽  
Static Performance ◽  
Flexible Mechanism

This paper describes the innovative design of a three-dimensional (3D) motion device based on a flexible mechanism, which is used primarily to produce accurate and fast micro-displacement. For example, the rapid contact and separation of the tool and the workpiece are realized by the operation of the 3D motion device in the machining process. This paper mainly concerns the device performance. A theoretical model for the static performance of the device was established using the matrix-based compliance modeling (MCM) method, and the static characteristics of the device were numerically simulated by finite element analysis (FEA). The Lagrangian principle and the finite element analysis method for device dynamics are used for prediction to obtain the natural frequency of the device. Under no-load conditions, the dynamic response performance and linear motion performance of the three directions were tested and analyzed with different input signals, and three sets of vibration trajectories were obtained. Finally, the scratching experiment was carried out. The detection of the workpiece reveals a pronounced periodic texture on the surface, which verifies that the vibration device can generate an ideal 3D vibration trajectory.

Analyses of Full-Scale Tank Car Shell Impact Tests

2007 ◽  
Author(s):  
Y. H. Tang ◽  
H. Yu ◽  
J. E. Gordon ◽  
M. Priante ◽  
D. Y. Jeong ◽  
...  
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Three Dimensional ◽  
Full Scale ◽  
Collision Dynamics ◽  
Dynamics Modeling ◽  
Dynamics Model ◽  
Rigid Plastic ◽  
Element Analysis ◽  
Closed Form Solutions

This paper describes analyses of a railroad tank car impacted at its side by a ram car with a rigid punch. This generalized collision, referred to as a shell impact, is examined using nonlinear (i.e., elastic-plastic) finite element analysis (FEA) and three-dimensional (3-D) collision dynamics modeling. Moreover, the analysis results are compared to full-scale test data to validate the models. Commercial software packages are used to carry out the nonlinear FEA (ABAQUS and LS-DYNA) and the 3-D collision dynamics analysis (ADAMS). Model results from the two finite element codes are compared to verify the analysis methodology. Results from static, nonlinear FEA are compared to closed-form solutions based on rigid-plastic collapse for additional verification of the analysis. Results from dynamic, nonlinear FEA are compared to data obtained from full-scale tests to validate the analysis. The collision dynamics model is calibrated using test data. While the nonlinear FEA requires high computational times, the collision dynamics model calculates gross behavior of the colliding cars in times that are several orders of magnitude less than the FEA models.

Design and analysis of a dual-mode driven parallel XY micromanipulator for micro/nanomanipulations

2012 ◽  
Vol 226 (12) ◽  
pp. 3043-3057 ◽  
Author(s):  
Hui Tang ◽  
Yangmin Li ◽  
Jiming Huang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Properties ◽  
Dynamics Modeling ◽  
Lagrange Equations ◽  
Element Analysis ◽  
Modeling And Analysis ◽  
The Matrix ◽  
High Bandwidth ◽  
Novel Design

This article presents a novel design of a flexure-based, piezoelectric actuated, completely decoupled, high-bandwidth, highresolution, and large stroke parallel XY micromanipulator with two amplification levers. The monolithic mechanism is featured with dual working modes, which meets different kinds of requirements in terms of high resolution and large workspace in micro/nano fields. In order to reduce the displacement loss, the modeling and analysis of bending motion of the levers are conducted; thereafter, compliance and stiffness modeling by employing the matrix method are established. Furthermore, the dynamics modeling and analysis via Lagrange equations are performed to improve the dynamic properties of the mechanism. The simulation results of finite element analysis indicate that the cross-coupling between the two axes is kept to 1.2%; meanwhile, the natural frequency of the mechanism is about 700 Hz, and the amplifier ratio is approximately 2.32. Both theoretical analysis and finite element analysis results well validate the performance of the proposed mechanism.

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