Constructing Continuous Strain and Stress Fields From Spatially Discrete Displacement Data in Soft Materials

2015 ◽  
Vol 83 (1) ◽  
Author(s):  
Wanru Liu ◽  
Rong Long
Keyword(s):  
Finite Element ◽  
Interpolation Method ◽  
Local Strain ◽  
Soft Materials ◽  
Element Model ◽  
Least Square ◽  
Stress Fields ◽  
Moving Least Square ◽  
Data Points ◽  
Mls Method

A recent study demonstrated that three-dimensional (3D) continuous displacement fields in transparent soft gels can be constructed from discrete displacement data obtained by optically tracking fluorescent particles embedded in the gels. Strain and stress fields were subsequently determined from gradients of the displacement field. This process was achieved through the moving least-square (MLS) interpolation method. The goal of this study is to evaluate the numerical accuracy of MLS in determining the displacement, strain, and stress fields in soft materials subjected to large deformation. Using an indentation model as the benchmark, we extract displacement at a set of randomly distributed data points from the results of a finite-element model, utilize these data points as the input for MLS, and compare resulting displacement, strain, and stress fields with the corresponding finite-element results. The calculation of strain and stress is based on finite strain kinematics and hyperelasticity theory. We also perform a parametric study in order to understand how parameters of the MLS method affect the accuracy of the interpolated displacement, strain, and stress fields. We further apply the MLS method to two additional cases with highly nonuniform deformation: a plate with a circular cavity subjected to large uniaxial stretch and a plane stress crack under large mode I loading. The results demonstrate the feasibility of using optical particle tracking together with MLS interpolation to map local strain and stress field in highly deformed soft materials.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

Finite element modeling of guyed back spars in cable logging

2004 ◽  
Vol 34 (4) ◽  
pp. 817-828 ◽  
Author(s):  
Albert Saravi ◽  
C Kevin Lyons
Keyword(s):  
Finite Element ◽  
Normal Stress ◽  
Cross Section ◽  
A Priori ◽  
Element Model ◽  
Transverse Cross Section ◽  
Stress Fields ◽  
Stress Concentrations ◽  
Maximum Normal Stress ◽  
Tree Method

In this study a finite element model of a back spar system was developed with three guylines opposing the skyline strap tension. In this paper the allowable skyline strap tension is the tension in the skyline strap that results in the maximum normal stress on a transverse cross section of the tree being equal to an assumed allowable stress. An iterative routine was developed to find the allowable skyline strap tension, and this routine was found to converge rapidly from initial values that were below and above the allowable skyline strap tension. Two algorithms were developed for finding the maximum normal stress on a transverse cross section of a tree, method 1 and method 2. If the plane that the tree displaced in was known a priori, then method 2 could be used, and it was found to be less sensitive to mesh coarseness. If the plane that the tree displaced in was not known a priori, then method 1 had to be used with a less coarse mesh. It was found that the stress concentrations due to simplified cable connections were not significant for rigging configurations that allowed a larger rigging point displacement. The rigging configurations that allowed larger rigging point displacements have stress fields that are dominated by bending, while for rigging configurations that allow only small rigging point displacements, the stress fields are dominated by axial compression.

Metamodeling Development for Vehicle Frontal Impact Simulation

2001 ◽  
Author(s):  
R. J. Yang ◽  
N. Wang ◽  
C. H. Tho ◽  
J. P. Bobineau ◽  
B. P. Wang
Keyword(s):  
Response Surface ◽  
Impact Analysis ◽  
Hybrid Approach ◽  
Latin Hypercube Sampling ◽  
Element Model ◽  
Least Square ◽  
Frontal Impact ◽  
Response Surface Methods ◽  
Moving Least Square ◽  
Highly Nonlinear

Abstract Response surface methods or metamodels are commonly used to approximate large engineering systems. This paper presents a new metric for evaluating a response surface method or a metamodeling technique. Five response surface methods are studied: Stepwise Regression, Moving Least Square, Kriging, Multiquadratic, and Adaptive and Interactive Modeling System. A real world frontal impact design problem is used as an example, which is a complex, highly nonlinear, transient, dynamic, large deformation finite element model. The optimal Latin Hypercube Sampling method is used to distribute the sampling points uniformly over the entire design space. The Root Mean Square Error is used as the error indicator to study the accuracy and convergence rate of the metamodels for this vehicle impact analysis. A hybrid approach/strategy for selecting the best metamodels of impact responses is proposed.

scholarly journals The High-Speed Train Seat Design Based on the Human Lumbar Biomechanical Analysis

2014 ◽  
Vol 6 ◽  
pp. 524802
Author(s):  
Yunpeng Guo ◽  
Guiqiu Song
Keyword(s):  
High Speed ◽  
Element Model ◽  
Least Square ◽  
Biomechanical Analysis ◽  
High Speed Train ◽  
Design Standards ◽  
Engineering Technology ◽  
Moving Least Square ◽  
Physical Ergonomics ◽  
The Finite Element Model

This paper, aimed at the problems of high-speed train seat design standards that lack biomechanical analysis, analyzed the lumbar force of sitting position and verified the validity of the finite element model of human lumbar L1–L5 that had been built by reverse engineering technology. Based on the lumbar force distribution, the methods of exterior penalty and moving least square were adopted to establish a high-speed train seat equation that caters for physical ergonomics and a new high-speed train seat model was designed so as to improve the comfort for passengers.

Finite element derivative recovery by moving least square interpolants

1994 ◽  
Vol 117 (1-2) ◽  
pp. 211-223 ◽  
Author(s):  
Mazen Tabbara ◽  
Ted Blacker ◽  
Ted Belytschko
Keyword(s):  
Finite Element ◽  
Least Square ◽  
Moving Least Square

A Method to Determine the Boundary Conditions of the Finite Element Model of a Slender Beam Using Measured Modal Parameters

1996 ◽  
Vol 118 (3) ◽  
pp. 474-478 ◽  
Author(s):  
Wang Fengquan ◽  
Chen Shiyu
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Finite Element Model ◽  
Interpolation Method ◽  
Element Model ◽  
Accurate Method ◽  
Modal Parameters ◽  
Computation Method ◽  
Modal Parameter ◽  
The Finite Element Model

In this paper, a method used to determine the boundary conditions of the Finite Element Model of a slender beam with measured structure modal parameters is presented. On deriving the method, the finite element model theory for dynamic calculating is used. Combined with the modal parameters from experiment, an FEM-modal parameter equation to determine the boundary conditions is put forward. For solving the equation, three methods are given. The first is the accurate method. The second is the full mode computation method by means of generalized inverse matrix. The third is the interpolation method of frequency. A numerical simulation with computer is given and the results of calculation fully verify the effectiveness of the method offered and also verify that the accuracy of the method is satisfying. Finally, an applied example is given and the results of calculation fully verify the effectiveness of the method offered.

Finite Element Simulation of the Upset Welding Process

1991 ◽  
Author(s):  
H. A. Nied
Keyword(s):  
Finite Element ◽  
Titanium Alloy ◽  
Elevated Temperature ◽  
Welding Process ◽  
Element Model ◽  
Stress Fields ◽  
Element Formulation ◽  
Deformation Characteristics ◽  
Element Simulation ◽  
Major Process

A finite element model of an elevated temperature upset welding process was developed to simulate the process and to study the role and sensitivity of the major process parameters. Particular attention was focused on the deformation characteristics by studying the displacement and stress fields generated for the purpose of obtaining a better understanding of this solid-state welding process. The paper describes the finite element formulation, the experiments used to validate the modeling, and a selected application for upset welding of a titanium alloy.

Direct Strength Analysis of Semi-Submersible Platform Structures

2004 ◽  
Author(s):  
Haibin Zhang ◽  
Huilong Ren ◽  
Yangshan Dai
Keyword(s):  
Finite Element ◽  
Interpolation Method ◽  
Fluid Dynamic ◽  
Dynamic Pressure ◽  
Three Dimensional ◽  
Element Model ◽  
Strength Analysis ◽  
Wave Load ◽  
Element Analysis ◽  
Wet Surface

A kind of direct strength analysis method of semi-submersible platform structures is presented in this paper. With the differences in shape of pontoon, column and beam being considered, the method of accumulative chord length cubic parameter spline function combined with analytic expression is adopted to generate the mesh of platform wet surface. The hydrodynamic coefficients of the platform are calculated by the three-dimensional potential flow theory of the linear hydrodynamic problem for platforms with low forward speed. The equations of platform motions are established and solved in frequency domain, and the responses of wave-induced loads on the platforms are calculated. According to the mesh of hydrodynamic computation, the fluid dynamic pressure field of platform wet surface is built, and the pressure loads on shell elements in the finite element model of the structure are calculated by the interpolation method. The calculation conditions and loads in the finite element analysis (FEA) of the platform structures are determined according to the design wave analysis approach. A computer program based on this method has been developed, and a calculation example of semi-submersible platform is illustrated. Analysis results show that this method is a satisfying approach for wave load computation and direct strength analysis of the semi-submersible platforms.

The Method of Modal Parameters to Determine the Boundary Condition of Finite Element Model

1991 ◽  
Author(s):  
Chen Shiyu ◽  
Wang Fengquan
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Finite Element Model ◽  
Interpolation Method ◽  
Element Model ◽  
Accurate Method ◽  
Modal Parameters ◽  
Computation Method ◽  
Modal Parameter ◽  
The Third

Abstract In this paper, a method used to determine the boundary condition of Finite Element Model with structure modal parameters is presented. On deriving the method, the theory of Finite Element Model for dynamic calculating is used. Combined with the modal parameters got from experiment, a FEM-Modal Parameter equation to determine the boundary condition is put forward. For solving the equation, three methods are given. The first is the accurate method. The second is the full mode computation method by means of generlized inverse matrix. The third is the interpolation method of frequency. An applied example is given and the results of calculation fully verify the effectiveness of the method offered.

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