A Slip Model for Finite-Element Plasticity

1978 ◽  
Vol 45 (3) ◽  
pp. 527-532 ◽  
Author(s):  
H. M. van Rij ◽  
P. G. Hodge
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Tangential Velocity ◽  
Element Model ◽  
Displacement Component ◽  
Tangential Component ◽  
Normal Displacement ◽  
Perfectly Plastic ◽  
Dimensional Finite Element

Conventional finite-element models are based on displacement or velocity fields which are at least continuous. However, it is known that perfectly plastic materials may exhibit discontinuities of the tangential velocity component along certain lines. In this investigation, a two-dimensional finite-element model is proposed which will allow for such discontinuities. A regular pattern of triangular elements is assumed. The elements are assumed to be rigid, and across the line separating any two adjoining elements the normal displacement component is continuous, but a discontinuity may exist in the tangential component. The defining equations—compatibility, equilibrium, and constitutive—are developed with the aid of the Principle of Virtual Work. Prandtl’s punch problem for contained flow is solved under plane strain conditions. Comparison is made with existing analytical and other numerical solutions, in order to evaluate the merits of allowing for discontinuities.

AN EFFICIENT PSEUDO THREE-DIMENSIONAL FINITE ELEMENT MODEL: PRESENTATION AND ANALYSIS OF TWO SOIL/FOUNDATION INTERACTION PROBLEMS

2005 ◽  
Vol 02 (02) ◽  
pp. 231-253 ◽  
Author(s):  
DJ. AMAR BOUZID ◽  
P. A. VERMEER ◽  
B. TILIOUINE ◽  
M. MIR
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Element Model ◽  
Combined Loading ◽  
Shear Stresses ◽  
Fe Method ◽  
Dimensional Finite Element ◽  
Soil Foundation ◽  
Three Dimensional Finite Element

A pseudo-three-dimensional numerical model has been developed for the analysis of full 3D soil problems under combined loading. The procedure called Vertical Slices Model takes advantage of finite element (FE) 2D numerical solutions in plane stress for building approximate 3D solutions by replacing the inter-slice interactions by fictitious body forces. Continuum slices are successively analyzed by the combination of the explicit 2D finite element (FE) method and finite difference (FD) method in iterative process. The three-dimensional aspect of the considered problem is preserved by satisfying the continuity of shear stresses developed at the inter-slices. The theory of the vertical slices model is developed first, and then encoded in a Fortran computer program. Next, the prediction capabilities of this program are illustrated with two classical geotechnical applications, namely; the laterally and the axially loaded single piles embedded in homogeneous and non-homogeneous elastic soils. Although approximate, the model proved its ability to capture the behavior of the two boundary value problems. Then, in terms of stiffness factors the approach is used to predict the behavior of an embedded rigid square footing and a pile under combined loading in a half-space where the stiffness shows a power law variation with depth.

Finite Element Analysis of Nonuniformity of Tires with Imperfections5

2007 ◽  
Vol 35 (3) ◽  
pp. 226-238 ◽  
Author(s):  
K. M. Jeong ◽  
K. W. Kim ◽  
H. G. Beom ◽  
J. U. Park
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Element Model ◽  
Radial Force ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Dimensional Finite Element ◽  
Force Variation ◽  
Three Dimensional Finite Element

Abstract The effects of variations in stiffness and geometry on the nonuniformity of tires are investigated by using the finite element analysis. In order to evaluate tire uniformity, a three-dimensional finite element model of the tire with imperfections is developed. This paper considers how imperfections, such as variations in stiffness or geometry and run-out, contribute to detrimental effects on tire nonuniformity. It is found that the radial force variation of a tire with imperfections depends strongly on the geometrical variations of the tire.

Approximate Macroscale Constitutive Relations Using a Finite Element Based Constitutive Equations for Microscale Contact

2008 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Finite Element ◽  
Contact Force ◽  
Rough Surfaces ◽  
Constitutive Relations ◽  
Cumulative Effect ◽  
Element Model ◽  
Tangential Component ◽  
Total Force ◽  
Asperity Contact ◽  
Elastic Plastic

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity-asperity constitutive relations from a finite element model of their elastic-plastic interaction. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. Multiscale modeling of the elastic-plastic rough surface contact is presented in which asperity-level FE-based constitutive relations are statistically summed to obtain total force in the normal and tangential direction. The equations derived are in the form of integral functions and provide expectation of contact force components between two rough surfaces. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. This is shown to yield upon statistical summation the cumulative effect resulting in the contact force between two rough surfaces with two components, one in the normal direction and a half-plane tangential component.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

Mechanical Simulation of Knee Movement in Basketball Shooting

2013 ◽  
Vol 336-338 ◽  
pp. 760-763
Author(s):  
Hui Yue
Keyword(s):  
Finite Element ◽  
Cruciate Ligament ◽  
Three Dimensional ◽  
Element Model ◽  
Basketball Player ◽  
Knee Movement ◽  
Dimensional Finite Element ◽  
Anterior Cruciate ◽  
Three Dimensional Finite Element

A short explanation of the finite element method as a powerful tool for mathematical modeling is provided, and an application using constitutive modeling of the behavior of ligaments is introduced. Few possible explanations of the role of water in ligament function are extracted from two dimensional finite element models of a classical ligament. The modeling is extended to a three dimensional finite element model for the human anterior cruciate ligament. Simulation of ligament force in pitching motion of basketball player is studied in this paper.

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