Fully Plastic Crack Problems, Part 1: Solutions by a Penalty Method

1984 ◽  
Vol 51 (1) ◽  
pp. 48-56 ◽  
Author(s):  
C. F. Shih ◽  
A. Needleman
Keyword(s):  
Finite Element ◽  
Numerical Method ◽  
Strain Hardening ◽  
Plane Strain ◽  
Penalty Method ◽  
Incompressible Material ◽  
Material Behavior ◽  
Reduced Integration ◽  
Wide Range ◽  
Crack Problems

We formulate a finite-element reduced integration penalty method applicable to plane-strain problems with incompressible material behavior. This numerical method is employed to generate crack solutions for pure power-hardening solids. For two configurations of interest in applications, an edge cracked panel subject to remote tension and an edge-cracked panel subject to remote bending, we obtain solutions for a wide range of crack lengths and strain-hardening behaviors.

scholarly journals Finite Element Software for Rubber Products Design

2018 ◽  
Vol 3 (1) ◽  
pp. 13-20
Author(s):  
Dávid Huri
Keyword(s):  
Finite Element ◽  
Complex Analysis ◽  
Large Deformations ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Material Models ◽  
Finite Element Software ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Different Types

Automotive rubber products are subjected to large deformations during working conditions, they often contact with other parts and they show highly nonlinear material behavior. Using finite element software for complex analysis of rubber parts can be a good way, although it has to contain special modules. Different types of rubber materials require the curve fitting possibility and the wide range choice of the material models. It is also important to be able to describe the viscoelastic property and the hysteresis. The remeshing possibility can be a useful tool for large deformation and the working circumstances require the contact and self contact ability as well. This article compares some types of the finite element software available on the market based on the above mentioned features.

scholarly journals Finite element modeling of lateral pipeline–soil interactions in dense sand

2016 ◽  
Vol 53 (3) ◽  
pp. 490-504 ◽  
Author(s):  
Kshama Roy ◽  
Bipul Hawlader ◽  
Shawn Kenny ◽  
Ian Moore
Keyword(s):  
Finite Element ◽  
Internal Friction ◽  
Plane Strain ◽  
Smooth Transition ◽  
Burial Depth ◽  
Angle Of Internal Friction ◽  
Dense Sand ◽  
Dilation Angle ◽  
Wide Range ◽  
Force Displacement

Finite element (FE) analyses of pipeline–soil interaction for pipelines buried in dense sand subjected to lateral ground displacements are presented in this paper. Analysis is performed — using the Arbitrary Lagrangian–Eulerian (ALE) method available in Abaqus/Explicit FE software — in the plane strain condition using the Mohr–Coulomb (MC) and modified Mohr–Coulomb (MMC) models. The MMC model considers a number of important features and properties of stress–strain and volume change behaviour of dense sand including the nonlinear pre- and post-peak behaviour with a smooth transition and the variation of the angle of internal friction and dilation angle with plastic shear strain, loading conditions (triaxial or plane strain), density, and mean effective stress. Comparing FE and experimental results, it is shown that the MMC model can better simulate the force–displacement response for a wide range of lateral displacements of the pipe for different burial depths, although the peak force on the pipe could be matched using the MC model. Examining the progressive development of zones of large inelastic shear deformation (shear bands), it is shown that the mobilized angle of internal friction and dilation angle vary along the length of the shear band; however, constant values are used in the MC model. A comprehensive parametric study is also performed to investigate the effects of pipeline diameter, burial depth, and soil properties. Many important aspects in the force–displacement curves and failure mechanisms are explained using the present FE analyses.

scholarly journals Application of Inverse Finite Element Method to Shape Sensing of Curved Beams

Sensors ◽  
2020 ◽  
Vol 20 (24) ◽  
pp. 7012
Author(s):  
Pierclaudio Savino ◽  
Francesco Tondolo ◽  
Marco Gherlone ◽  
Alexander Tessler
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Load Transfer ◽  
Beam Element ◽  
Material Behavior ◽  
Curved Beams ◽  
Engineering Structures ◽  
Wide Range ◽  
Inverse Finite Element Method ◽  
Element Method

Curved beam, plate, and shell finite elements are commonly used in the finite element modeling of a wide range of civil and mechanical engineering structures. In civil engineering, curved elements are used to model tunnels, arch bridges, pipelines, and domes. Such structures provide a more efficient load transfer than their straight/flat counterparts due to the additional strength provided by their curved geometry. The load transfer is characterized by the bending, shear, and membrane actions. In this paper, a higher-order curved inverse beam element is developed for the inverse Finite Element Method (iFEM), which is aimed at reconstructing the deformed structural shapes based on real-time, in situ strain measurements. The proposed two-node inverse beam element is based on the quintic-degree polynomial shape functions that interpolate the kinematic variables. The element is C2 continuous and has rapid convergence characteristics. To assess the element predictive capabilities, several circular arch structures subjected to static loading are analyzed, under the assumption of linear elasticity and isotropic material behavior. Comparisons between direct FEM and iFEM results are presented. It is demonstrated that the present inverse beam finite element is both efficient and accurate, requiring only a few element subdivisions to reconstruct an accurate displacement field of shallow and deep curved beams.

Assessment and Extension of an Analytical Formulation for Prediction of Residual Stress in Autofrettaged Thick Cylinders

2005 ◽  
Author(s):  
Anthony P. Parker
Keyword(s):  
Residual Stress ◽  
Plane Strain ◽  
Bauschinger Effect ◽  
Incompressible Material ◽  
Simple Modification ◽  
Linear Behavior ◽  
Wide Range ◽  
End Conditions ◽  
Von Mises ◽  
Recent Formulation

A recent formulation due to Huang and Cui provides an analytic method for calculating residual stresses in autofrettaged tubes exhibiting non-linear behavior (including Bauschinger effect) during manufacture. The formulation incorporates Von Mises criterion but is limited in its application to plane strain end conditions and an incompressible material (i.e. Poisson’s ratio 0.5) with a fixed unloading behavior. Comparisons indicate that, by selecting unloading behavior typical of that at the bore, the method produces reliable results for both A723 type steels and for steels which exhibit significant strain hardening and/or more dramatic Bauschinger effect. Numerical comparisons show that open-end, compressible conditions produce results which differ from the plane strain, incompressible case, but that these differences may be accurately corrected using a straightforward, pragmatic process. It is concluded that a simple modification of the Huang & Cui procedure may be used to perform extremely accurate straightforward spreadsheet calculations of residual stress in autofrettaged tubes manufactured from a wide range of steels under various end conditions. The Huang & Cui formulation also provides a reliable and highly accurate means for validating numerical formulations including Finite Element methods.

Failure Behaviour of Notched Sheet Specimen Under Plane Strain Deformation

2006 ◽  
Author(s):  
Xinjian Duan ◽  
Kevin Spencer ◽  
Mukesh Jain ◽  
David S. Wilkinson
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Plane Strain ◽  
Failure Process ◽  
Element Model ◽  
Failure Behaviour ◽  
Fracture Evolution ◽  
Damage Indicator ◽  
Plane Strain Deformation ◽  
Wide Range

The failure behaviour of notched AA5754 specimen subject to plane strain deformation is examined by the use of a heterogeneous finite element model. A ductile damage indicator triggered model is applied together with the use of element deletion technique for virtualization of fracture evolution. The predicted characteristics of the failure process under a wide range of triaxiality (0.33 to 2.5) fits well with those experimental observations in the literature.

A Comparison of Methods for Predicting Residual Stresses in Strain-Hardening, Autofrettaged Thick Cylinders, Including the Bauschinger Effect

2005 ◽  
Vol 128 (2) ◽  
pp. 217-222 ◽  
Author(s):  
Michael C. Gibson ◽  
Amer Hameed ◽  
Anthony P. Parker ◽  
John G. Hetherington
Keyword(s):  
Finite Element ◽  
High Pressure ◽  
Strain Hardening ◽  
Plane Strain ◽  
Bauschinger Effect ◽  
Pressure Vessels ◽  
Operating Pressure ◽  
Working Pressure ◽  
Element Analysis ◽  
Compressive Stresses

High-pressure vessels, such as gun barrels, are autofrettaged in order to increase their operating pressure and fatigue life. Autofrettage causes plastic expansion of the inner section of the cylinder, setting up residual compressive stresses at the bore after relaxation. Subsequent application of pressure has to overcome these compressive stresses before tensile stresses can be developed, thereby increasing its fatigue lifetime and safe working pressure. This paper presents the results from a series of finite element models that have been developed to predict the magnitude of these stresses for a range of end conditions: plane stress and several plane-strain states (open and closed ended, plus true plane strain). The material model is currently bilinear and allows consideration of strain hardening and the Bauschinger effect. Results are compared to an alternative numerical model and a recent analytical model (developed by Huang), and show close agreement. This demonstrates that general purpose finite element analysis software may be used to simulate high-pressure vessels, justifying further refining of the models.

On determination of material parameters from loading and unloading responses in nanoindentation with a single sharp indenter

2006 ◽  
Vol 21 (4) ◽  
pp. 995-1011 ◽  
Author(s):  
Lugen Wang ◽  
S.I. Rokhlin
Keyword(s):  
Finite Element ◽  
Strain Hardening ◽  
Yield Stress ◽  
Finite Element Simulations ◽  
Strain Hardening Exponent ◽  
Scaling Functions ◽  
Stress And Strain ◽  
Wide Range ◽  
Loading And Unloading

This paper quantitatively describes the loading-unloading response in nanoindentation with sharp indenters using scaling analyses and finite element simulations. Explicit forward and inverse scaling functions for an indentation unloading have been obtained and related to those functions for the loading response [L. Wang et al., J. Material Res.20(4), 987–1001 (2005)]. The scaling functions have been obtained by fitting the large deformation finite element simulations and are valid from the elastic to the full plastic indentation regimes. Using the explicit forward functions for loading and unloading, full indentation responses for a wide range of materials can be obtained without use of finite element calculations. The corresponding inverse scaling functions allow one to obtain material properties from the indentation measurements. The relation between the work of indentation and the ratio between hardness and modulus has also been studied. Using these scaling functions, the issue of nonuniqueness of the determination of material modulus, yield stress, and strain-hardening exponent from nanoindentation measurements with a single sharp indenter has been further investigated. It is shown that a limited material parameter range in the elastoplastic regime can be defined where the material modulus, yield stress, and strain-hardening exponent may be determined from only one full indentation response. The error of such property determination from scattering in experimental measurements is determined.

Analytical and finite element predictions of residual stresses in cold worked fastener holes

1995 ◽  
Vol 30 (4) ◽  
pp. 291-304 ◽  
Author(s):  
C Poussard ◽  
M J Pavier ◽  
D J Smith
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Residual Stresses ◽  
Aluminium Alloy ◽  
Strain Hardening ◽  
Plane Strain ◽  
Plane Stress ◽  
Analytical Models ◽  
Fe Model ◽  
Fe Simulations

Two-dimensional finite element (FE) studies, for plane stress, plane strain and axisymmetric conditions, were conducted to simulate 4 per cent cold working of a 6.35 mm diameter hole in a 6 mm thick plate of 2024 T 351 aluminium alloy. The simulations were used to assess the influence of strain hardening, the role of reversed yielding and through-thickness residual stress distributions. Experiments were also conducted to determine the tensile and compressive stress-strain response of the aluminium alloy, revealing a pronounced Bauschinger effect and non-linear strain hardening in compression. The FE simulations and results from several earlier analytical models were compared and substantial differnces found in the region of reversed yielding. Approximations used to model the compressive deformation behaviour of the material overestimate the compressive residual stresses at the hole edge. From the axisymmetric FE model a residual stress gradient through the plate thickness was found. The plane stress and plane strain assumptions used in the earlier analytical models did not satisfactorily approximate the three-dimensional residual stress fields obtained from the FE simulations.

A finite-element programme for the plane-strain analysis of rubber

1975 ◽  
Vol 10 (1) ◽  
pp. 25-31 ◽  
Author(s):  
P B Lindley
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Degrees Of Freedom ◽  
Strain Analysis ◽  
Strain Energy Function ◽  
Computation Time ◽  
Incompressible Material ◽  
Quadrilateral Elements ◽  
Triangular Elements ◽  
Classical Elasticity Theory

For a highly incompressible material the use of triangular elements in plane-strain finite-element analyses restricts the number of degrees of freedom. A computer programme is developed which uses quadrilateral elements, and various methods of reducing computation time are employed. A strain-energy function is proposed which will enable solutions to be obtained at strains well beyond those of linear classical elasticity theory.

Finite Element and Gradient-Based Optimization Tools for Multi-Parameter Nanoindentation Characterization of Materials With Non-Linear Stress/Strain Behavior

2004 ◽  
Author(s):  
Timothy C. Ovaert ◽  
Jianjun Wang
Keyword(s):  
Data Mining ◽  
Finite Element ◽  
Mechanical Test ◽  
Material Behavior ◽  
Analysis Tool ◽  
Unknown Parameters ◽  
Creep Tests ◽  
Wide Range ◽  
Non Linear ◽  
Gradient Based

The nanoindentation method is becoming increasingly popular for materials characterization, particularly for thin-films, coatings, and other materials that do not easily lend themselves to standard mechanical test methods. However, nanoindentation methods are limited when it comes to their description of a material behavior that deviates from simple elastic or visco-elastic responses. In this paper, we describe a four-parameter constitutive model that has been implemented in a PC-based analysis tool that combines non-linear finite element modeling with data mining gradient-based optimization methods to solve for the unknown parameters from an experimental nanoindentation creep curve. This “VNDM” (virtual nanoindentation and data mining) method, then, is used to complement experimental nanoindentation creep tests for more thorough material characterization. The results verify that the parametric model is capable of describing a wide-range of material behavior, including elastic, visco-elastic, and visco-plastic responses.

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