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.

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.

A non-smooth Newton method for the solution of magnetostatic field problems with hysteresis

2019 ◽  
Vol 38 (5) ◽  
pp. 1584-1594 ◽  
Author(s):  
Stephan Willerich ◽  
Hans-Georg Herzog
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Linear Equations ◽  
Element Formulation ◽  
Magnetostatic Field ◽  
Generalized Jacobian ◽  
Content Type ◽  
Non Linear ◽  
Generalized Framework ◽  
Gradient Based

Purpose The use of gradient-based methods in finite element schemes can be prevented by undefined derivatives, which are encountered when modeling hysteresis in constitutive material laws. This paper aims to present a method to deal with this problem. Design/methodology/approach Non-smooth Newton methods provide a generalized framework for the treatment of minimization problems with undefined derivatives. Within this paper, a magnetostatic finite element formulation that includes hysteresis is presented. The non-linear equations are solved using a non-smooth Newton method. Findings The non-smooth Newton method shows promising convergence behavior when applied to a model problem. The numbers of iterations for magnetization curves with and without hysteresis are within the same range. Originality/value Mathematical tools like Clarke's generalized Jacobian are applied to magnetostatic field problems with hysteresis. The relation between the non-smooth Newton method and other methods for solving non-linear systems with hysteresis like the M(B)-iteration is established.

Finite Element Analysis of a Locked Bolt With an Initial Crack

2009 ◽  
Author(s):  
Jean Paul Kabche ◽  
Mauri´cio Rangel Pacheco ◽  
Ivan Thesi ◽  
Luiz Carlos Largura
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Operating Conditions ◽  
Material Behavior ◽  
Isotropic Hardening ◽  
Stress Concentrations ◽  
Engineering Structures ◽  
Element Analysis ◽  
Micro Cracks ◽  
Non Linear

Bolted connections are largely employed in various types of engineering structures to transfer loads from one member to another. In particular, the off-shore industry has made extensive use of these connections, predominantly at the sub-sea level. In spite of their advantages, bolted joints are critical regions and may become sources of structural weakness due to large stress concentrations. Under severe operating conditions, micro-cracks can develop in the bolt, creating regions of elevated stress which may significantly reduce the integrity of the connection and ultimately lead to failure. This paper presents the three-dimensional finite element analysis of a steel locked bolt assembly aimed to assess the effect of micro-cracks on the structural integrity of the assembly using the commercial finite element package ANSYS. Non-linear contact between the bolt and nut threads is considered, where frictional sliding between components is allowed. A bi-linear isotropic hardening model is used to account for non-linear material behavior. The assembly is loaded by applying a pre-load of fifty percent of the yield stress of the material, according to the API-6A Norm. Two geometric models are investigated: a healthy locked bolt assembly with no initial cracks; and a damaged model, where a circular crack is introduced at the root of the bolt threads. The effect of the crack size is studied by modeling the crack with three different radius sizes. The J-Integral fracture mechanics methodology was used to study the stress concentrations in the damaged model.

scholarly journals Time-temperature behavior of carbon/epoxy laminates under creep loading

2020 ◽  
Author(s):  
Heitor L. Ornaghi ◽  
José Humberto S. Almeida ◽  
Francisco M. Monticeli ◽  
Roberta M. Neves ◽  
Maria Odila H. Cioffi
Keyword(s):  
Composite Laminates ◽  
Material Behavior ◽  
Short Term ◽  
Creep Tests ◽  
Advanced Composite ◽  
Wide Range ◽  
Temperature Superposition ◽  
Term Creep ◽  
Creep Loading ◽  
Short Term Creep

Abstract The time-temperature creep behavior of advanced composite laminates is herein determined through a comprehensive set of experiments and analytical modeling. A complete structure versus property relationship is determined through a wide range of temperature and applied stress levels at the three states of the composite: glassy, glass transition, and rubbery regions. Weibull, Eyring, Burger, and Findley models are employed to predict the experimental data and to better elucidate the material behavior. Experimental creep tests are carried out under ten min and two days aiming at calibrating fitting parameters, which are essential to validate short-term creep tests. The Weibull and Eyring models are more suitable for determining the time-temperature superposition (TTS) creep response in comparison to the Burger and Findley models.

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.

scholarly journals COMPARISON OF COMPUTER-AIDED INTEGRATION TECHNIQUES WHEN OBTAINING INITIAL DISPLACEMENTS MATRIX FOR GEOMETRICALLY NON-LINEAR LAMINATED FINITE ELEMENT /KOMPIUTERINIŲ INTEGRAVIMO TECHNOLOGIJŲ PALYGINIMAS SUDARANT GEOMETRIŠKAI NETIESINIO SLUOKSNIUOTOJO BAIGTINIO ELEMENTO PRADINIŲ POSLINKIŲ MATRICĄ

2001 ◽  
Vol 7 (5) ◽  
pp. 352-358
Author(s):  
Valentinas Kulinič
Keyword(s):  
Finite Element ◽  
Personal Computer ◽  
Stiffness Matrix ◽  
Iteration Process ◽  
Elastic Stiffness ◽  
Laminated Plates ◽  
Initial Displacement ◽  
Tangent Stiffness Matrix ◽  
Wide Range ◽  
Non Linear

Geometrical non-linearity of the laminated element has not been realized so far in the widely known commercial finite element method packages such as ABAQUS, ALGOR, ANSYS, COSMOS although researches in that field are actively carried out. On the other hand, there is a lot of problems where large displacements and deformations must be dealt with to obtain a precise decision. A wide range of composite orthotopic materials is used in constructions and other fields of technology. Various numerical methods were implemented to handle laminated plates and shells, however most of them are intended for application only with particular types of the structures. The author's aim is to develop a geometrically nonlinear finite element that could be effectively used for analysis of various laminated slabs regardless of their shape, thickness of laminae, properties of materials, direction of orthotropy axes, way of loading and boundary conditions. Obtaining and handling the element's initial displacement matrix used in the iteration process is a highly complicated issue requiring significant amount of computer resources to be involved. One of the most important aims of the research is to develop an element which could be used not only in an expensive multiprocessor mainframes, but also in an usual personal computer. For the structure, a sophisticated finite element TRIPLT having 50 degrees of freedom is used. The geometrical matrix for this element is obtained involving L-coordinates' array while displacements and rotations in the middle of the element are expressed through the nodal displacements (rotations), their derivatives, and displacements (rotations) in the central point. Linear and non-linear components for the geometrical matrix are shown in Eqs 2 and 5. The behaviour of a geometrical non-linear finite elements structure is described by Eq 8. The tangent stiffness matrix consists of the conventional linear elastic stiffness matrix, initial stress matrix and initial displacements matrix which is obtained by Eq 10, using both analytical and/or numerical integrating. The analytical integrating involves expanding of the appropriate expressions into basic matrices (Eqs 11, 12) and using formula 15. The initial displacement matrix in term of constitutive matrix's elements and the basic matrices is shown in Eqs 13 and 14. Numerical integrating is conducted by two methods: those using Hammer and Gauss-Radau weight coefficients. Numerical approach is applied both to the basic matrices and factorised expressions of submatrices involving intermediate arrays and matrices (Eqs 23, 24). Two ways of obtaining the intermediate arrays and matrices are discussed. Because of high complexity of the procedures involved the computer algebra system Mathematica was used for the integrating and recording FORTRAN codes. Comparison of the effectiveness of all the procedures is presented in a table. The investigation results show that the initial displacement matrix obtained by means of numerical integration involves a small amount of arithmetic operations to be handled with a usual personal computer.

Caisson Capacity in Clay: VHM Resistance Envelope: Part 3—Extension to Shallow Foundations

2011 ◽  
Author(s):  
S. Kay ◽  
E. Palix
Keyword(s):  
Shear Strength ◽  
Load Resistance ◽  
Analysis Tool ◽  
Foundation Soil ◽  
Finite Element Program ◽  
Near Surface ◽  
Wide Range ◽  
Soil Shear Strength ◽  
Non Linear ◽  
Element Program

Suction embedded caissons are efficient and economic solutions to anchor floating structures. A more recent caisson application is to support seafloor structures such as manifolds, PLEMs, pumps, etc. For a deepwater hydrocarbon field, many types of seafloor structures are required, each with their own characteristics and slightly different design. Caisson designs increasingly use resistance envelope methodology. This eliminates non-linear 3D FE analyses (except for assessing responses or soil reactions), and facilitates probabilistic and optimisation analyses. In general, there is a requirement for a reliable method of assessing caisson capacity under general VHM load. Resistance envelope equations for “deep” circular caissons (1.5 < L/D < 6) have been presented by Kay and Palix (2010) for a wide range of soil undrained shear strength profiles. This paper extends the study to cover near-surface caissons (i.e. 0 ≤ L/D ≤ 1.5). As in previous studies, a quasi 3D non-linear finite element program (HARMONY) was the primary numerical analysis tool. Three soil shear strength profiles were investigated for 13 caisson embedment ratios. In the range 0 ≤ L/D ≤ 1.5, VHM envelope shapes transform from a “scallop” at L/D ≈ 0 into a “tongue” above a critical caisson embedment ratio (L/D)crit of about 0.5 The equations originally developed for the rotated ellipse/ellipsoid (i.e. “tongue”-shaped envelope) in Kay and Palix (2010) for L/D ≤ 1.5 have been extended for (L/D)crit ≥ L/D. All parameters are simple functions of L/D and soil shear strength profile. Major limitations and assumptions made were (a) foundation-soil tension was permitted and (b) no internal scoop failure (i.e. within the soil plug inside the caisson) was possible. These are important for low L/D: both may adversely affect VHM resistance.

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.

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

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