Analysis of elastic functionally graded materials under large displacements via high-order tetrahedral elements

The purpose of this study is to present a position based tetrahedral finite element method of any order to accurately predict the mechanical behavior of solids constituted by functionally graded elastic materials and subjected to large displacements. The application of high-order elements makes it possible to overcome the volumetric and shear locking that appears in usual homogeneous isotropic situations or even in non-homogeneous cases developing small or large displacements. The use of parallel processing to improve the computational efficiency, allows employing high-order elements instead of low-order ones with reduced integration techniques or strain enhancements. The Green-Lagrange strain is adopted and the constitutive relation is the functionally graded Saint Venant-Kirchhoff law. The equilibrium is achieved by the minimum total potential energy principle. Examples of large displacement problems are presented and results confirm the locking free behavior of high-order elements for non-homogeneous materials. (C) 2011 Elsevier B.V. All rights reserved.

A Design Method for Flexure-Based Compliant Mechanisms on the Basis of Stiffness and Stress Characteristics

Geometric nonlinearities of flexure hinges introduced by large deflections often complicate the analysis of compliant mechanisms containing such members, and therefore, Pseudo-Rigid-Body Models (PRBMs) have been well proposed and developed by Howell [1994] to analyze the characteristics of slender beams under large deflection. These models, however, fail to approximate the characteristics for the deep beams (short beams) or the other flexure hinges. Lobontiu's work [2001] contributed to the diverse flexure hinge analysis building on the assumptions of small deflection, which also limits the application range of these flexure hinges and cannot analyze the stiffness and stress characteristics of these flexure hinges for large deflection. Therefore, the objective of this thesis is to analyze flexure hinges considering both the effects of large-deflection and shear force, which guides the design of flexure-based compliant mechanisms. The main work conducted in the thesis is outlined as follows. 1. Three popular types of flexure hinges: (circular flexure hinges, elliptical flexure hinges and corner-filleted flexure hinges) are chosen for analysis at first. 2. Commercial software (Comsol) based Finite Element Analysis (FEA) method is then used for correcting the errors produced by the equations proposed by Lobontiu when the chosen flexure hinges suffer from large deformation. 3. Three sets of generic design equations for the three types of flexure hinges are further proposed on the basis of stiffness and stress characteristics from the FEA results. 4. A flexure-based four-bar compliant mechanism is finally studied and modeled using the proposed generic design equations. The load-displacement relationships are verified by a numerical example. The results show that a maximum error about the relationship between moment and rotation deformation is less than 3.4% for a flexure hinge, and it is lower than 5% for the four-bar compliant mechanism compared with the FEA results.

Numerical methods in Nonlinear Analysis of shell structures

The design of shell and spatial structures represents an important challenge even with the use of the modern computer technology.If we concentrate in the concrete shell structures many problems must be faced,such as the conceptual and structural disposition, optimal shape design, analysis, construction methods, details etc. and all these problems are interconnected among them. As an example the shape optimization requires the use of several disciplines like structural analysis, sensitivity analysis, optimization strategies and geometrical design concepts. Similar comments can be applied to other space structures such as steel trusses with single or double shape and tension structures. In relation to the analysis the Finite Element Method appears to be the most extended and versatile technique used in the practice. In the application of this method several issues arise. First the derivation of the pertinent shell theory or alternatively the degenerated 3-D solid approach should be chosen. According to the previous election the suitable FE model has to be adopted i.e. the displacement,stress or mixed formulated element. The good behavior of the shell structures under dead loads that are carried out towards the supports by mainly compressive stresses is impaired by the high imperfection sensitivity usually exhibited by these structures. This last effect is important particularly if large deformation and material nonlinearities of the shell may interact unfavorably, as can be the case for thin reinforced shells. In this respect the study of the stability of the shell represents a compulsory step in the analysis. Therefore there are currently very active fields of research such as the different descriptions of consistent nonlinear shell models given by Simo, Fox and Rifai, Mantzenmiller and Buchter and Ramm among others, the consistent formulation of efficient tangent stiffness as the one presented by Ortiz and Schweizerhof and Wringgers, with application to concrete shells exhibiting creep behavior given by Scordelis and coworkers; and finally the development of numerical techniques needed to trace the nonlinear response of the structure. The objective of this paper is concentrated in the last research aspect i.e. in the presentation of a state-of-the-art on the existing solution techniques for nonlinear analysis of structures. In this presentation the following excellent reviews on this subject will be mainly used.

Numerical and experimental investigation of structural stiffness influence on ratcheting convection cell in granular soils under cyclic loading

Lateral cyclic loaded structures in granular soils can lead to an accumulation of irreversible strains by changing their mechanical response (densification) and forming a closed convective cell in the upper layer of the bedding. In the present thesis the convective cell dimension, formation and grain migration inside this closed volume have been studied and presented in relation to structural stiffness and different loads. This relation was experimentally investigated by applying a cyclic lateral force to a scaled flexible vertical element embedded in dry granular soil. The model was monitored with a camera in order to derive the displacement field by means of the PIV technique. Modelling large soil deformation turns out to be difficult, using mesh-based methods. Consequently, a mesh-free approach (DEM) was chosen in order to investigate the granular flow with the aim of extracting interesting micromechanical information. In both the numerical and experimental analyses the effect of different loading magnitudes and different dimensions of the vertical element were considered. The main results regarded the different development, shape and dimensions of the convection cell and the surface settlements. Moreover, the Discrete Element Method has proven to give satisfactory results in the modelling of large deformation phenomena such as the ratcheting convective cell.

An analysis of the effect of process parameters on the formability of sheet metal

This investigation is in two parts, theory and experimental verification. (1) Theoretical Study In this study it is, for obvious reasons, necessary to analyse the concept of formability first. For the purpose of the present investigation it is sufficient to define the four aspects of formability as follows: (a) the formability of the material at a critical section, (b) the formability of the material in general, (c) process efficiency, (d) proportional increase in surface area. A method of quantitative assessment is proposed for each of the four aspects of formability. The theoretical study also includes the distinction between coaxial and non-coaxial strains which occur, respectively, in axisymmetrical and unsymmetrical forming processes and the inadequacy of the circular grid system for the assessment of formability is explained in the light of this distinction. (2) Experimental Study As one of the bases of the experimental work, the determination of the end point of a forming process, which sets the limit to the formability of the work material, is discussed. The effects of three process parameters on draw-in are shown graphically. Then the delay of fracture in sheet metal forming resulting from draw-in is analysed in kinematical terms, namely, through the radial displacements, the radial and the circumferential strains, and the projected thickness of the workpiece. Through the equilibrium equation of the membrane stresses, the effect on the shape of the unsupported region of the workpiece, and hence the position of the critical section is explained. Then, the effect of draw-in on the four aspects of formability is discussed throughout this investigation. The triangular coordinate system is used to present and analyse the triaxial strains involved. This coordinate system has the advantage of showing all the three principal strains in a material simultaneously, as well as representing clearly the many types of strains involved in sheet metal work.

Two dimensional analysis of inflatable structures by the positional FEM

This paper presents a, simple two dimensional frame formulation to deal with structures undergoing large motions due to dynamic actions including very thin inflatable structures, balloons. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions. Velocity, acceleration and strain are achieved directly from positions, not. displacements, characterizing the novelty of the proposed technique. A non-dimensional space is created and the deformation function (change of configuration) is written following two independent mappings from which the strain energy function is written. The classical New-mark equations are used to integrate time. Dumping and non-conservative forces are introduced into the mechanical system by a rheonomic energy function. The final formulation has the advantage of being simple and easy to teach, when compared to classical Counterparts. The behavior of a bench-mark problem (spin-up maneuver) is solved to prove the formulation regarding high circumferential speed applications. Other examples are dedicated to inflatable and very thin structures, in order to test the formulation for further analysis of three dimensional balloons.

Recycling Krylov subspaces for efficient large-scale electrical impedance tomography

Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the resulting electric potentials are measured. Then, based on the measurements, an estimation algorithm obtains the three-dimensional internal admittivity distribution that corresponds to the image. One of the main goals of medical EIT is to achieve high resolution and an accurate result at low computational cost. However, when the finite element method (FEM) is employed and the corresponding mesh is refined to increase resolution and accuracy, the computational cost increases substantially, especially in the estimation of absolute admittivity distributions. Therefore, we consider in this work a fast iterative solver for the forward problem, which was previously reported in the context of structural optimization. We propose several improvements to this solver to increase its performance in the EIT context. The solver is based on the recycling of approximate invariant subspaces, and it is applied to reduce the EIT computation time for a constant and high resolution finite element mesh. In addition, we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver. The numerical results show the effectiveness of our approach: the proposed algorithm is faster than the preconditioned conjugate gradient (CG) algorithm. The results also show that even on a standard PC without parallelization, a high mesh resolution (more than 150,000 degrees of freedom) can be used for image estimation at a relatively low computational cost. (C) 2010 Elsevier B.V. All rights reserved.

Using the level set method to model endogenous lava dome growth

Modeling volcanic phenomena is complicated by free-surfaces often supporting large rheological gradients. Analytical solutions and analogue models provide explanations for fundamental characteristics of lava flows. But more sophisticated models are needed, incorporating improved physics and rheology to capture realistic events. To advance our understanding of the flow dynamics of highly viscous lava in Peléean lava dome formation, axi-symmetrical Finite Element Method (FEM) models of generic endogenous dome growth have been developed. We use a novel technique, the level-set method, which tracks a moving interface, leaving the mesh unaltered. The model equations are formulated in an Eulerian framework. In this paper we test the quality of this technique in our numerical scheme by considering existing analytical and experimental models of lava dome growth which assume a constant Newtonian viscosity. We then compare our model against analytical solutions for real lava domes extruded on Soufrière, St. Vincent, W.I. in 1979 and Mount St. Helens, USA in October 1980 using an effective viscosity. The level-set method is found to be computationally light and robust enough to model the free-surface of a growing lava dome. Also, by modeling the extruded lava with a constant pressure head this naturally results in a drop in extrusion rate with increasing dome height, which can explain lava dome growth observables more appropriately than when using a fixed extrusion rate. From the modeling point of view, the level-set method will ultimately provide an opportunity to capture more of the physics while benefiting from the numerical robustness of regular grids.

Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

Mantle convection modeling with viscoelastic/brittle lithosphere: Numerical methodology and plate tectonic modeling

The earth's tectonic plates are strong, viscoelastic shells which make up the outermost part of a thermally convecting, predominantly viscous layer. Brittle failure of the lithosphere occurs when stresses are high. In order to build a realistic simulation of the planet's evolution, the complete viscoelastic/brittle convection system needs to be considered. A particle-in-cell finite element method is demonstrated which can simulate very large deformation viscoelasticity with a strain-dependent yield stress. This is applied to a plate-deformation problem. Numerical accuracy is demonstrated relative to analytic benchmarks, and the characteristics of the method are discussed.

Anisotropic convection model for the earth's mantle

The paper presents a theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including the folding and kinking of multi-layered visco-elastic rock (Muhlhaus et al. [1,2]). The orientation of slip planes in the context of crystallographic slip is determined by the normal vector - the director - of these surfaces. The model is applied to simulate anisotropic mantle convection. We compare the evolution of flow patterns, Nusselt number and director orientations for isotropic and anisotropic rheologies. In the simulations we utilize two different finite element methodologies: The Lagrangian Integration Point Method Moresi et al [8] and an Eulerian formulation, which we implemented into the finite element based pde solver Fastflo (www.cmis.csiro.au/Fastflo/). The reason for utilizing two different finite element codes was firstly to study the influence of an anisotropic power law rheology which currently is not implemented into the Lagrangian Integration point scheme [8] and secondly to study the numerical performance of Eulerian (Fastflo)- and Lagrangian integration schemes [8]. It turned out that whereas in the Lagrangian method the Nusselt number vs time plot reached only a quasi steady state where the Nusselt number oscillates around a steady state value the Eulerian scheme reaches exact steady states and produces a high degree of alignment (director orientation locally orthogonal to velocity vector almost everywhere in the computational domain). In the simulations emergent anisotropy was strongest in terms of modulus contrast in the up and down-welling plumes. Mechanisms for anisotropic material behavior in the mantle dynamics context are discussed by Christensen [3]. The dominant mineral phases in the mantle generally do not exhibit strong elastic anisotropy but they still may be oriented by the convective flow. Thus viscous anisotropy (the main focus of this paper) may or may not correlate with elastic or seismic anisotropy.

Predicting the mechanical behavior of amorphous polymeric materials under strain through multi-scale simulation

Polymeric materials have become the reference material for high reliability and performance applications. However, their performance in service conditions is difficult to predict, due in large part to their inherent complex morphology, which leads to non-linear and anisotropic behavior, highly dependent on the thermomechanical environment under which it is processed. In this work, a multiscale approach is proposed to investigate the mechanical properties of polymeric-based material under strain. To achieve a better understanding of phenomena occurring at the smaller scales, the coupling of a finite element method (FEM) and molecular dynamics (MD) modeling, in an iterative procedure, was employed, enabling the prediction of the macroscopic constitutive response. As the mechanical response can be related to the local microstructure, which in turn depends on the nano-scale structure, this multiscale approach computes the stress-strain relationship at every analysis point of the macro-structure by detailed modeling of the underlying micro- and meso-scale deformation phenomena. The proposed multiscale approach can enable prediction of properties at the macroscale while taking into consideration phenomena that occur at the mesoscale, thus offering an increased potential accuracy compared to traditional methods.

Estudo de Ferramentas FEA Comerciais na Simulação Numérica de Processos de Conformação de Chapas Metálicas. Aplicação à Indústria Automóvel.

Os componentes obtidos através da conformação plástica de chapas têm uma grande importância, tanto na etapa de concepção do produto como na etapa de produção na indústria automóvel. Isto comprova-se pelo facto de, em média, cada automóvel integrar cerca de 500 componentes estampados para construir o chassis e a carroçaria [Alves 2003]. Deste total de componentes, 50 são de grandes dimensões (portas, tejadilho, painéis inferior e laterais, entre outros) e necessitam, em média, de cinco ferramentas para o seu fabrico, sendo o custo estimado para cada ferramenta de 230 000 € [Col 2000, Alves 2003]. Para além da indústria automóvel, a conformação plástica de chapas metálicas é um processo tecnológico presente nas indústrias relativas à aeroespacial, petrolífera, decoração, alimentar, entre outras. Do ponto de vista do enquadramento económico, cerca de 20% do custo total de um automóvel novo é devido à incorporação de componentes metálicos estampados. [Alves 2003]. A pressão do “Mercado Global” faz com que os custos relativos à matéria-prima, energia e mão-de-obra sejam uma constante em termos de redução do seu impacte no orçamento das empresas fornecedoras destes produtos. É neste contexto que surge a necessidade da realização deste estudo de Benchmark de Softwares, tornando-se bastante importante, quer ao nível da competitividade industrial, quer ao nível da inovação para novos produtos. A análise por elementos finitos desempenha um papel primordial no tryout virtual e otimização das ferramentas e processos de conformação plástica. Os objetivos principais deste estudo de simulação numérica são a identificação e comparação dos resultados obtidos pelo AUTOFORM e pelo PAMSTAMP, para cada uma das variáveis identificadas como as mais influentes na robustez dos processos de estampagem de chapa metálica. Estas variáveis identificadas são: consumo de material (Draw-in) após conformação; forças de conformação; valores de variação de espessura e dos valores de extensão e resultados de Springback. Os resultados obtidos são comparados com os resultados experimentais e, desta forma, avalia-se a capacidade inovadora e a eficácia de cada um dos softwares, obtendo-se assim, uma orientação mais real para o software mais indicado aos objetivos impostos pela indústria automóvel. Para este efeito, a indústria automóvel, como maior impulsionador e motor da investigação na área da simulação numérica aplicada aos processos de estampagem, tem aderido em peso ao Benchmarking. Um exemplo disto, é o que acontece nas conferências Numisheet. O Benchmark #2 da conferência Numisheet 2008 é analisado pormenorizadamente e os resultados numéricos e experimentais são comparados e apresentados. Dois materiais distintos (aço HC260LAD e liga de alumínio AC170), assim como três modelos com geometrias diferentes (com e sem freios) são apresentados neste relatório. Com vista à redução dos ciclos tentativa-erro, tem-se adotado ciclos virtuais ou numéricos e tem-se incrementado a interatividade entre as fases de concepção e projeto, num conceito muito próprio, mas cada vez mais abrangente, denominado “produção virtual”. É nesta filosofia que se insere a simulação numérica dos processos de conformação de chapa.

Matala-aktiivisen metallijätteen aktiivisuusmittaukset Loviisan voimalaitoksella

Tämän diplomityön lähtökohtana oli metallijätteen mittausmenetelmien kehittäminen Loviisan voimalaitoksella. Työn taustalla oli myös Säteilyturvakeskuksen antaman ohjeen YVL 8.2 ’Ydinjätteiden ja käytöstä poistettujen ydinlaitosten vapauttaminen valvonnasta’ uusinta. Työssä arvioitiin miten YVL 8.2 -ohjeen päivitys vaikuttaa Loviisan voimalaitoksen metallijätteen käsittelyyn vapautusmenettelyn osalta. Diplomityössä arvioitiin eri aktiivisuusmittausmenetelmien havaitsemia aktiivisuuksia metallijätteessä. Metallijätteen mittausmenetelmien arviointi aloitettiin kirjalliseen materiaaliin tutustumisella, jonka jälkeen mittausmenetelmiä verrattiin kokeellisesti. Verrattavia mittauksia olivat suora kontaminaatiomittaus, gammaspektrometrinen mittaus, kuiva-, märkä-, ja happopyyhintänäytteet sekä mittaus Condor E -monitorilla. Diplomityö sisältää myös arvioinnin ajoneuvojen säteilymittauslaitteiston käytöstä metallijätteen valvonnasta vapauttamisessa. Työssä arvioitiin myös mittausmenetelmän vaikutusta logistiikkaketjuun Loviisan voimalaitoksella ja kaiken metallijätteen loppusijoittamisen vaikutuksia. Nykyinen metallijätteen vapautusmenettely on raskas, eikä täysin uusitun ohjeen YVL 8.2 vaatimusten mukainen. Diplomityön tuloksena metallijätteen käsittelymenetelmäksi suositellaan metallijätteen vapauttamista valvonnasta seuraavin menettelyin. Pieni metallijäte tulisi huolellisen esimittauksen jälkeen pakata ja analysoida gammaspektrometrisesti. Suuret metallijätekappaleet tulisi analysoida pyyhintänäytteiden perusteella. Pyyhintänäytteiden analysointi kannattaisi suorittaa gammaspektrometrillä, koska sillä saavutetaan tarkin tulos ja se on täysin ohjeen YVL 8.2 vaatimusten mukainen. Loppusijoitusluolaan tulisi sijoittaa mahdollisimman pieni määrä vapauttamiskelpoista metallijätettä. Myös ajoneuvojen säteilymittauslaitteiston käyttöä varmentavana mittauksena tulisi tehostaa.

Modelling metal cutting using modern ductile fracture mechanics: Quantitative explanations for some longstanding problems

The assumption that negligible work is involved in the formation of new surfaces in the machining of ductile metals, is re-examined in the light of both current Finite Element Method (FEM) simulations of cutting and modern ductile fracture mechanics. The work associated with separation criteria in FEM models is shown to be in the kJ/m2 range rather than the few J/m2 of the surface energy (surface tension) employed by Shaw in his pioneering study of 1954 following which consideration of surface work has been omitted from analyses of metal cutting. The much greater values of surface specific work are not surprising in terms of ductile fracture mechanics where kJ/m2 values of fracture toughness are typical of the ductile metals involved in machining studies. This paper shows that when even the simple Ernst–Merchant analysis is generalised to include significant surface work, many of the experimental observations for which traditional ‘plasticity and friction only’ analyses seem to have no quantitative explanation, are now given meaning. In particular, the primary shear plane angle φ becomes material-dependent. The experimental increase of φ up to a saturated level, as the uncut chip thickness is increased, is predicted. The positive intercepts found in plots of cutting force vs. depth of cut, and in plots of force resolved along the primary shear plane vs. area of shear plane, are shown to be measures of the specific surface work. It is demonstrated that neglect of these intercepts in cutting analyses is the reason why anomalously high values of shear yield stress are derived at those very small uncut chip thicknesses at which the so-called size effect becomes evident. The material toughness/strength ratio, combined with the depth of cut to form a non-dimensional parameter, is shown to control ductile cutting mechanics. The toughness/strength ratio of a given material will change with rate, temperature, and thermomechanical treatment and the influence of such changes, together with changes in depth of cut, on the character of machining is discussed. Strength or hardness alone is insufficient to describe machining. The failure of the Ernst–Merchant theory seems less to do with problems of uniqueness and the validity of minimum work, and more to do with the problem not being properly posed. The new analysis compares favourably and consistently with the wide body of experimental results available in the literature. Why considerable progress in the understanding of metal cutting has been achieved without reference to significant surface work is also discussed.