Importance of considering a material micro-failure criterion in the numerical modelling of the shot peening process applied to parabolic leaf springs

Shot peening is a cold-working mechanical process in which a shot stream is propelled against a component surface. Its purpose is to introduce compressive residual stresses on component surfaces for increasing the fatigue resistance. This process is widely applied in springs due to the cyclical loads requirements. This paper presents a numerical modelling of shot peening process using the finite element method. The results are compared with experimental measurements of the residual stresses, obtained by the X-rays diffraction technique, in leaf springs submitted to this process. Furthermore, the results are compared with empirical and numerical correlations developed by other authors.

Systemic risk in dynamical networks with stochastic failure criterion

Complex non-linear interactions between banks and assets we model by two time-dependent Erdos-Renyi network models where each node, representing a bank, can invest either to a single asset (model I) or multiple assets (model II). We use a dynamical network approach to evaluate the collective financial failure -systemic risk- quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided into sub-periods, where within each sub-period banks may contiguously fail due to links to either i) assets or ii) other banks, controlled by two parameters, probability of internal failure p and threshold T-h ("solvency" parameter). The systemic risk decreases with the average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller T-h), the smaller the systemic risk -for some Th values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic ii) controlled by probability p(2) -a condition for the bank to be solvent (active) is stochasticthe- systemic risk decreases with decreasing p(2). We analyse the asset allocation for the U.S. banks. Copyright (C) EPLA, 2014

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion for high strain and ballistic applications is presented. A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson–Cook failure criterion. The weakening in the elastic law and in the Johnson–Cook-like constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. Additionally, the mesh size dependency on the prediction of the fracture patterns was studied, showing that was crucial to predict such patterns

A failure criterion for fillet welds

The work constitutes a study of the strength of mild steel fillet welds subject to static loading, and the behaviour of flange welded beam-column connections under combined bending and shear. Tests are conducted on short welds in the as-welded and stress relieved conditions, and also on full-size beam-column connections. It is shown that welds under compression have a lower strength than when under tension. Failure of the fillet weld is initiated at the weld root, the important factor controlling the initiation being weld ductility. The greater the residual stress, the lower the weld ductility and ultimate strength. Thermal stress relieving increases strength by as much as 30%. Weld failure plane is rarely at the throat and varies from 0° to 45° depending upon loading condition. Failure plane average stresses are related by a circular function which is expressed in terms of externally applied forces at limit state. The tension weld of a flange-welded beam-column connection always fails before the compression weld. The shear load sharing between the welds is a complex function of elastic compression of the web, elastic/plastic deformation of the flanges, load/deformation characteristics, and the type of load application. Bearing forces between the compression flange and column face produce low level bearing stresses and frictional forces which make a negligible contribution to shear load resistance. Three modes of connection failure are possible; 'end mode', 'bending mode' and 'shear mode', with a sudden change taking place between the two latter.

An experimental and numerical study of ductile failure under quasi-static and impact loadings of Inconel 718 nickel-base superalloy

A numerical and experimental study of ballistic impacts at various temperatures on precipitation hardened Inconel 718 nickel-base superalloy plates has been performed. A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion has been implemented in LS-DYNA non-linear finite element code to model the mechanical behaviour of such an alloy. The ballistic impact tests have been carried out at three temperatures: room temperature (25 °C), 400 °C and 700 °C. The numerical study showed that the mesh size is crucial to predict correctly the shear bands detected in the tested plates. Moreover, the mesh size convergence has been achieved for element sizes on the same order that the shear bands. The residual velocity as well as the ballistic limit prediction has been considered excellent for high temperature ballistic tests. Nevertheless, the model has been less accurate for the numerical simulations performed at room temperature, being though in reasonable agreement with the experimental data. Additionally, the influence that the Lode angle had on quasi-static failure patterns such as cup-cone and slanted failure has been studied numerically. The study has revealed that the combined action of weakened constitutive equations and Lode angle dependent failure criterion has been necessary to predict the previously-mentioned failure patterns

Anisotropic viscous models of large-deformation Mohr-Coulomb failure

We have developed a way to represent Mohr-Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. We also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems.

An anisotropic viscous representation of Mohr-Coulomb failure for use is modelling coupled mantle-continent dynamics

In mantle convection models it has become common to make use of a modified (pressure sensitive, Boussinesq) von Mises yield criterion to limit the maximum stress the lithosphere can support. This approach allows the viscous, cool thermal boundary layer to deform in a relatively plate-like mode even in a fully Eulerian representation. In large-scale models with embedded continental crust where the mobile boundary layer represents the oceanic lithosphere, the von Mises yield criterion for the oceans ensures that the continents experience a realistic broad-scale stress regime. In detailed models of crustal deformation it is, however, more appropriate to choose a Mohr-Coulomb yield criterion based upon the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favorably oriented with respect to the stress field. As coupled crust/mantle models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantle convection problems coupled to large-scale crustal deformation. Our approach uses an orthotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation - neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane which is formally equivalent in any symmetric formulation. It is also important to allow strain-weakening of the material. The material should remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-Integration-point finite element code and will show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion, and comparisons between mantle convection models using the von Mises versus the Mohr-Coulomb yield criteria. The formulation itself is general and applies to 2D and 3D problems, although it is somewhat more complicated to identify the slip plane in 3D.

Wall material properties of yeast cells. Part II. Analysis

In the preceding paper (Part I) force-deformation data were measured with the compression experiment in conjunction with the initial radial stretch ratio and the initial wall-thickness to cell-radius ratio for baker's yeast (Saccharomyces cerevisiae). In this paper, these data have been analysed with the mechanical model of Smith et al. (Smith, Moxham & Middelberg (1998) Chemical Engineering Science, 53, 3913-3922) with the wall constitutive behaviour defined a priori as incompressible and linear-elastic. This analysis determined the mean Young's modulus ((E) over bar), mean maximum von Mises stress-at-failure (<(sigma)over bar>(VM,f)) and mean maximum von Mises strain-at failure (<(epsilon)over bar>(VM,f)) to be (E) over bar = 150 +/- 15 MPa, <(sigma)over bar>(VM,f) = 70 +/- 4 MPa and <(epsilon)over bar>(VM,f) = 0.75 +/- 0.08, respectively. The mean Young's modulus was not dependent (P greater than or equal to 0.05) on external osmotic pressure (0-0.8 MPa) nor compression rate (1.03-7.68 mu m/s) suggesting the incompressible linear-elastic relationship is representative of the actual cell-wall constitutive behaviour. Hydraulic conductivities were also determined and were comparable to other similar cell types (0-2.5 mu m/MPa s). The hydraulic conductivity distribution was not dependent on external osmotic pressure (0-0.8 MPa) nor compression rate (1.03-7.68 mu m/s) suggesting inclusion of cell-wall permeability in the mechanical model is justified. <(epsilon)over bar>(VM,f) was independent of cell diameter and to a first-approximation unaffected (P greater than or equal to 0.01) by external osmotic pressure and compression rate, thus providing a reasonable failure criterion. This criterion states that the cell-wall material will break when the strain exceeds <(epsilon)over bar>(VM,f) = 0.75 +/- 0.08. Variability in overall cell strength during compression was shown to be primarily due to biological variability in the maximum von Mises strain-at-failure. These data represent the first estimates of cell-wall material properties for yeast and the first fundamental analysis of cell-compression data. They are essential for describing cell-disruption at the fundamental level of fluid-cell interactions in general bioprocesses. They also provide valuable new measurements for yeast-cell physiologists. (C) 2000 Elsevier Science Ltd. All rights reserved.

The mechanical properties of Saccharomyces cerevisiae

Cell-wall mechanical properties play an integral part in the growth and form of Saccharomyces cerevisiae, In contrast to the tremendous knowledge on the genetics of S. cerevisiae, almost nothing is known about its mechanical properties. We have developed a micromanipulation technique to measure the force required to burst single cells and have recently established a mathematical model to extract the mechanical properties of the cell wall from such data, Here we determine the average surface modulus of the S, cerevisiae cell wall to be 11.1 +/- 0.6 N/m and 12.9 +/- 0.7 N/m in exponential and stationary phases, respectively, giving corresponding Young's moduli of 112 +/- 6 MPa and 107 +/- 6 MPa, This result demonstrates that yeast cell populations strengthen as they enter stationary phase by increasing wall thickness and hence the surface modulus, without altering the average elastic properties of the cell-wall material. We also determined the average breaking strain of the cell wall to be 82% +/- 3% in exponential phase and 80% +/- 3% in stationary phase, This finding provides a failure criterion that can be used to predict when applied stresses (e,g,, because of fluid flow) will lead to wall rupture, This work analyzes yeast compression experiments in different growth phases by using engineering methodology.

Determination of stresses around a cylindrical single pile caused by horizontal movements of soils with the finitive element method

This study was carried out with the aim of modeling in 2D, in plain strain, the movement of a soft cohesive soil around a pile, in order to enable the determination of stresses resulting along the pile, per unit length. The problem in study fits into the large deformations problem and can be due to landslide, be close of depth excavations, to be near of zones where big loads are applied in the soil, etc. In this study is used an constitutive Elasto-Plastic model with the failure criterion of Mohr-Coulomb to model the soil behavior. The analysis is developed considering the soil in undrained conditions. To the modeling is used the finite element program PLAXIS, which use the Updated Lagrangian - Finite Element Method (UL-FEM). In this work, special attention is given to the soil-pile interaction, where is presented with some detail the formulation of the interface elements and some studies for a better understand of his behavior. It is developed a 2-D model that simulates the effect of depth allowing the study of his influence in the stress distribution around the pile. The results obtained give an important base about how behaves the movement of the soil around a pile, about how work the finite element program PLAXIS and how is the stress distribution around the pile. The analysis demonstrate that the soil-structure interaction modeled with the UL-FEM and interface elements is more appropriate to small deformations problems.

Desenvolvimento de uma ferramenta para cálculo de estruturas em material compósito

Os desafios à engenharia moderna são cada vez maiores, pretendendo-se quase sempre obter estruturas mais leves, com propriedades mecânicas atrativas e muitas vezes com geometrias complexas. Com tais requisitos, um dos materiais que tem vindo a ter uma crescente aplicação é o material compósito. Contudo, no que toca ao cálculo estrutural destes materiais, tudo se torna mais complexo, já que são materiais que geralmente são formados por empilhamento de várias camadas de material heterogéneo, podendo estas encontrarem-se dispostas segundo diferentes orientações. Assim, a utilização de um software que permita a previsão das propriedades mecânicas de uma estrutura em material compósito através da micromecânica, a aplicação da Teoria Clássica dos Laminados e de um critério de rotura, como por exemplo o de Tsai-Hill, é fundamental para agilizar o processo de estudo da estrutura a fabricar. Para dar uma resposta a tal necessidade foi desenvolvida uma aplicação, em MATLAB® GUI, denominada CAFE – Composite Analysis For Engineers, com ambiente gráfico apelativo, que permite determinar todas as variáveis importantes no estudo de estruturas em material compósito. Esta aplicação visa suportar e agilizar a aprendizagem desta área do conhecimento, permitindo também o acesso ao código de cálculo por parte do utilizador, de modo a conhecerem-se as equações utilizadas e, eventualmente, ser alvo de futuros desenvolvimentos. O programa desenvolvido foi alvo de validação, recorrendo-se para tal, a uma comparação dos resultados obtidos entre o respetivo programa e por um outro programa de grande fiabilidade. Assim sendo, concluiu-se que o software CAFE apresenta resultados válidos, encontrando-se apto a ser utilizado.

Komposiittivaipan moderni optimisuunnittelu ja toteutus

Tavoitteena tällä tutkimuksella on soveltaa modernin optimisuunnittelun keinoja komposiittimuovisen nestesäiliön lieriömäisen vaipparakenteen suunnittelemiseksi optimaalisen tyydyttäviksi valmistustekniikan ja kustannusten kannalta. Kuormituksia on kahdenlaisia. Säiliön sisällä on neste, joka tuottaa hydrostaattisen painekuorman ja järjestelmään kytketty puhallin tuottaa ulkoisen ylipaineen. Säiliöt ovat pystysäiliöitä ja ne tukeutuvat alustaan suoran pohjalaatan avulla. FEM- malleissa kuoren alaosat ovat jäykästi kiinnitettyjä ja yläosissa säteensuuntaiset siirtymät ovat estettyjä. Materiaaleiksi kuoreen on valittu kahdella eri menetelmällä lujitetut komposiittimateriaalit. Kantavan kerroksen toimintona on kantaa kuormat. Sulkukerros toimii korroosiosuojana ja sen lujuus on kantavaa kerrosta pienempi. Keinoina käytetään ensin innovatiivista suunnittelua optimaalisten lähtövaihtoehtojen ideoimiseksi ja valitsemiseksi jatkokehittelyä varten. Tavoitteena on asiakkaan tyytyväisyyden maksimointi huomioiden tuotteen kustannukset ja kesto. Yhtenä suunnittelun keinona on käytetty kuoriteoriaa ja komposiittien materiaalimalleja. Kestoehtoina on sovellettu komposiiteille soveltuvia kriteerejä. Toisena keinona käytetään FEM-laskentaa. Elementtityypiksi on valittu kaksiulotteinen kuorielementti, jossa on ortotrooppisen ainemallin mukaiset materiaaliominaisuudet. Jännitystuloksien merkittävyys keston kannalta selvitettiin Tsai-Hillin kriteerillä. Tuloksina saatiin ensin innovoitua rakenteelle kaksi päävaihtoehtoa, joita alettiin optimoida. Valitussa ratkaisussa on huomioitu kokonaisuus ja eri yksityiskohdat, kuten paino, jäykisteet kustannustehokkuus, valmistusnopeus, laatu, hävikit, päästöt, lujuus ja kilpailukykyinen myyntihinta. Yhteenvetona voidaan todeta, että käytetyt keinot ovat hyvin tehokkaita ja niillä voidaan suunnitella ja toteuttaa komposiittirakenteita, jotka tyydyttävät optimaalisesti loppukäyttäjän teknis- taloudelliset vaatimukset. Lisäksi tulokset osoittavat, että standardin ja FEM-laskennan ennustukset ovat lähellä toisiaan sylinterimäisillä kuoriosilla, mutta standardit suosittavat suurempia mittoja itse jäykisteille.

Effect of partial-thickness tear on loading capacities of the supraspinatus tendon: a finite element analysis.

Partial-thickness tears of the supraspinatus tendon frequently occur at its insertion on the greater tubercule of the humerus, causing pain and reduced strength and range of motion. The goal of this work was to quantify the loss of loading capacity due to tendon tears at the insertion area. A finite element model of the supraspinatus tendon was developed using in vivo magnetic resonance images data. The tendon was represented by an anisotropic hyperelastic constitutive law identified with experimental measurements. A failure criterion was proposed and calibrated with experimental data. A partial-thickness tear was gradually increased, starting from the deep articular-sided fibres. For different values of tendon tear thickness, the tendon was mechanically loaded up to failure. The numerical model predicted a loss in loading capacity of the tendon as the tear thickness progressed. Tendon failure was more likely when the tendon tear exceeded 20%. The predictions of the model were consistent with experimental studies. Partial-thickness tears below 40% tear are sufficiently stable to persist physiotherapeutic exercises. Above 60% tear surgery should be considered to restore shoulder strength.

A Practical Micro Mechanical Model Based Local Approach Methodology for the Analysis of Ductile Fracture of Welded T-Joints

This thesis concentrates on developing a practical local approach methodology based on micro mechanical models for the analysis of ductile fracture of welded joints. Two major problems involved in the local approach, namely the dilational constitutive relation reflecting the softening behaviour of material, and the failure criterion associated with the constitutive equation, have been studied in detail. Firstly, considerable efforts were made on the numerical integration and computer implementation for the non trivial dilational Gurson Tvergaard model. Considering the weaknesses of the widely used Euler forward integration algorithms, a family of generalized mid point algorithms is proposed for the Gurson Tvergaard model. Correspondingly, based on the decomposition of stresses into hydrostatic and deviatoric parts, an explicit seven parameter expression for the consistent tangent moduli of the algorithms is presented. This explicit formula avoids any matrix inversion during numerical iteration and thus greatly facilitates the computer implementation of the algorithms and increase the efficiency of the code. The accuracy of the proposed algorithms and other conventional algorithms has been assessed in a systematic manner in order to highlight the best algorithm for this study. The accurate and efficient performance of present finite element implementation of the proposed algorithms has been demonstrated by various numerical examples. It has been found that the true mid point algorithm (a = 0.5) is the most accurate one when the deviatoric strain increment is radial to the yield surface and it is very important to use the consistent tangent moduli in the Newton iteration procedure. Secondly, an assessment of the consistency of current local failure criteria for ductile fracture, the critical void growth criterion, the constant critical void volume fraction criterion and Thomason's plastic limit load failure criterion, has been made. Significant differences in the predictions of ductility by the three criteria were found. By assuming the void grows spherically and using the void volume fraction from the Gurson Tvergaard model to calculate the current void matrix geometry, Thomason's failure criterion has been modified and a new failure criterion for the Gurson Tvergaard model is presented. Comparison with Koplik and Needleman's finite element results shows that the new failure criterion is fairly accurate indeed. A novel feature of the new failure criterion is that a mechanism for void coalescence is incorporated into the constitutive model. Hence the material failure is a natural result of the development of macroscopic plastic flow and the microscopic internal necking mechanism. By the new failure criterion, the critical void volume fraction is not a material constant and the initial void volume fraction and/or void nucleation parameters essentially control the material failure. This feature is very desirable and makes the numerical calibration of void nucleation parameters(s) possible and physically sound. Thirdly, a local approach methodology based on the above two major contributions has been built up in ABAQUS via the user material subroutine UMAT and applied to welded T joints. By using the void nucleation parameters calibrated from simple smooth and notched specimens, it was found that the fracture behaviour of the welded T joints can be well predicted using present methodology. This application has shown how the damage parameters of both base material and heat affected zone (HAZ) material can be obtained in a step by step manner and how useful and capable the local approach methodology is in the analysis of fracture behaviour and crack development as well as structural integrity assessment of practical problems where non homogeneous materials are involved. Finally, a procedure for the possible engineering application of the present methodology is suggested and discussed.

Modélisation radiobiologique pour la planification des traitements en radiothérapie à partir de données d’imagerie spécifiques aux patients

Un modèle de croissance et de réponse à la radiothérapie pour le glioblastome multiforme (GBM) basé le formalisme du modèle de prolifération-invasion (PI) et du modèle linéaire-quadratique a été développé et implémenté. La géométrie spécifique au patient est considérée en modélisant, d'une part, les voies d'invasion possibles des GBM avec l'imagerie du tenseur de diffusion (DTI) et, d'autre part, les barrières à la propagation à partir des images anatomiques disponibles. La distribution de dose réelle reçue par un patient donné est appliquée telle quelle dans les simulations, en respectant l'horaire de traitement. Les paramètres libres du modèle (taux de prolifération, coefficient de diffusion, paramètres radiobiologiques) sont choisis aléatoirement à partir de distributions de valeurs plausibles. Un total de 400 ensembles de valeurs pour les paramètres libres sont ainsi choisis pour tous les patients, et une simulation de la croissance et de la réponse au traitement est effectuée pour chaque patient et chaque ensemble de paramètres. Un critère de récidive est appliqué sur les résultats de chaque simulation pour identifier un lieu probable de récidive (SPR). La superposition de tous les SPR obtenus pour un patient donné permet de définir la probabilité d'occurrence (OP). Il est démontré qu'il existe des valeurs de OP élevées pour tous les patients, impliquant que les résultats du modèle PI ne sont pas très sensibles aux valeurs des paramètres utilisés. Il est également démontré comment le formalisme développé dans cet ouvrage pourrait permettre de définir un volume cible personnalisé pour les traitements de radiothérapie du GBM.