Modeling the Axial Splitting and Curling of Metal Tubes under Crush Loads

Plastic deformation and splitting are two important mechanisms of energy dissipation when metal tubes undergo axial crushing. Isotropic J2 plasticity theory combined with a failure criterion is used to model axial splitting and curling of metal tubes undergoing axial crush. The proposed material model is implemented within a finite element (FE) framework using the user material subroutine VUMAT option available in the commercial code ABAQUS. Experimental results from literature are used to validate the model. The predicted splitting and curling patterns as well as the load-displacement response agree well with the experimental observations. The present material model is also used to predict the number of axial cracks in splitting the tube.     

Simultaneous surface and tetrahedron mesh adaptation using mesh‐free techniques

We present a method to adapt a tetrahedron mesh together with a surface mesh with respect to a size criterion. The originality of our work lies in the fact that both surface and tetrahedron mesh adaptation are carried out simultaneously and that no CAD is required to adapt the surface mesh. The adaptation procedure consists of splitting or removing interior and surface edges which violate a given size criterion. The enrichment process is based on a bisection technique. In order to guarantee mesh conformity during the refinement process, all possible remeshing configurations of tetrahedra have been examined. Once the tetrahedron mesh has been adapted, surface nodes are projected on a geometrical model. The building of a surface model from discrete data has already been presented in this journal. The method is based on a mesh‐free technique called Hermite Diffuse Interpolation. Surface and volume mesh optimization procedures are carried out during the adaptation and at the end of the process to enhance the mesh. Copyright © 2003 John Wiley & Sons, Ltd.     

A two objective optimisation model for order splitting among parallel suppliers

To correctly split an order among parallel suppliers is one of the most important ways to improve the agility and competitiveness of a supply chain. For this order splitting problem, an evaluation criterion of production load equilibrium among parallel suppliers is introduced and a two objective order splitting model is developed to minimise the comprehensive cost and balance the production loads among the selected suppliers. The procedure of the suppliers’ selection is proposed and non-dominated sorting genetic algorithm (NSGA-II) is applied to find the feasible solution set of Pareto. The simulation results indicate that the proposed model and algorithm is capable of obtaining satisfactory solutions.     

Crack formation and fracture energy of normal and high strength concrete

The crack path through composite materials such as concrete depends on the mechanical interaction of inclusions with the cement-based matrix. Fracture energy depends on the deviations of a real crack from an idealized crack plane. FRACTURE energy and strain softening of normal, high strength, and self-compacting concrete have been determined by means of the wedge splitting test. In applying the numerical model called “numerical concrete” crack formation in normal and high strength concrete is simulated. Characteristic differences of the fracture process can be outlined. Finally results obtained are applied to predict shrinkage cracking under different boundary conditions. Crack formation of high strength concrete has to be seriously controlled in order to achieve the necessary durability of concrete structures.     

Nonlinear fracture mechanics and plasticity of the split cylinder test

The split cylinder test is subjected to an analysis combining nonlinear fracture mechanics and plasticity. The fictitious crack model is applied for the analysis of splitting tensile fracture, and the Mohr-Coulomb yield criterion is adopted for modelling the compressive crushing/sliding failure. Two models are presented, a simple semi-analytical model based on analytical solutions for the crack propagation in a rectangular prismatic body, and a finite element model including plasticity in bulk material as well as crack propagation in interface elements. A numerical study applying these models demonstrates the influence of varying geometry or constitutive properties. For a split cylinder test in load control it is shown how the ultimate load is either plasticity dominated or fracture mechanics dominated. The transition between the two modes is related to changes in geometry or constitutive properties. This implies that the linear elastic interpretation of the ultimate splitting force in term of the uniaxial tensile strength of the material is only valid for special situations, e.g. for very large cylinders. Furthermore, the numerical analysis suggests that the split cylinder test is not well suited for determining the tensile strength of early age or fibre reinforced concrete.     

Validation and data splitting in predictive regression modeling of honing surface roughness data

Model validation is critical in predicting the performance of manufacturing processes. In predictive regression, proper selection of variables helps minimize the model mismatch error, proper selection of models helps reduce the model estimation error, and proper validation of models helps minimize the model prediction error. In this paper, the literature is briefly reviewed and a rigorous procedure is proposed for evaluating the validation and data splitting methods in predictive regression modeling. Experimental data from a honing surface roughness study will be used to illustrate the methodology. In particular, the individual versus average data splitting methods as well as the fivefold versus threefold cross-validation methods are compared. This paper shows that statistical tests and prediction errors evaluation are important in subset selection and cross-validation of predictive regression models. No statistical differences were found between the fivefold and the threefold cross-validation methods, and between use of the individual and average data splitting methods in predictive regression modeling.     

Multicomponent model of deformation and detachment of a biofilm under fluid flow

A novel biofilm model is described which systemically couples bacteria, extracellular polymeric substances (EPS) and solvent phases in biofilm. This enables the study of contributions of rheology of individual phases to deformation of biofilm in response to fluid flow as well as interactions between different phases. The model, which is based on first and second laws of thermodynamics, is derived using an energetic variational approach and phase-field method. Phase-field coupling is used to model structural changes of a biofilm. A newly developed unconditionally energy-stable numerical splitting scheme is implemented for computing the numerical solution of the model efficiently. Model simulations predict biofilm cohesive failure for the flow velocity between and m s⁻¹ which is consistent with experiments. Simulations predict biofilm deformation resulting in the formation of streamers for EPS exhibiting a viscous-dominated mechanical response and the viscosity of EPS being less than . Higher EPS viscosity provides biofilm with greater resistance to deformation and to removal by the flow. Moreover, simulations show that higher EPS elasticity yields the formation of streamers with complex geometries that are more prone to detachment. These model predictions are shown to be in qualitative agreement with experimental observations.     

Return mapping algorithms and consistent tangent operators in ferroelectroelasticity

Return mapping algorithms for a rather general class of phenomenological rate‐independent models for ferroelectroelastic materials are presented. The fully coupled thermodynamically consistent three‐dimensional constitutive model with two internal variables (remanent polarization vector and remanent strain tensor) proposed by C. M. Landis in 2002 is used for the simulation of electromechanical hysteresis effects in polycrystalline ferroelectric ceramics. Based on the operator splitting methodology, the return mapping algorithm employs the closest point projection scheme to obtain an efficient and robust integration of the constitutive model. The consistent tangent operator is obtained in closed form by linearizing the return mapping algorithm, and is found to be non‐symmetric in the general case due to the dependence of the switching criterion on internal variables. Conditions that provide the symmetry of the consistent tangent matrix are analyzed. The compactness and generality of the received relations are achieved by means of using the thermodynamically based compact notations combining mechanical and electrical values. Both the cases scalar potential finite element (FE) formulation (primary variables: strain and electric field) and vector potential FE formulation (primary variables: strain and electric displacement) are considered. The accuracy and robustness of the algorithms are assessed through numerical examples. Copyright © 2009 John Wiley & Sons, Ltd.     

Frost heave and phase front instability in freezing soils

The main equations and conditions at the phase transition front are presented for a generalized model of secondary frost heave in freezing fine-grained soils. The analytical criterion for the stability/instability of the freezing phase front in porous media is derived. This criterion is obtained for the occurrence of the frost heave process by using the perturbation method in a two-dimensional, coupled heat and mass transfer model. This model assumes that the non-instantaneous crystallization process takes place in the kinetic zone, and that the rate of crystallization is a function of supercooling. This corresponds to the Arrhenius form equation and agrees with experimental investigations. The perturbation analysis of the freezing front shows that the stability criterion depends upon 1) the Stefan and Peclet numbers, 2) a parameter describing the phase transition kinetics and also 3) dimensionless parameters which characterize the frost heave process. Employing Fourier synthesis, actual front shape evolution is calculated. It is seen that the front displays a periodic morphology whose scale is essentially unrelated to that of the initial (starting) perturbation. The effect of the non-instantaneous kinetics on the front shape evolution is described. As is shown in results, the kinetics has a stabilizing effect and, in this case, the perturbations grow more slowly. The theoretical stability/instability conditions as predicted from the derived criterion were found to be in agreement with experimental investigations of the formation of soil cryogenic structure in the freezing process. On the basis of the asymptotic solution the engineering approach for the calculation of the heave rate and maximal frost penetration depth values — main characteristics for design and construction in cold regions, is presented. The good agreement between calculated values and experimental data is observed.     

A note on modelling the capacitated lot-sizing problem with set-up carryover and set-up splitting

The capacitated lot-sizing problem with set-up carryover and set-up splitting (CLSP-SCSS) is formulated as a mixed integer linear program. We define set-up carryover as the production of a product that is continued over from one period to another without incurring an extra set-up. Set-up splitting occurs when the set-up for a product is started at the end of a period and completed at the beginning of the next period. We allow product dependent set-ups. Initial experimentation highlights the importance of including set-up splitting in the CLSP model. In 12 out of the 18 problem instances tested, our model yielded better solutions or removed infeasibility when compared with a CLSP model without set-up splitting.     

Lot-splitting approach of a hybrid manufacturing system under CONWIP production control: a mathematical model

This paper discusses the advantages of lot splitting in hybrid manufacturing environments where cellular and functional layouts are combined under Constant Work in Process (CONWIP) production control. The proposed model fills a research gap in the related literature by applying lot splitting and pull production simultaneously. A linear CONWIP control mathematical model that minimises the average flow time is developed in case of lot splitting. The developed model has sequence-dependent set-up times. The demand level, coefficient of variation (CV) impact and set-up time reduction effect on CONWIP production control are also investigated. The model is solved using GAMS21.6 optimisation software; the optimal backlog list, the number and size of sublots are reported. The proposed model is compared with lot production under push control in different settings as well as with two different heuristics from the literature. Experimental results indicate that in all settings, the lot splitting is more advantageous than lot production in terms of average flow time. CV has a greater effect than set-up time reduction on average flow time.     

Numerical Simulation of Detonation and Multi-Material Interface Tracking

In this paper, we report high resolution simulations using a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third-order TVD Runge-Kutta time stepping method to examine the features of the detonation for gas and condensed explosives. A two-stage chemical reaction model and an ignition and growth model are employed to describe the chemical reaction process for gas and condensed explosives. Based on the Steger-Warming vector flux splitting method, a splitting method is employed when the vector flux does not satisfy the homogeneity property for simulating detonation wave propagation for condensed explosives. The sensibility of flame propagation process and explosion overpressure on obstacles is also numerically performed. Meanwhile, an interface tracking algorithm is developed and coupled with a two-dimensional multi-material code indigenously for simulating the response of materials to impact, shocks and detonations. Numerical experiments are performed to investigate the influences of liner cone angle, wall thickness and initiation mode on shaped charge jet formation process. The results of calculations show good agreement with experimental results, and indicate that the interface treatment algorithm is especially suitable for simulating explosive loading on thin-wall structure such as shape charges.     

Ultrasound detection of externally induced microthrombi cloud formation: a theoretical study

A mathematical model for the formation of microaggregates (microthrombi) of fibrin polymers in blood flow is considered. It is assumed that the former are induced by an external source (which may be of inflammatory or tumor nature) located in a tissue near the vessel. In either case, specific agents (e.g. cytokines) are emitted from that pathological site. Such substances permeate through the vessel wall to act as primary activators of blood coagulation. A mathematical criterion to describe the formation of an intravascular microthrombi cloud, which is interpreted as an early indicator of subsequent macroscopic thrombi formation is discussed. Such criteria are compared with available experimental detection tests for microthrombi cloud formation by means of ultrasound techniques. Moreover, a similarity-type relation is proposed that links the location of the unfolding microthrombi cloud and the place at which such primary activator reaches the vessel wall.     

Coupled stress and energy criterion for composite failure: Pointwise versus averaged evaluation of the stress criterion

Abstract

In this work, failure loads and failure modes of single lap adhesive joints between composite laminates are investigated. To this aim, a coupled stress and energy criterion is applied and results are compared to numerical reference solutions using cohesive zone modeling and to experimental values from literature. Possible failure modes are adhesive failure along the adherend/adhesive interface, adherend failure as intralaminar failure in the first ply closest to the adhesive layer and interlaminar failure between the first and second ply. Suitable failure criteria adressing the different failure modes are implemented within the framework of the coupled criterion. The stress criterion is carried out in a pointwise or in an averaged manner, called point method or line method respectively. It is shown that two physically sound failure modes can only be predicted using the stress criterion in an averaged manner since the pointwise evaluation does not allow the formation of certain types of cracks.     

Elastic anisotropy and micro-damage processes in polycrystalline ice

This paper discusses numerical predictions of a microstructural damage model for polycrystalline ice which is presented in a companion paper [1]. The results are relevant for ice deforming at the high end of the quasi-static domain of loading. First, the fracture mechanics-based model of damage is investigated by comparing model predictions of the stresses to form (nucleate) the first microcracks with test data. This is followed by a detailed simulation of loading under uniaxial compression using the damage model and an internal variable creep model, also summarized in the companion paper [1]. This simulation allows the prediction of the evolving damaged elastic properties, and delineates the relative contribution of creep and microcracking to the total deformation.The importance of load history on the deformation response is then illustrated by studying the influence of load path in biaxial loading. In these simulations, the competition between the mechanisms of failure by shear faulting and axial splitting is discussed in terms of the development of compliance anisotropy in the damaged body. Finally, the critical crack density is used as a macroscopic failure criterion to predict compressive strengths in the ductile-to-brittle transitional domain of strain rates, and its validity in more general states of stress involving different failure modes is questioned.     

Wave speeds, shear bands and the second-order work for incrementally nonlinear constitutive models

The paper discusses the consequences of the incremental nonlinearity of a constitutive model of a solid for the analyses of characteristic wave speeds, acceleration waves, the second-order work criterion and shear band formation. Incremental nonlinearity may entail qualitative changes in the results as compared to incrementally linear models. Certain well-known correlations cannot be established if the constitutive equation is assumed to be incrementally nonlinear. In particular, the spectra of the characteristic wave speeds and the acceleration wave speeds become continuous and are described by different equations. The second-order work criterion as a sufficient condition of uniqueness of the incremental boundary value problem loses its applicability in bifurcation analyses, unless the applicability can be proved for a particular type of nonlinearity. The singularity of the acoustic tensor in the general nonlinear case correlates neither with the vanishing of the second-order work nor with the shear band formation.     

Polymers toughened with rubber microspheres: an analytical solution for stresses and strains in the rubber particles at equilibrium and rupture

Large strains in rubber toughened polymers cause void formation and growth in the rubber particles and yielding in the matrix. Void formation usually precedes plasticity in the matrix around the particle and previous papers have proposed models for the relationship between rubber surface energy, volume strain energy and void growth. In this paper, it is shown that another volume criterion must also be satisfied arising from the fact that in all these models, no decohesion is allowed at the particle-matrix interface. A fracture mechanics approach, where linear and nonlinear elasticity are assumed for the matrix and the rubber particle, respectively, is used to define a void formation criterion depending on the rubber fracture surface energy. After formation, the stability of the void is examined, taking into account the volume conservation between matrix and particle and the stress due to surface tension when the void size is very small. A size effect is observed, indicating that voids cannot grow in small particles. The required value of fracture energy in a particle on a microscopic scale is discussed.     

Multiple-beam wedge-plate shear interferometer for collimation testing

We describe a modification of the wedge-plate shear interferometer for collimation testing. The surface of the wedge plate is coated to increase the reflectivity such that multiple-beam interference takes place resulting in sharp fringes. In addition to sharpening the fringes also tend to split when the test beam is noncollimated. This splitting has been used as a test criterion for collimation testing. Experimental results are presented.     

Changes in atomic and electronic structures of amorphous WO3 films due to electrochemical ion insertion

The structural changes in amorphous WO₃ films were investigated both on the atomic and electronic levels, and the experimental findings were interpreted using molecular orbital calculations. Electrochemical fast intercalation resulted in the splitting of a peak in the valence band region of the X-ray photoelectron spectrum. This splitting could be attributed to the formation of non-bridging oxygen. Decomposition of WO₆ units into WO₄ units could also be inferred from the data. This decomposition was, however, not responsible for the split of the photoelectron peak. From the population analyses it was found that the average bond strength decreased due to the intercalation, while select WO bonds increased in strength. It was expected that these changes in the chemical bonding character lead to localization of electrons and distortion of WO₆ units, which was consistent with the theoretical interpretations of electrochromism, the intervalence charge transfer model and the small polaron absorption theory.     

A MODEL FOR FATIGUE DEFECT NUCLEATION IN THERMITE RAIL WELDS

Abstract— A fatigue model for thermite rail welds is presented in this paper. The aim of the model is to provide a means for predicting the types of rail-head fatigue defects that might form under a given set of railway operating conditions and to provide an estimate of the life consumed during stage I growth of incipient fatigue cracks. Eshelby's equivalent inclusion method is incorporated in the model so that an assessment of the effects of metallurgical discontinuities can be made. Findley's critical-plane fatigue parameter is used as the criterion for computing fatigue damage. Results from using this model indicate that pores are the more damaging of the discontinuities typically present in thermite rail welds which also contain alumina inclusions. The shape and orientation of pores is predicted to have a strong influence on rail-head fatigue defect formation in thkwermite rail welds.