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Friction and Wear Modelling in Fiber-Reinforced Composites
Get PDFThis work presents new contact constitutive laws for friction and wear modelling in fiber-reinforced plastics (FRP). These laws are incorporated to a numerical methodology which allows us to solve the contact problem taking into account the anisotropic tribological properties on the interfaces. This formulation uses the Boundary Element Method for computing the elastic influence coefficients. Furthermore, the formulation considers micromechanical models for FRP that also makes it possible to take into account the fiber orientation relative to the sliding direction, the fiber volume fraction, the aspect ratio of fibers, or the fiber arrangement. The proposed contact and wear laws, as well as the numerical methodology, are applied to compute and study wear in a carbon FRP. In these studies, it can be observed how the fiber orientation, micromechanics, or sliding orientation affect the normal and tangential contact compliance, as well as the contact traction distribution and wear evolution
Solving Embedded Crack Problems Using the Numerical Green’s Function and a meshless Coupling Procedure: Improved Numerical Integration
Get PDFAn iterative coupling procedure using different meshless methods is presented to solve linear elastic fracture mechanic (LEFM) problems. The domain of the problem is decomposed into two sub-domains, where each one is addressed using an appropriate meshless method. The method of fundamental solutions (MFS) based on the numerical Green’s function (NGF) procedure to generate the fundamental solution has been chosen for modeling embedded cracks in the elastic medium and the meshless local Petrov-Galerkin (MLPG) method has been chosen for modeling the remaining sub-domain. Each meshless method runs independently, coupled with an iterative update of interface variables to achieve the final convergence. The coupling procedure is easy to apply for any LEFM problems with one or more cracks and can save time in the construction of the problem representation by points. In addition, different numerical integral approaches are tested for to compute integrals of the MLPG method.
The iterative solution procedure presented yields good results as compared with the boundary element method and alternative solutions for stress intensity factor computations
MLPG Refinement Techniques for 2D and 3D Diffusion Problems
Get PDFMeshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations. One of pure meshless methods main applications is for implementing Adaptive Discretization Techniques. In this paper, we describe our fresh node–wise refinement technique, based upon estimations of the “local” Total Variation of the approximating function. We numerically analyze the accuracy and efficiency of our MLPG–based refinement. Solutions to test Poisson problems are approximated, which undergo large variations inside small portions of the domain. We show that 2D problems can be accurately solved. The gain in accuracy with respect to uniform discretizations is shown to be appreciable. By extending our procedure to 3D problems, we prove by experiments that good improvements in efficiency can be obtained
Global Approximation for a Simulation Model Based on the RBF Response Surface Set
Get PDFThe use of multi-dimensional global approximation for a complex black-box function (such as a simulation or an analysis model) is steadily growing in the past decade. It can be applied in many fields such as parameter experiment, sensibility analyses real-time simulation, and design/control optimization. However, the widespread use of approximation methods is hampered by the lack of the ability to approximate a complex simulation model which characterizes the dynamic feature with multiple inputs and multiple outputs (MIMO) in a large domain. In this paper, a novel global approximation method for simulation models based on the RBF response surface set is proposed. Firstly, incremental building technique of RBF response surface set was studied, and was applied to approximate MIMO models. Several mathematical tests were presented to demonstrate the feasibility and effectiveness of the technique. Secondly, the approximation for complex simulation models, especially for dynamic models with state variables, was addressed. A simple test was given to illustrate the approximation process and effectiveness of a simulation model. Lastly, as an engineering application, the proposed method was utilized to approximate the power-train of a pure electric vehicle, and the approximation model was successfully applied in real-time simulation platform
Numerical Solution for a Class of Linear System of Fractional Differential Equations by the Haar Wavelet Method and the Convergence Analysis
Get PDFIn this paper, a class of linear system of fractional differential equations is considered. It has been solved by operational matrix of Haar wavelet method which converts the problem into algebraic equations. Moreover the convergence of the method is studied, and three numerical examples are provided to demonstrate the accuracy and efficiency
Cauchy Problem for the Heat Equation in a Bounded Domain Without Initial Value
Get PDFWe consider the determination of heat flux within a body from the Cauchy data. The aim of this paper is to seek an approach to solve the onedimensional heat equation in a bounded domain without initial value. This problem is severely ill-posed and there are few theoretic results. A quasi-reversibility regularization method is used to obtain a regularized solution and convergence estimates are given. For numerical implementation, we apply a method of lines to solve the regularized problem. From numerical results, we can see that the proposed method is reasonable and feasible
Simulations of Blood Drop Spreading and Impact for Bloodstain Pattern Analysis
Get PDFBloodstain pattern analysis (BPA) in forensic science is an important tool to solve crime scenes. The complex dynamic behavior of blood drops poses great challenges for accurate fluid dynamic simulations. In this paper, we specifically focus on simulations of blood drop spreading and impact, which may involve contact line hysteresis and spattering of drops as they interact with solid surfaces. Here, we set up a numerical framework that combines (1) the connectivity-free front tracking (CFFT) method for modeling multiphase (air and liquid) flows and (2) a dynamic contact line model for modeling fluid-solid contact line. Both components are necessary in simulating drop spreading and impact which involve the prediction of the contact line movement and drop spattering. The “connectivityfree” approach refers to the explicit representation of the drop interface points without logical connectivities, which relieves the maintenance and bookkeeping of the interface when the topology goes through large changes as a drop impacts onto a solid surface. It also provides a direct means to couple the dynamic contact line model to form initial contact line and track the contact line movement without reconnecting the points on the interface. Drop spreading and moving on horizontal and oblique planes are studied to show the accuracy and the capability of this coupled algorithm to handle contact line problems. To further validate the method, a drop impacting on a solid obstacle is also performed to demonstrate the flexibility and robustness of the method
Patient-Specific Modeling in Urogynecology: A Meshfree Approach
Get PDFMechanical deformation of tissues in the female pelvic floor is believed to be central to understanding a number of important aspects of women’s health, particularly pelvic floor dysfunction. A 2008 study of US women reported the prevalence of pelvic floor disorders in the 20 and 39 years range as 9.7% with the prevalence increasing with age until it reaches roughly 50% in the 80 and older age group [Nygaard, Barber, Burgio, and et al (2008)]. Clinical observation indicates a strong correlation between problems such as pelvic organ prolapse/urinary incontinence and vaginal childbirth. It is thought that childbirth parameters like fetal weight, duration of labor, and pelvic bony and soft tissue geometry can modulate the level of injury sustained during childbirth. However, it is difficult to study the impact of childbirth parameters non-destructively in living women. Therefore, realistic, efficient, computational modeling capabilities are necessary to study the mechanical response of the organs and muscles during childbirth under varying conditions, in order to develop and test hypotheses for childbirth related injury. Furthermore, manufacturers of embedded prosthetic devices, such as those used to treat prolapse, may benefit from the ability to predict the mechanical performance of their prostheses in situ, and this potential benefit highlights the need for a capability to rapidly develop analytical models of the pelvic floor. This paper discusses an algorithm to automatically generate an analysis-suitable geometry from medical images. The automated analysis capability is demonstrated in modeling vaginal contracture, as might occur in cases of women treated with radiation for cervical cancer
3D Echo-Based Patient-Specific Computational Left Ventricle Models to Quantify Material Properties and Stress/Strain Differences between Ventricles with and without Infarct
Get PDFIdentifying ventricle material properties and its infarct area after heart attack noninvasively is of great important in clinical applications. An echo-based computational modeling approach was proposed to investigate left ventricle (LV) mechanical properties and stress conditions using patient-specific data. Echo data was acquired from one healthy volunteer (male, age: 58) and a male patient (age: 60) who had an acute inferior myocardial infarction one week before echo image acquisition. Standard echocardiograms were obtained using an ultrasound machine (E9, GE Mechanical Systems, Milwaukee, Wisconsin) with a 3V probe and data were segmented for model construction. Finite element models were constructed to obtain ventricle stress and strain conditions. A pre-shrink process was applied so that the model ventricle geometries under end-of-systole pressure matched in vivo data. Our results indicated that the modeling approach has the potential to be used to determine ventricle material properties. The equivalent Young’s modulus value from the healthy LV (LV1) was about 30% softer than that of the infarct LV (LV2) at end of diastole, but was about 100% stiffer than that of LV2 at end of systole. This can be explained as LV1 has more active contraction reflected by stiffness variations. Using averaged values, at end-systole, longitudinal curvature from LV2 was 164% higher than that from LV1. LV stress from LV2 was 82% higher than that from LV1. At end-diastole, L-curvature from LV2 was still 132% higher than that from LV1, while LV stress from LV2 was only 9% higher than that from LV1. Longitudinal curvature and stress showed the largest differences between the two ventricles, with the LV with infarct having higher longitudinal curvature and stress values. Large scale studies are needed to further confirm our findings
The JEREMI-Project on Thermocapillary Convection in Liquid Bridges. Part A: Overview of Particle Accumulation Structures
Get PDFThe rapid accumulation of particles suspended in a thermocapillary liquid bridge is planned to be investigated during the JEREMI experiment on the International Space Station scheduled for 2016. An overview is given of the current status of experimental and numerical investigations of this phenomenon