Crack mechanical failure in lithium niobate crystal under ion irradiation; novel simulation by extended finite elements

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion-generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

High-accuracy adaptive simulations of a Petri dish exposed to electromagnetic radiation

This paper analyses numerically the electric field distribution of a liquid contained in a Petri dish when exposed to electromagnetic waves excited in a rectangular waveguide. Solutions exhibit high-gradients due to the presence of the dielectric liquid contained in the dish. Furthermore, electromagnetic fields within the dielectric have a dramatically lower value than on the remaining part of the domain, which difficults its simulation. Additionally, various singularities of different intensity appear along the boundary of the Petri dish. To properly reproduce and numerically study those effects, we employ a highly-accurate hp-adaptive finite element method. Results of this study demonstrate that the electric field generated within the circular Petri dish is non-homogeneous, and thus, a better shape, size, or location of the dish is needed to achieve an equally distributed radiation enabling the uniform growth of cell cultives.

The Boundary Element Method in elastodynamics

As is well known B.E.M. is obtained as a mixture of the integral representation formula of classical elasticity and the discretization philosophy of the finite element method (F.E.M.). The paper presents the application of B.E.M. to elastodynamic problems. Both the transient and steady state solutions are presented as well as some techniques to simplify problems with a free-stress boundary.

High fidelity simulations of failure in fiber-reinforced composites

Los ensayos virtuales de materiales compuestos han aparecido como un nuevo concepto dentro de la industria aeroespacial, y disponen de un vasto potencial para reducir los enormes costes de certificación y desarrollo asociados con las tediosas campañas experimentales, que incluyen un gran número de paneles, subcomponentes y componentes. El objetivo de los ensayos virtuales es sustituir algunos ensayos por simulaciones computacionales con alta fidelidad. Esta tesis es una contribución a la aproximación multiescala desarrollada en el Instituto IMDEA Materiales para predecir el comportamiento mecánico de un laminado de material compuesto dadas las propiedades de la lámina y la intercara. La mecánica de daño continuo (CDM) formula el daño intralaminar a nivel constitutivo de material. El modelo de daño intralaminar se combina con elementos cohesivos para representar daño interlaminar. Se desarrolló e implementó un modelo de daño continuo, y se aplicó a configuraciones simples de ensayos en laminados: impactos de baja y alta velocidad, ensayos de tracción, tests a cortadura. El análisis del método y la correlación con experimentos sugiere que los métodos son razonablemente adecuados para los test de impacto, pero insuficientes para el resto de ensayos. Para superar estas limitaciones de CDM, se ha mejorado la aproximación discreta de elementos finitos enriqueciendo la cinemática para incluir discontinuidades embebidas: el método extendido de los elementos finitos (X-FEM). Se adaptó X-FEM para un esquema explícito de integración temporal. El método es capaz de representar cualitativamente los mecanismos de fallo detallados en laminados. Sin embargo, los resultados muestran inconsistencias en la formulación que producen resultados cuantitativos erróneos. Por último, se ha revisado el método tradicional de X-FEM, y se ha desarrollado un nuevo método para superar sus limitaciones: el método cohesivo X-FEM estable. Las propiedades del nuevo método se estudiaron en detalle, y se concluyó que el método es robusto para implementación en códigos explícitos dinámicos escalables, resultando una nueva herramienta útil para la simulación de daño en composites. Virtual testing of composite materials has emerged as a new concept within the aerospace industry. It presents a very large potential to reduce the large certification costs and the long development times associated with the experimental campaigns, involving the testing of a large number of panels, sub-components and components. The aim of virtual testing is to replace some experimental tests by high-fidelity numerical simulations. This work is a contribution to the multiscale approach developed in Institute IMDEA Materials to predict the mechanical behavior of a composite laminate from the properties of the ply and the interply. Continuum Damage Mechanics (CDM) formulates intraply damage at the the material constitutive level. Intraply CDM is combined with cohesive elements to model interply damage. A CDM model was developed, implemented, and applied to simple mechanical tests of laminates: low and high velocity impact, tension of coupons, and shear deformation. The analysis of the results and the comparison with experiments indicated that the performance was reasonably good for the impact tests, but insuficient in the other cases. To overcome the limitations of CDM, the kinematics of the discrete finite element approximation was enhanced to include mesh embedded discontinuities, the eXtended Finite Element Method (X-FEM). The X-FEM was adapted to an explicit time integration scheme and was able to reproduce qualitatively the physical failure mechanisms in a composite laminate. However, the results revealed an inconsistency in the formulation that leads to erroneous quantitative results. Finally, the traditional X-FEM was reviewed, and a new method was developed to overcome its limitations, the stable cohesive X-FEM. The properties of the new method were studied in detail, and it was demonstrated that the new method was robust and can be implemented in a explicit finite element formulation, providing a new tool for damage simulation in composite materials.

Towards a Modeling Environment for Earth Systems Simulations

The developments of models in Earth Sciences, e.g. for earthquake prediction and for the simulation of mantel convection, are fare from being finalized. Therefore there is a need for a modelling environment that allows scientist to implement and test new models in an easy but flexible way. After been verified, the models should be easy to apply within its scope, typically by setting input parameters through a GUI or web services. It should be possible to link certain parameters to external data sources, such as databases and other simulation codes. Moreover, as typically large-scale meshes have to be used to achieve appropriate resolutions, the computational efficiency of the underlying numerical methods is important. Conceptional this leads to a software system with three major layers: the application layer, the mathematical layer, and the numerical algorithm layer. The latter is implemented as a C/C++ library to solve a basic, computational intensive linear problem, such as a linear partial differential equation. The mathematical layer allows the model developer to define his model and to implement high level solution algorithms (e.g. Newton-Raphson scheme, Crank-Nicholson scheme) or choose these algorithms form an algorithm library. The kernels of the model are generic, typically linear, solvers provided through the numerical algorithm layer. Finally, to provide an easy-to-use application environment, a web interface is (semi-automatically) built to edit the XML input file for the modelling code. In the talk, we will discuss the advantages and disadvantages of this concept in more details. We will also present the modelling environment escript which is a prototype implementation toward such a software system in Python (see www.python.org). Key components of escript are the Data class and the PDE class. Objects of the Data class allow generating, holding, accessing, and manipulating data, in such a way that the actual, in the particular context best, representation is transparent to the user. They are also the key to establish connections with external data sources. PDE class objects are describing (linear) partial differential equation objects to be solved by a numerical library. The current implementation of escript has been linked to the finite element code Finley to solve general linear partial differential equations. We will give a few simple examples which will illustrate the usage escript. Moreover, we show the usage of escript together with Finley for the modelling of interacting fault systems and for the simulation of mantel convection.

The programming language python in earth system simulations

-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Modelling and simulations of ductile iron solidification-induced variations in mechanical behaviour on component and microstructural level

The mechanical behaviour and performance of a ductile iron component is highly dependent on the local variations in solidification conditions during the casting process. Here we show a framework which combine a previously developed closed chain of simulations for cast components with a micro-scale Finite Element Method (FEM) simulation of the behaviour and performance of the microstructure. A casting process simulation, including modelling of solidification and mechanical material characterization, provides the basis for a macro-scale FEM analysis of the component. A critical region is identified to which the micro-scale FEM simulation of a representative microstructure, generated using X-ray tomography, is applied. The mechanical behaviour of the different microstructural phases are determined using a surrogate model based optimisation routine and experimental data. It is discussed that the approach enables a link between solidification- and microstructure-models and simulations of as well component as microstructural behaviour, and can contribute with new understanding regarding the behaviour and performance of different microstructural phases and morphologies in industrial ductile iron components in service.

Projeto de caixa de madeira para manga (Mangifera Indica L.)

Losses of horticulture product in Brazil are significant and among the main causes are the use of inappropriate boxes and the absence of a cold chain. A project for boxes is proposed, based on computer simulations, optimization and experimental validation, trying to minimize the amount of wood associated with structural and ergonomic aspects and the effective area of the openings. Three box prototypes were designed and built using straight laths with different configurations and areas of openings (54% and 36%). The cooling efficiency of Tommy Atkins mango (Mangifera Indica L.) was evaluated by determining the cooling time for fruit packed in the wood models and packed in the commercially used cardboard boxes, submitted to cooling in a forced-air system, at a temperature of 6ºC and average relative humidity of 85.4±2.1%. The Finite Element Method was applied, for the dimensioning and structural optimization of the model with the best behavior in relation to cooling. All wooden boxes with fruit underwent vibration testing for two hours (20 Hz). There was no significant difference in average cooling time in the wooden boxes (36.08±1.44 min); however, the difference was significant in comparison to the cardboard boxes (82.63±29.64 min). In the model chosen for structural optimization (36% effective area of openings and two side laths), the reduction in total volume of material was 60% and 83% in the cross section of the columns. There was no indication of mechanical damage in the fruit after undergoing the vibration test. Computer simulations and structural study may be used as a support tool for developing projects for boxes, with geometric, ergonomic and thermal criteria.

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

Analysis of a Three-Phase LSPMM by Numerical Method

Line-start permanent magnet motor (LSPMM) is a very attractive alternative to replace induction motors due to its very high efficiency and constant speed operation with load variations. However, designing this kind of hybrid motor is hard work and requires a good understanding of motor behavior. The calculation of load angle is an important step in motor design and can not be neglected. This paper uses the finite element method to show a simple methodology to calculate the load angle of a three-phase LSPMM combining the dynamic and steady-state simulations. The methodology is used to analyze a three-phase LSPMM.

Efficient Modeling of Thin Wires in a Lossy Medium by Finite Elements Applied to Grounding Systems

A procedure is proposed to accurately model thin wires in lossy media by finite element analysis. It is based on the determination of a suitable element width in the vicinity of the wire, which strongly depends on the wire radius to yield accurate results. The approach is well adapted to the analysis of grounding systems. The numerical results of the application of finite element analysis with the suitably chosen element width are compared with both analytical results and those computed by a commercial package for the analysis of grounding systems, showing very good agreement.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods

A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.

A biomimetic piezoelectric pump: Computational and experimental characterization

Flow pumps have been developed for classical applications in Engineering, and are important instruments in areas such as Biology and Medicine. Among applications for this kind of device we notice blood pump and chemical reagents dosage in Bioengineering. Furthermore, they have recently emerged as a viable thermal management solution for cooling applications in small-scale electronic devices. This work presents the performance study of a novel principle of a piezoelectric flow pump which is based oil the use of a bimorph piezoelectric actuator inserted in fluid (water). Piezoelectric actuators have some advantages over classical devices, such as lower noise generation and ease of miniaturization. The main objective is the characterization of this piezoelectric pump principle through computational simulations (using finite element software), and experimental tests through a manufactured prototype. Computational data, Such as flow rate and pressure curves, have also been compared with experimental results for validation purposes. (C) 2009 Elsevier B.V. All rights reserved.

Modeling technique for honeycomb FRP deck bridges via finite elements

Honeycomb structures have been used in different engineering fields. In civil engineering, honeycomb fiber-reinforced polymer (FRP) structures have been used as bridge decks to rehabilitate highway bridges in the United States. In this work, a simplified finite-element modeling technique for honeycomb FRP bridge decks is presented. The motivation is the combination of the complex geometry of honeycomb FRP decks and computational limits, which may prevent modeling of these decks in detail. The results from static and modal analyses indicate that the proposed modeling technique provides a viable tool for modeling the complex geometry of honeycomb FRP bridge decks. The modeling of other bridge components (e.g., steel girders, steel guardrails, deck-to-girder connections, and pier supports) is also presented in this work.

Prediction of rock alteration patterns: a potential tool in mineral exploration

Hydrothermal alteration of a quartz-K-feldspar rock is simulated numerically by coupling fluid flow and chemical reactions. Introduction of CO2 gas generates an acidic fluid and produces secondary quartz, muscovite and/or pyrophyllite at constant temperature and pressure of 300 degrees C and 200 MPa. The precipitation and/or dissolution of the secondary minerals is controlled by either mass-action relations or rate laws. In our simulations the mass of the primary elements are conserved and the mass-balance equations are solved sequentially using an implicit scheme in a finite-element code. The pore-fluid velocity is assumed to be constant. The change of rock volume due to the dissolution or precipitation of the minerals, which is directly related to their molar volume, is taken into account. Feedback into the rock porosity and the reaction rates is included in the model. The model produces zones of pyrophyllite quartz and muscovite due to the dissolution of K-feldspar. Our model simulates, in a simplified way, the acid-induced alteration assemblages observed in various guises in many significant mineral deposits. The particular aluminosilicate minerals produced in these experiments are associated with the gold deposits of the Witwatersrand Basin.