Mixed finite elements with independent strain interpolation for isotropic and orthotropic damage

Tesi per compendi de publicacionsThe numerical modelling of fracture has been an active topic of research for over five decades. Most of the approaches employed rely on the use of the Finite Element Method, which has shown to be an effective and cost-efficient tool for solving many physical phenomena. However, the issue of the spurious dependency of the computed solution with the mesh orientation in cracking problems has raised a great concern since its early reports in the 1980s. This matter has proved to be a major challenge in computational solid mechanics; it affects numerous methods employed to solve the problem, in which the computed crack trajectories are spuriously dependent on the arrangement of the finite element (FE) mesh employed. When performing a structural analysis and, in particular, when computing localized failure, it is fundamental to use a reliable and mesh objective method to be able to trust the results produced by the FE code in terms of the fracture paths, bearing capacity, collapse mechanism and nonlinear responses. In this doctoral thesis, the mixed e/u strain/displacement finite element method is used together with multiple isotropic and orthotropic damage constitutive laws for the numerical modelling of quasi-brittle fracture with mesh objectivity. The independent interpolation of the strains increases the accuracy of the computed solution, guaranteeing the local convergence of the stress and strain fields. This feature is a crucial improvement over the standard FE formulation in solid mechanics where the strains are computed as local derivatives of the displacements and the local convergence of the resulting stresses and strains is not ensured. The enhanced precision provided by the mixed formulation in the area near the crack tip is decisive for obtaining unbiased numerical results with regard to the orientation of the FE mesh. The strain-driven format of the mixed formulation enables to readily consider different constitutive laws defined in a stress-strain structure in the numerical simulations. The thesis includes the study of the effect of the material model employed in the resulting crack trajectories as well as the analysis of the relative performance of several isotropic and orthotropic damage behaviors in mode I, mode II, mode III and mixed mode fracture problems. In this work specific isotropic and orthotropic damage laws are proposed for the numerical modelling of fracture under cyclic loading, which include tensile and compressive damage, stiffness recovery due to crack closure and reopening, as well as irreversible strains. Also, the capacity of the proposed model in reproducing the structural size effect is examined, which is an essential requirement for models aiming at computing quasi-brittle behavior. In this thesis, a comprehensive comparison of the mixed FE formulation with other techniques employed for computing fracture, specifically the Extended Finite Element Method (XFEM) and the Phase-field model, is made, revealing the cost-efficiency of the proposed Mixed Finite Element Method for modelling quasi-brittle cracking with mesh objectivity. This allows to perform the analysis of real-scale structures, in 2D and 3D, with enhanced accuracy, demonstrating the applicability of this method in the engineering practice. The validation of the model is performed with an extensive comparison of computed results with existing experimental tests and numerical benchmarks. The capacity of the mixed formulation in reproducing force-displacement curves, crack trajectories and collapse mechanisms with enhanced accuracy is demonstrated in detail.En esta tesis doctoral, el método de los elementos finitos mixtos e/u deformación/desplazamiento es utilizado junto con varias leyes constitutivas de daño isótropo y ortótropo para la modelización numérica de la fractura cuasi-frágil de forma objetiva con respecto a la orientación de la malla. La interpolación independiente de las deformaciones aumenta la precisión de la solución calculada, garantizando la convergencia local de los campos de tensiones y deformaciones. Esta característica representa una mejora crucial con respecto a la formulación estándar de elementos finitos de la mecánica de sólidos, donde las deformaciones se calculan como derivadas locales de los desplazamientos y la convergencia local de las tensiones y deformaciones resultantes no está garantizada. La mayor precisión aportada por la formulación mixta en la zona cercana a la punta de la fisura es decisiva para obtener resultados numéricos que no presenten una dependencia espuria con la orientación de la malla de elementos finitos. El formato expresado en función de la deformación de la formulación mixta permite considerar directamente diferentes leyes constitutivas que siguen una estructura tensión-deformación para su uso en las simulaciones numéricas. La tesis incluye el estudio del efecto que tiene la ley constitutiva utilizada en la trayectoria de las fisuras resultantes, así como el análisis del desempeño relativo de varias leyes de daño isótropas y ortótropas en problemas de fractura en modo I, modo II, modo III y modo mixto. En este trabajo se proponen leyes de daño isótropo y ortótropo específicas para la modelización numérica de la fractura bajo carga cíclica, que incluyen daño a tracción y a compresión, recuperación de la rigidez por el cierre y reapertura de fisuras, así como deformaciones irreversibles. Además, se comprueba la capacidad del modelo propuesto para reproducir el efecto tamaño, que es un requisito esencial para los modelos que tengan como objetivo calcular el comportamiento cuasi-frágil de los materiales. En la tesis se realiza una comparación exhaustiva de la formulación mixta de elementos finitos con otras técnicas que se utilizan para calcular el problema, específicamente el Método de los Elementos Finitos Extendidos (XFEM) y el modelo Phase-field, revelando la eficiencia computacional del Método de los Elementos Finitos Mixtos propuesto para modelizar la rotura cuasi-frágil de forma objetiva con respecto a la malla. Ello permite realizar el análisis de estructuras de tamaño real, en 2D y 3D, con mayor precisión, demostrando la aplicabilidad del método a problemas reales de ingeniería. La validación del modelo se realiza con una comparación de resultados calculados con ensayos de laboratorio existentes y con simulaciones de casos teóricos de referencia. Se demuestra la capacidad de la formulación mixta para reproducir curvas fuerza-desplazamiento, trayectorias de fisuras y mecanismos de colapso con precisión mejorada.Postprint (published version

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Challenges, tools and applications of tracking algorithms in the numerical modelling of cracks in concrete and masonry structures

The final publication is available at Springer via http://dx.doi.org/10.1007/s11831-018-9274-3The importance of crack propagation in the structural behaviour of concrete and masonry structures has led to the development of a wide range of finite element methods for crack simulation. A common standpoint in many of them is the use of tracking algorithms, which identify and designate the location of cracks within the analysed structure. In this way, the crack modelling techniques, smeared or discrete, are applied only to a restricted part of the discretized domain. This paper presents a review of finite element approaches to cracking focusing on the development and use of tracking algorithms. These are presented in four categories according to the information necessary for the definition and storage of the crack-path. In addition to that, the most utilised criteria for the selection of the crack propagation direction are summarized. The various algorithmic issues involved in the development of a tracking algorithm are discussed through the presentation of a local tracking algorithm based on the smeared crack approach. Challenges such as the modelling of arbitrary and multiple cracks propagating towards more than one direction, as well as multi-directional and intersecting cracking, are detailed. The presented numerical model is applied to the analysis of small- and large-scale masonry and concrete structures under monotonic and cyclic loading.Peer ReviewedPostprint (author's final draft

Ono: an open platform for social robotics

In recent times, the focal point of research in robotics has shifted from industrial ro- bots toward robots that interact with humans in an intuitive and safe manner. This evolution has resulted in the subfield of social robotics, which pertains to robots that function in a human environment and that can communicate with humans in an int- uitive way, e.g. with facial expressions. Social robots have the potential to impact many different aspects of our lives, but one particularly promising application is the use of robots in therapy, such as the treatment of children with autism. Unfortunately, many of the existing social robots are neither suited for practical use in therapy nor for large scale studies, mainly because they are expensive, one-of-a-kind robots that are hard to modify to suit a specific need. We created Ono, a social robotics platform, to tackle these issues. Ono is composed entirely from off-the-shelf components and cheap materials, and can be built at a local FabLab at the fraction of the cost of other robots. Ono is also entirely open source and the modular design further encourages modification and reuse of parts of the platform

Review of the Synergies Between Computational Modeling and Experimental Characterization of Materials Across Length Scales

With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many applications in the development, characterization and design of complex material systems. This manuscript provides a broad and comprehensive overview of recent trends where predictive modeling capabilities are developed in conjunction with experiments and advanced characterization to gain a greater insight into structure-properties relationships and study various physical phenomena and mechanisms. The focus of this review is on the intersections of multiscale materials experiments and modeling relevant to the materials mechanics community. After a general discussion on the perspective from various communities, the article focuses on the latest experimental and theoretical opportunities. Emphasis is given to the role of experiments in multiscale models, including insights into how computations can be used as discovery tools for materials engineering, rather than to "simply" support experimental work. This is illustrated by examples from several application areas on structural materials. This manuscript ends with a discussion on some problems and open scientific questions that are being explored in order to advance this relatively new field of research.Comment: 25 pages, 11 figures, review article accepted for publication in J. Mater. Sc

Challenges, tools and applications of tracking algorithms in the numerical modelling of cracks in concrete and masonry structures

The importance of crack propagation in the structural behaviour of concrete and masonry structures has led to the development of a wide range of finite element methods for crack simulation. A common standpoint in many of them is the use of tracking algorithms, which identify and designate the location of cracks within the analysed structure. In this way, the crack modelling techniques, smeared or discrete, are applied only to a restricted part of the discretized domain. This paper presents a review of finite element approaches to cracking focusing on the development and use of tracking algorithms. These are presented in four categories according to the information necessary for the definition and storage of the crack-path. In addition to that, the most utilised criteria for the selection of the crack propagation direction are summarized. The various algorithmic issues involved in the development of a tracking algorithm are discussed through the presentation of a local tracking algorithm based on the smeared crack approach. Challenges such as the modelling of arbitrary and multiple cracks propagating towards more than one direction, as well as multi-directional and intersecting cracking, are detailed. The presented numerical model is applied to the analysis of small- and large-scale masonry and concrete structures under monotonic and cyclic loading

Tracking localized cracks in the computational analysis of masonry structures

Numerical methods aid significantly the engineering efforts towards the conservation of existing masonry structures and the design of new ones. Among them, macro-mechanical finite element methods based on the smeared crack approach are commonly preferred as an affordable choice for the analysis of large masonry structures. Nevertheless, they usu-ally result in a non-realistic representation of damage as smeared over large areas of the structure, which hampers the correct interpretation of the damage pattern. Additionally, a more critical pathology of this approach is the mesh-dependency, which influences nota-bly the safety and stability predictions. To overcome these limitations, this thesis proposes a novel computational tool based on the {enrichment} of the classical smeared crack approach with a local tracking algorithm. The objective of this localized damage model is the realistic and efficient non-linear anal-ysis of masonry structures with an enhanced representation of cracking. The non-linear behaviour of masonry is simulated through the adoption of a continuum damage mechanics model with two damage indices, allowing the differentiation between the tensile and compressive mechanical responses of masonry. In this context, a novel explicit formulation for the evolution of irreversible strains is proposed and implemented. Two new expressions are derived for the regularization of the tensile and compressive softening responses according to the crack-band approach, ensuring the mesh-size objec-tivity of the damage model. The simulation of the structural behaviour of masonry structures under versatile loading and boundary conditions necessitates some developments in the context of local tracking algorithms. To this end, this thesis presents the enhancement of local tracking algorithms with novel procedures that make possible the simulation of multiple, arbitrary and inter-secting cracking under monotonic and cyclic loading. Additionally, the effect of different crack propagation criteria is investigated and the selection among more than one potential failure planes is tackled. The proposed localized damage model is validated through the simulation of a series of structural examples. These vary from small-scale tests on concrete specimens with few dominant cracks, to medium and large-scale masonry structures with multiple tensile, shear and flexural cracking. The analyses are compared with analytical, experimental and numerical results obtained with alternative methods available in the literature. Overall, the localized damage model developed in this thesis largely improves the mesh-independency of the classical smeared crack approach and reproduces crack patterns and collapse mech-anisms in an efficient and realistic way.Los métodos numéricos son decisivos en la ingeniería para la conservación de estructuras de mampostería existentes y el diseño de estructuras nuevas. Entre ellos, los métodos macro-mecánicos de elementos finitos, basados en el concepto de fisuras distribuidas, son habitualmente los preferidos como opción asequible para el análisis de grandes estructuras de mampostería. Sin embargo, suelen resultar en a una representación poco realista del daño, distribuido en grandes áreas de la estructura, lo que impide la correcta interpretación del patrón de daño. Además, esta metodología presenta una patología más crítica, la dependencia de la malla, que influye notablemente en las predicciones de seguridad y estabilidad. Para superar estas limitaciones, esta tesis propone una nueva herramienta numérica basada en el enriquecimiento del clásico enfoque de fisuras distribuidas con un algoritmo de trazado local. El objetivo de este modelo de daño localizado es el análisis no-lineal de las estructuras de mampostería de manera realista y eficiente con una representación mejora-da de fisuras. El comportamiento no lineal de la mampostería se simula a través de la adopción de un modelo de mecánica de daño continuo con dos índices de daño, permitiendo la diferenciación entre las respuestas mecánicas de tensión y compresión de la mampostería. En este contexto, se propone e implementa una nueva formulación explícita para la evolución de deformaciones irreversibles. Se derivan dos nuevas expresiones para la regularización del ablandamiento de tracción y compresión según el ancho de banda de la fisura, garantizan-do la objetividad del modelo de daño al respecto del tamaño de la malla. La simulación del comportamiento estructural de las estructuras de mampostería en condiciones de carga y contorno generales precisa de algunos desarrollos en el contexto de los algoritmos locales de trazado. Con este objetivo, se presenta la mejora de los algoritmos locales de trazado con nuevos procedimientos que posibilitan la simulación de fisuración múltiple, arbitraria e secante bajo cargas monótonas y cíclicas. Además, se investiga el efecto de diferentes criterios de propagación de fisuras y se aborda la selección entre más de un plano de falla posible. El modelo de daño localizado propuesto se valida mediante la simulación de una serie de ejemplos estructurales. Éstos van desde pruebas a pequeña escala en probetas de hormigón, con pocas fisuras dominantes, hasta estructuras de mampostería de mediana y gran escala con fisuración múltiple de tracción, de cortante y de flexión. Los análisis se comparan con los resultados analíticos, experimentales y numéricos obtenidos con métodos alternativos disponibles en la literatura. El modelo de daño localizado mejora en gran medida la independencia de la malla del clásico método de fisuras distribuidas y reproduce patrones de daño y mecanismos de colapso de una manera eficiente y realist

Testing and Modelling of SLM manufactured Ti-6Al-4V alloy under low cycle fatigue and creep conditions

Selective laser melting (SLM) is a promising additive manufacturing (AM) process for high strength or high manufacturing costs metals such as Ti-6Al-4V widely applied in aeronautical industry components with high material waste or complex geometry. However, the disadvantage or challenge of AM is the unpredictable fatigue and creep properties of AM components. To realize the wide application of structural components manufactured by AM technology, their creep/fatigue failure and damage mechanism need to be understood so that the life of AM components can be predicted reliably. In this thesis, tensile and fracture mechanics type specimens were machined in accordance with the relevant ASTM standards from fabricated SLM with different heat treatment methods. All the specimens were post-treated with the same machined smooth surface and heated to relieve the residual stress. Various mechanical tests of the standard samples were performed to obtain the properties aiming to identify the critical factors influencing these properties. The room temperature tests carried out in this work include the tensile test, low cycle fatigue (LCF) test, crack growth rate investigation, and fracture toughness test. The LCF test was conducted using the standard samples in the low cycle fatigue (LCF) regime. The failure mechanism is observed by identifying the influence of post-processing methods. Scanning electron microscopy (SEM) techniques and optical microscopy (OM) are used to investigate the microstructural and fracture surface features of different types of specimens. In addition, a microstructure-based multistage fatigue model was applied to predict the LCF lives, which shows good agreement with the experimental results. Crack growth rate and fracture toughness tests were carried out and analyzed on the CT samples. Different build orientations and heat treatment methods effects on the fracture toughness and FCG rate were observed. A novel approach is presented to show a relationship between the FCG rate and microstructure characteristic using the database for the FCG tests and their microstructure and fractography analysis established from the experiments carried out. It was found that HIP treatment can help to reduce the effects of building directions due to the elimination of anisotropy. Furthermore, when the crack growth direction is perpendicular to the manufacturing direction, the crack growth rate is sensitive to the heat treatment method. The high-temperature properties test was largely focused on constant load uniaxial and notched bar creep tests under a continuous temperature environment. The uniaxial creep test of four types of SLM manufactured samples was carried out under 600℃ conditions at two stress levels. The notch acuity sensitivity investigation was conducted using the double sharp and blunt notched bar at 90 MPa, 600℃ and 100 MPa, 500℃, respectively. It is observed that no obvious defects were found in the fracture surface and crack profile. By comparing and analyzing the creep test results, the HIP-treated sample have a prior creep failure duration time to all the other manufacturing parameters. This demonstrates that the slightly elongated microstructure samples can help to improve the creep resistance by the characterization investigation. From the notched bar experimental results, the sharp notched bars have longer creep time and less strain deformation in the whole creep test process. The creep cracking behavior at the specific proper temperature was investigated and verified. A continuum damage mechanics-based model was proposed using a custom user subroutine in FE analysis software Abaqus to simulate the creep cracking damage evolution behaviors. The model applied a grain and grain boundary scale in meshing the creep cracking region using a CT geometry the same as that for the creep cracking test. The high temperature and mechanical properties were obtained from the test in this project. Considering that the defects were not detected in the fracture surface or crack profile, the FE model was operated without any distribution of voids. The microstructural features like average grain size and shape were described and generated in terms of meshing elements. The simulation results were found to be conservative and are validated by comparing them with the fracture behavior and crack propagation of the CT samples. The present work shows that in future work on creep testing and modeling of the additively manufactured material, looking at the effects of voids and interstitials in the microstructure, the damage simulation can be developed to more accurately describe creep under both uniaxial and multiaxial conditions.Open Acces