Object oriented design of a thermo-mechanical FEM code

An object oriented design is presented for a computer program that can perform\ud thermo-mechanically coupled analyzes. The target of the design is a \ud exible and robust\ud computer program. It should be easy to adapt and extend, re-using existing code, without\ud interfering with already established algorithms.\ud The program uses publicly available toolkits that are currently emerging as C++ pack-\ud ages. First of all the Standard C++ Library (formerly Standard Template Library) is\ud used for packing items in container classes. Secondly the matrix and vector operations\ud are derived from the Template Numerical Toolkit (TNT) and �nally (not essentially for\ud the numerical part) a graphical user interface is made, based on the wxWindows package,\ud that can generate a GUI for Motif and MS-Windows with the same code.\ud Attention is given to the design of classes such as speci�c elements and material classes\ud based on more general classes. A hierarchy of classes is constructed where general behavior\ud is put high in the hierarchy and speci�c behavior low. The choice between inheritance and\ud aggregation is made at several levels

Statistical higher-order multi-scale method for nonlinear thermo-mechanical simulation of random composite materials with temperature-dependent properties

Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite materials with complicated random microstructures remains a challenging issue. In this paper, we develop a novel statistical higher-order multi-scale (SHOMS) method for nonlinear thermo-mechanical simulation of random composite materials, which is designed to overcome limitations of prohibitive computation involving the macro-scale and micro-scale. By virtue of statistical multi-scale asymptotic analysis and Taylor series method, the SHOMS computational model is rigorously derived for accurately analyzing nonlinear thermo-mechanical responses of random composite materials both in the macro-scale and micro-scale. Moreover, the local error analysis of SHOMS solutions in the point-wise sense clearly illustrates the crucial indispensability of establishing the higher-order asymptotic corrected terms in SHOMS computational model for keeping the conservation of local energy and momentum. Then, the corresponding space-time multi-scale numerical algorithm with off-line and on-line stages is designed to efficiently simulate nonlinear thermo-mechanical behaviors of random composite materials. Finally, extensive numerical experiments are presented to gauge the efficiency and accuracy of the proposed SHOMS approach

Constitutive model for fibre-reinforced composite materials exposed to high temperature

A la pàgina XIX del Sumari manquen: la pàgina 333: "Original publications" i les pàgines 335 a 361 "Bibliography"The high strength-weight ratio of composite materials have made them one of the best materials for the design of light-weight structures. However, its special complexity has made them not suitable for the design of structures with a relative complexity or with numerous structural component and pieces. Hence, the importance in the development of adequate constitutive models which allow simulating the micro-macro scale interaction of composites, and to address the intrinsic and natural flexibility of composites that is not as relevant in traditional materials. Meanwhile, the mechanical development of these materials is a mature research branch with more than four groundbreaking decades of life, this is not certainly met at the thermo-mechanical level which is still in an early stage and, consequently, limiting the extensive use of composites in real world and complex structures, particularly structures in which a strong and detailed fulfilment of fire criteria is necessary. E.g., this is the very situation in the large-length ship design sector, where the share in the market for ships built using composite material, tends to be very reduced and closely accompanied by tools which serve to perform structural health monitoring, in order to palliate, the amount of high uncertainty of the present thermo-mechanical response, found in the design of these structures. The present thesis focuses on the development, formulation-wise and computational implementation, of a numerical model in order to predict the non-linear constitutive behaviour of fibre-reinforced plastic (FRP) composites exposed to thermal degradation due to high temperatures. This very model is cemented in the groundbreaking development of constitutive mechanical formulations specially tailored for composites also known as rule of mixtures -- in this present context, the formulation is the so-called serial-parallel rule of mixtures -- which establish a set of closure equations to obtain the suitable micro-macro scale interaction of the composite structure and, at the same time, to take into account the characterisation of the internal and state variables of the constituent phases. Apart, the ultimate objective of this thesis, in this special context -- where a structure is under thermal loads or, what is the same, exposed to fire -- it is mandatory to develop a consistent formulation and tool to perform what is referred to as a fire collapse assessment analysis. The utilisation of a more sophisticated thermal degradation or pyrolysis formulation, based on the present existing formulations, will be employed in order to obtain the internal and state variables of the thermal degradation process. Thus, the outcome of this analysis will serve as means to obtain the unknown thermal state of the structure and complete the thermo-mechanical analysis. The formulation of the thermo-mechanical problem is adapted to be used in laminated non-linear constitutive shells. The use of shells is a necessity for the right optimisation of the computational cost of analysing structures with a high number of structural reinforcements or divisions, such as the ones that appear regularly during the ship design process of large ship structures.Per als materials compostos, la seva relació esforç-pes elevada ha fet d'ells un dels millors materials per al disseny d'estructures lleugeres. No obstant això, la seva especial complexitat, fa d'ells un difícil treball quan es tracta del disseny d'estructures amb una certa complexitat, o, en l'existència de nombroses divisions estructurals i peces. En conseqüència, el desenvolupament de models constitutius adients és de vital importància, en especial aquells que permeten la simulació de la interacció per la micro-macro escala dels compostos, i que resolguin la flexibilitat natural i intrínseca d'aquests materials avançats, qüestió que no és tan rellevant per al disseny de materials tradicionals. Mentrestant, el desenvolupament de teories mecàniques per aquests materials es troba ja a la seva maduració, amb més de quatre dècades de descobriments en aquesta branca. D'altra banda, en qüestions que involucren l'anàlisi termo-mecànica, el paradigma es considera relativament verd, el qual limita l'aplicació extensiva dels compostos en aplicacions pràctiques i d'estructures complexes, de fet, és particularment limitant en el disseny d'estructures que requereixen del compliment d'exigents i detallats criteris relatius al foc. E.g., això mateix succeeix en el disseny d'embarcacions de grans eslores, on la quota de mercat dels vaixells construïts mitjançant materials compostos sol ser reduïda, i estretament acompanyada per eines de monitoratge de la integritat estructural, per així poder pal·liar la gran incertesa vinculada a la resposta termo-mecànica, fruit de les capacitats del disseny comercial actual. L'actual tesi se centra en el desenvolupament, de manera teòrica, i amb corresponent implementació computacional, d'un model numèric capaç de predir el comportament no-linear constitutiu de compostos plàstics amb fibra embedida (FRP) quan aquests són exposats a altes temperatures i en conseqüència a la degradació tèrmica. Aquest mateix model està inspirat en els desenvolupaments, pioners i excepcionals, de models constitutius mecànics, els quals estan pensats per a compostos. Aquestes teories formen part de la família de les regles de barreges, en particular, la formulació escollida és la famosa regla de barreges sèrie-paral·lel, la qual estableix un conjunt d'equacions de tancament per així obtenir l'adequada interacció del material compost a la micro-macro escala. Aquesta formulació, a la mateixa vegada, té en compte la caracterització i evolució de tant variables internes com d'estat, per a les constitutives, en aquest context es tractaria de la fibra i la matriu. Per una altra banda, l'objectiu últim d'aquesta tesi, dins d'aquest context particular, on una estructura és sotmesa a càrregues tèrmiques, o en altres paraules, s'exposa al foc, és de forçosa necessitat el desenvolupament d'una formulació consistent i una eina capaç de verificar el que es podria batejar com una anàlisi de col·lapse al foc. L'ús d'una formulació més sofisticada per la degradació tèrmica o piròlisi, basada en formulació existent, serà empleat per així aconseguir les variables internes i d'estat dels processos de degradació tèrmica. En conseqüència, els resultats d'aquesta anàlisi tèrmica serveixen per a obtenir el desconegut estat tèrmic de l'estructura, la distribució de temperatura a través de l'espessor del laminat, i complementar l'anàlisi del model termo-mecànic. La formulació del problema termo-mecànic és adaptada per ser usada en làmines no lineals de materials compostos. Fer servir làmines és una necessitat per a la correcta optimització del cost computacional derivat de l'anàlisi d'estructures amb un alt nombre de reforços o divisions, anàlisis que són freqüentment trobats dins del procés del disseny d'embarcacions de grans eslores.Para los materiales compuestos, su relación esfuerzo-peso elevada ha hecho de ellos uno de los mejores materiales para el diseño de estructuras ligeras. No obstante, su especial complejidad, hace de ellos un arduo trabajo cuando se trata del diseño de estructuras con una cierta complejidad, o, en la existencia de numerosas divisiones estructurales o piezas. Consecuentemente, el desarrollo de modelos constitutivos adecuados es de importancia, en especial aquellos que permiten la simulación de la interacción para la micro-macro escala de los compuestos, y que resuelven la flexibilidad natural e intrínseca de estos materiales avanzados, cuestión que no es tan relevante para el diseño de materiales tradicionales. Mientras tanto, el desarrollo de teorías mecánicas para estos materiales se encuentra en su madurez, con más de cuatro décadas de hallazgos en esta rama. En contraposición, en cuestiones que atañen el análisis termo-mecánico, el paradigma se encuentra relativamente verde, lo cual limita la aplicación extensiva de los compuestos en aplicaciones prácticas y estructuras complejas, de hecho, es particularmente limitante en el diseño de estructuras que requieren del cumplimiento de exigentes y detallados criterios relativos al fuego. E.g., esto mismo sucede en el diseño de embarcaciones de grandes esloras, donde la cuota de mercado de los buques construidos mediante materiales compuestos suele ser reducida, y estrechamente acompañada por herramientas de monitorización de la integridad estructural, para así poder paliar la gran incertidumbre vinculada a la respuesta termo-mecánica, fruto de las capacidades del diseño comercial actual. La actual tesis se centra en el desarrollo, de manera teórica, y con su correspondiente implementación computacional, de un modelo numérico capaz de predecir el comportamiento no-lineal constitutivo de compuestos plásticos con fibra embebida (FRP) cuando estos son expuestos a altas temperaturas y en consecuencia a la degradación térmica. Este mismo modelo está inspirado en los desarrollos, pioneros y excepcionales, de modelos constitutivos mecánicos, las cuales están pensadas para compuestos. Estas teorías forman parte de la familia de las reglas de mezclas, en particular, la formulación escogida es la renombrada regla de mezclas serie-paralelo, la cual establece un conjunto de ecuaciones de cierre para así obtener la adecuada interacción del material compuesto en la micro-macro escala. Esta formulación, a su misma vez, tiene en cuenta la caracterización y evolución de tanto variables internas como de estado, para las fases constituyentes, en este contexto se trataría de la fibra y la matriz. Por otra banda, el objetivo último de esta tesis, dentro de este contexto particular, donde una estructura se somete a cargas térmicas, o, en otras palabras, se expone al fuego, es de forzosa necesidad el desarrollo de una formulación consistente y una herramienta capaz de verificar lo que se puede acuñar como un análisis de colapso al fuego. El uso de una formulación más sofisticada para la degradación térmica o pirolisis, basada en formulación existente, será empleado para así obtener las variables internas y de estado de los procesos de degradación térmica. En consecuencia, los resultados de este análisis térmico sirven para obtener el desconocido estado térmico de la estructura, la distribución de temperatura a través del espesor del laminado, y complementar el análisis termo-mecánico. La formulación del problema termo mecánico es adaptada para ser usada en láminas no lineales de materiales compuestos. Usar láminas es una necesidad para la correcta optimización del coste computacional derivado del análisis de estructuras con un alto número de refuerzos o divisiones, análisis que son frecuentemente encontrados en el proceso de diseño de embarcaciones de grandes esloras.Postprint (published version

Multiscale thermo-hydro-mechanical-chemical coupling effects for fluid-infiltrating crystalline solids and geomaterials: theory, implementation, and validation

Extreme climate change and demanding energy resources have led to new geotechnical engineering challenges critical for sustainable development and resilient infrastructure of our society. Applications such as geological disposal of nuclear waste and carbon dioxide, artificial ground freezing, and hydraulic fractures all require an in-depth understanding of the thermo-hydro-mechanical coupling mechanisms of geomaterials subjected to various environmental impact. This dissertation presents a multiphysical computational framework dedicated to address the issues related to those unconventional applications. Our objective is not only incorporating multiphysical coupling effects at the constitutive laws, but also taking into account the nonlocal effects originated from the flow of pore-fluid, thermal convection and diffusion among solid and fluid constituents, and crystallization and recrystallization of crystals in the pore space across length scales. By considering these coupling mechanisms, we introduce a single unified model capable of predicting complex thermo-hydro-mechanical responses of geological and porous media across wide spectra of temperature, confining pressure and loading rate. This modeling framework applies to two applications, i.e., the freezing and thawing of frozen soil and the modeling of anisotropic crystal plasticity/fracture response of rock salt. Highlights of the key ingredients of the models cover the stabilization procedure used for the multi-field finite element, the return mapping algorithm for crystal plasticity, the micromorphic regularization of the Modified Cam-Clay model, and the strategy for enhancing computational efficiency of solvers, such as pre-conditioner, adaptive meshing, and internal variable mapping. By introducing the multiphysical coupling mechanisms explicitly, our computational geomechanics model is able to deliver more accurate and consistent results without introducing a significant amount of additional material parameters. In a parallel effort, we analyze the impact of thermo-hydro-mechanical (THM) coupling effects on the dynamic wave propagation and strain localization in a fully saturated softening porous medium. The investigation starts with deriving the characteristic polynomial corresponding to the governing equations of the THM system. The theoretical analysis based on the Abel–Ruffini theorem reveals that the roots of the characteristic polynomial for the THM problem cannot be expressed algebraically. Our analysis concludes that the rate-dependence introduced by multiphysical coupling may not regularize the THM governing equations when softening occurs

Theory and computation of electromagnetic fields and thermomechanical structure interaction for systems undergoing large deformations

For an accurate description of electromagneto-thermomechanical systems, electromagnetic fields need to be described in a Eulerian frame, whereby the thermomechanics is solved in a Lagrangean frame. It is possible to map the Eulerian frame to the current placement of the matter and the Lagrangean frame to a reference placement. We present a rigorous and thermodynamically consistent derivation of governing equations for fully coupled electromagneto-thermomechanical systems properly handling finite deformations. A clear separation of the different frames is necessary. There are various attempts to formulate electromagnetism in the Lagrangean frame, or even to compute all fields in the current placement. Both formulations are challenging and heavily discussed in the literature. In this work, we propose another solution scheme that exploits the capabilities of advanced computational tools. Instead of amending the formulation, we can solve thermomechanics in the Lagrangean frame and electromagnetism in the Eulerian frame and manage the interaction between the fields. The approach is similar to its analog in fluid structure interaction, but more challenging because the field equations in electromagnetism must also be solved within the solid body while following their own different set of transformation rules. We additionally present a mesh-morphing algorithm necessary to accommodate finite deformations to solve the electromagnetic fields outside of the material body. We illustrate the use of the new formulation by developing an open-source implementation using the FEniCS package and applying this implementation to several engineering problems in electromagnetic structure interaction undergoing large deformations