46 research outputs found
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
Un modelo no-lineal de homogeneización para pórticos de hormigón armado confinado - Tratamiento de la estructura como material compuesto
Se propone desarrollar un modelo para el análisis de estructuras de barras de hormigón armado confinado con cercos y con capacidad de soportar el cortante. Por una parte se pretende desarrollar un modelo homogeneizado que asegure una buena solución estructural y que pueda ser introducido en un programa clásico de estructuras de barras. Por otra parte se quiere desarrollar también un modelo más riguroso, detallado y exacto que sea introducido en un programa de elementos finitos.En este trabajo se desarrolla
un modelo para el análisis de estructuras
de barras
de hormigón
armado
que considera el comportamiento no lineal de la armad
ura longitudinal, de los cercos
y
del hormigón. El estudio del estado del conocimiento que se ha realizado muestra que el
confinamie
nto
,
aportado por los cercos
,
altera el comportamiento no lineal de las barras,
añadiéndo
les
res
istencia y ductilidad
, mejo
rando su respuesta y que, por lo tanto, el confinamiento
debe ser incluido en un análisis estructural avanzado. L
a respuesta
no lineal
de la
s
estructura
s
cambia
,
especialmente
en las etapas avanzadas del proc
eso de carga, mejorando sobre todo
su
resistencia y
su comportamiento post pico. En consecuencia, el confinamiento no puede ser
ignorado por el ingeniero a la hora de proyectar o eva
luar el comportamiento de las estructuras
de hormigón armado.
El análisis numérico del efecto
de
l
confinamiento
producido por
los cercos sobre una barra es
difícil de realizar debido a los complejos fenómenos no lineales originados por la plastificación
de
los cercos y de la armadura longitudinal,
así como
por el comportamiento no l
ineal de la matriz
de hormigón
. Es especialmente difícil modelizar correctamente el estado tensional y
deformacional en tres dimensiones, alterado por la no linealidad de los mat
eriales, puesto que el
problema depende de muchos parámetros, algunos de los cuales son difíciles de cuantificar
y
,
también,
por la compleja interacción que se produce entre los materiales componentes
. Por esto,
en el presente trabajo se ha desarrollado un
modelo
de uso sencillo
para estructuras de barras
de
hormigón armado confinado
. Dicho modelo
, que
se basa en la teoría de la homogeneización,
trata
la estructura como
u
n
material compuesto
,
asegura
una buena solución
al análisis
estructural y
puede
ser introducido
fácilmente
en un programa clásico de estructuras de barras.
E
l
comportamie
nto no lineal de los materiales que
se ha implementado considera el modelo de daño
para la degradación del hormigón y el modelo elasto
-
plástico para el del acero. El
modelo no
lineal
unidimensional
desarrollado
se ha introducido en un programa de ordenador para calcular
estructuras
de barras
considerando el conf
inam
iento del hormigón armado cread
o en Matlab.
Los
resultados calculados con el programa desarrollado han s
ido validados mediante comparación con
resultados obtenidos
con modelos basados en otros métodos y con resultados de ensayos
experimentales
de
otros investigadores.
Los ejemplos de cálculo han mostrado que es necesario
considerar el confinamiento en el cál
culo
de la estructura
ya que la presencia de los cercos afecta de forma significativa la resist
encia, la
ductilidad
y el daño de las barras de hormigón armado. Los ejemplos estudiados muestran que la
respuesta de la estructura varía de forma significativa
en función de parámetros como la
separación entre cercos o su diámetro.
El modelo y el programa desarrollados facilitan considerar el efecto del confinamiento en el
cálculo de la estructura, de forma que pueda ser utilizado de manera habitual en la prácti
ca de
proyecto. Los ejemplos muestran que incluir
en el análisis
el confinamiento
producido
por los
cercos
es posible
y necesario para determinar el comportamiento real de la estructura. Se abre así
la puerta a la posibilidad de considerar este fenómeno en
el diseño de forma
práctica, eficiente y
habitual
Appraisement of planar, bending and twisting cracks in 3D with isotropic and orthotropic damage models
The final publication is available at Springer via http://dx.doi.org/10.1007/s10704-018-0261-3This paper discusses the modeling of cracking in quasi-brittle materials using isotropic and orthotropic damage constitutive laws. A mixed strain/displacement finite element formulation is used, taking advantage of its enhanced precision and its enforced interelemental strain continuity. On the one hand, this formulation avoids the spurious mesh dependency of the computed solution associated to standard elements and does not require the use of tracking techniques. On the other hand, it greatly alleviates the spurious stress locking associated to the use of orthotropic models on standard finite elements. The performance of several isotropic and orthotropic damage constitutive laws is assessed through an extensive comparison with analytical solutions, numerical tests and experimental evidence reported in the literature. The behavior of the different damage models in terms of crack surface, collapse mechanism and force displacement curves is investigated performing 3D analyses in several conditions including Mode I, Mixed Mode and Mode III fracture. When performing the appraisement of planar, bending and twisting cracks, the enhanced accuracy of the mixed formulation allows for a distinct assessment of the several damage models considered. Aspects related to the behavior of damage models, such as the influence of Poisson’s ratio, the shape of the damage surface and the adoption of isotropic and orthotropic models are investigated and noteworthy conclusions are drawn.Peer ReviewedPostprint (author's final draft
Architecture of a multi-crack model with full closing, reopening and sliding capabilities
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-020-01836-yThis paper discusses the finite element modeling of cracking of quasi-brittle materials under cyclic loading. A damage based crack model is proposed, which considers tensile and compressive damage, irreversible strains upon unloading in compression, as well as micro-crack closure-reopening effects with special attention to the sliding of open cracks (MCRS). The model is implemented in conjunction with a mixed strain/displacement finite element formulation which provides enhanced accuracy and guarantees mesh size and bias independent results. Two distinct damage models are developed. The first one is based on the classical fixed orthotropic crack models and the second is an isotropic version. Both of them incorporate the necessary elements to furnish full MCRS capabilities. The model is demonstrated through several examples of application and comparison with experimental evidence, in mode I, mode II and mixed mode monotonic and cyclic loading.Financial support from the Spanish Ministry of Economy and Business via the ADaMANT (Computational Framework for Additive Manufacturing of Titanium Alloy) project (Proyectos de I + D (Excelencia) DPI2017-85998-P) is gratefully acknowledged. The support provided by the Spanish Ministry of Education to Mr. Gabriel Barbat via the FPU program is also acknowledged.Peer ReviewedPostprint (author's final draft
Out-of-plane seismic response and failure mechanism of masonry structures using finite elements with enhanced strain accuracy
The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are the material properties, the quality of the walls, the geometry of the structure, the connections between structural elements and the stiffness of the diaphragms. During the last years, a wide variety of numerical methods has been employed to assess the out-ofplane behaviour of unreinforced masonry structures. Finite element macro-modelling approaches are among the most famous as they allow modelling large structures at a reasonable computational cost. However, macro-modelling approaches may result in a non-realistic representation of localized cracks and a dependency of the numerical solution on the finite element mesh. Mixed strain/displacement finite elements have been recently proposed as a remedy to the above numerical pathologies. Due to the independent interpolation of strains and displacements these finite element formulations are characterized by an enhanced accuracy in strain localization and crack propagation problems, being at the same time practically mesh independent. For these reasons, mixed finite elements are employed in this work for the out-of-plane assessment of unreinforced masonry structures, being at the same time their first real-scale application. A full-scale experimental campaign of two masonry structures, a stone and a brick one, subjected to shaking-table tests is chosen as reference benchmark. Their structural response under seismic actions is numerically assessed through nonlinear static analysis. The proposed approach is validated through the comparison of the numerical results with the experimental ones, as well as with the results obtained using standard irreducible finite elements
Out-of-plane seismic response and failure mechanism of masonry structures using finite elements with enhanced strain accuracy
The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are the material properties, the quality of the walls, the geometry of the structure, the connections between structural elements and the stiffness of the diaphragms.
During the last years, a wide variety of numerical methods has been employed to assess the out-of-plane behaviour of unreinforced masonry structures. Finite element macro-modelling approaches are among the most famous as they allow modelling large structures at a reasonable computational cost. However, macro-modelling approaches may result in a non-realistic representation of localized cracks and a dependency of the numerical solution on the finite element mesh.
Mixed strain/displacement finite elements have been recently proposed as a remedy to the above nu-merical pathologies. Due to the independent interpolation of strains and displacements these finite element formulations are characterized by an enhanced accuracy in strain localization and crack propagation problems, being at the same time practically mesh independent. For these reasons, mixed finite elements are employed in this work for the out-of-plane assessment of unreinforced masonry struc-tures, being at the same time their first real-scale application. A full-scale experimental campaign of two masonry structures, a stone and a brick one, subjected to shaking-table tests is chosen as reference benchmark. Their structural response under seismic actions is numerically assessed through nonlinear static analysis. The proposed approach is validated through the comparison of the numerical results with the experimental ones, as well as with the results obtained using standard irreducible finite ele-ments.Peer ReviewedPostprint (author's final draft
Probabilistic estimation of annual lost economic production due to premature deaths because of earthquakes
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Human and Ecological Risk Assessment: An International Journal on 2016, available online at: http://www.tandfonline.com/10.1080/10807039.2015.1095072A methodology to estimate, in a probabilistic way, the annual cost to society of premature deaths because of earthquakes is proposed in this article. The methodology makes use of results obtained by means of prospective and probabilistic seismic risk assessments where expected deaths caused by the collapse of buildings are obtained. Those results, combined with demographic and macroeconomic indicators such as the age distribution, life expectancy at birth, and per capita gross domestic product, are used to estimate the cost to society in terms of lost productivity due to premature mortality because of earthquakes. The proposed methodology does not attempt to estimate nor assign a cost to human lives at any stage, but the one associated to lost productivity at the societal level. One of the descriptors of the methodology is part of the components of the disability adjusted life year, a widely used metric in the public health field that estimates the burden of diseases based mostly on historical data. As an example, the methodology is applied to Medellin, the second largest city of Colombia, finding that the cost of lost productivity due to premature mortality because of earthquakes has a similar order of magnitude to the direct physical losses in the public and private building stock calculated in a previous probabilistic seismic risk assessment.Peer ReviewedPostprint (author's final draft
Methodology and applications for the benefit cost analysis of the seismic risk reduction in building portfolios at broadscale
This article presents a methodology for an estimate of the benefit cost ratio of the seismic risk reduction in buildings portfolio at broadscale, for a world region, allowing comparing the results obtained for the countries belonging to that region. This methodology
encompasses (1) the generation of a set of random seismic events and the evaluation of the spectral accelerations at the buildings location; (2) the estimation of the buildings built area, the economic value, as well as the classification in structural typologies; (3) the development of vulnerability curves for each typology; (4) the estimation of the annual average loss of the buildings portfolio in the current conditions as well as in the case of a hypothetical structural intervention. The benefit cost ratio is estimated as the difference between the estimates of the present value of these two annual average losses, divided by the retrofitting costs. This methodology has been applied to the portfolio of public schools of 14 countries ofLatinAmerica and the Caribbean, for evaluating the feasibility of the seismic risk reduction at a national scale
Prioritizing interventions to reduce seismic vulnerability in school facilities in Colombia
Colombian seismic code NSR-98 establishes the requirement for the seismic vulnerability analysis and, if necessary, the strengthening of public facilities (schools). Due to the investments required by risk reduction programs, it is necessary to establish criteria for assigning priorities for the interventions. This article proposes a methodology for obtaining a Benefit-Cost Ratio (BCR) at the
subnational level, by assessing the expected annual average loss of the built area of public schools and the retrofitting cost. The BCR is estimated as the difference between the estimates of the net present value for status quo and retrofitted states, these two divided by the retrofitting costs. According to the BCR, 47.3% of the total school built area of Colombia should be retrofitted where the retrofitting
costs correspond to 25% of the total investment. Proposed BCR is useful for prioritizing regions in function of the feasibility of reducing the seismic vulnerability of the schools
Probabilistic estimation of annual lost economic production due to premature deaths because of earthquakes
A methodology to estimate, in a probabilistic way, the annual cost to society of premature deaths because of earthquakes is proposed in this article. The methodology makes use of results obtained by means of prospective and probabilistic seismic risk assessments where expected deaths caused by the collapse of buildings are obtained. Those results, combined with demographic and macroeconomic indicators such as the age distribution, life expectancy at birth, and per capita gross domestic product, are used to estimate the cost to society in terms of lost productivity due to premature mortality because of earthquakes. The proposed methodology does not attempt to estimate nor assign a cost to human lives at any stage, but the one associated to lost productivity at the societal level. One of the descriptors of the methodology is part of the components of the disability adjusted life year, a widely used metric in the public health field that estimates the burden of diseases based mostly on historical data. As an example, the methodology is applied to Medellín, the second largest city of Colombia, finding that the cost of lost productivity due to premature mortality because of earthquakes has a similar order of magnitude to the direct physical losses in the public and private building stock calculated in a previous probabilistic seismic risk assessment