Factores de intensidad de tensiones en problemas con cierre de grieta

Se presenta en este trabajo la aplicación de un programa de contacto con pequeños desplazamientos y deformaciones entre materiales ortótropos y elásticos a la determinación de factores de intensidad de tensiones en grietas con labios en contacto, parcial o totalmente. El método de análisis empleado es el método de los elementos de contorno (M.E.C.). El programa incluye elementos lineales, cuadráticos y elementos singulares para reproducir el estado tensional en bordes de grieta. Se sigue un proceso de subregionalización con cada uno de los labios de la grieta en la subregión distinta, lo que permite la singularidad derivada de nudos dobles. Las condiciones de contacto entre dos sólidos se imponen de forma explícita, lo que permite la incorporación de diferentes zonas de contacto entre los cuerpos, con diferentes coeficientes de rozamiento en cada una de ellas, . Ja forma simple. Los factores de intensidad de tensiones se obtienen mediante la utilización de elementos singulares con nudo a 114 que dan resultados suficientemente buenos a efectos ingenieriles. Finalmente se estudia la influencia de la longitud de grieta y coeficiente de rosamiento en problemas de flexión.Peer Reviewe

Propagación de grietas en materialea ortótropos mediante el método de los elementos de contorno

Se presenta en este trabajo la aplicación del Metodo de los Elementos de Contorno (M.E.C.) a la determinación de factores de intensidad de tensiones (F.I.T.) y la predicción del ángulo de propagación de grietas en materiales ortótropos. El programa incluye elementos lineales, cuadráticos y elementos singulares para reproducir el estado tensional de bordes de grieta. Se sigue un proceso de subregionalización con cada uno de los labios de grieta en una subregión distinta, lo que evita la singularidad derivada de nudos dobles. Se estudian y comparan distintos métodos para la evaluación del F.I.T. y se obtiene el valor de los mismos en distintos casos de interés. Se utiliza el método de la tensión circunferencial máxima para la determinación del ángulo de propagación y se realiza el seguimiento de este ángulo en un caso específico.The application of the Boundary Element Method (BEM) to the computation of the stress intensity factors (SIF) and the crack propagation angle in orthotropic materials is the aim of this paper. The computer program includes isoparametric linear, quadratic and quarter-pointtraction- singular elements in order to obtain the stress distribution around the crack edges. A multidomain approach is followed in order to avoid the geometrical singularity that appears in the double-node method. Different methods to compute the SIF are compared and severa1 SIFs computed for some cases. Finally, the maximun circunferencial stress approach is used to obtain the crack propagation angle in a mixed-mode propagation problein in an ortliotropic material.Peer Reviewe

Determinación de tensiones de contacto entre materiales ortótropos mediante el M.E.C

Se presenta en este trabajo la formulación e implementación del problema de contacto con pequeños desplazamientos y deformaciones entre materiales ortótropos y elásticos mediante el método de los elementos de contorno. El programa incluye elementos isoparamétricos lineales, cuadráticos y singulares con nudo a 1/4, imponiendo de forma explícita las condiciones de contacto entre dos sólidos. Permite la incorporación de diferentes zonas de contacto entre los cuerpos, con diferentes coeficientes de rozamiento para cada uno de ellos. El algoritmo de resolución optimiza la disposición de las ecuaciones, de forma que el número de éstas a resolver en cada uno de los pasos del proceso incremental sea mínimo. Se incluyen distintas aplicaciones, entre ellas la determinación de tensiones de contacto en uniones roblonadas entre laminados de material compuesto o el estudio de la influencia del contacto entre bordes de grieta en la determinación de los factores de intensidad de tensiones efectivos en los extremos de la misma.Peer Reviewe

Computational multiscale solvers for continuum approaches

Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper

Propagación de grietas en materialea ortótropos mediante el método de los elementos de contorno

Se presenta en este trabajo la aplicación del Metodo de los Elementos de Contorno (M.E.C.) a la determinación de factores de intensidad de tensiones (F.I.T.) y la predicción del ángulo de propagación de grietas en materiales ortótropos. El programa incluye elementos lineales, cuadráticos y elementos singulares para reproducir el estado tensional de bordes de grieta. Se sigue un proceso de subregionalización con cada uno de los labios de grieta en una subregión distinta, lo que evita la singularidad derivada de nudos dobles. Se estudian y comparan distintos métodos para la evaluación del F.I.T. y se obtiene el valor de los mismos en distintos casos de interés. Se utiliza el método de la tensión circunferencial máxima para la determinación del ángulo de propagación y se realiza el seguimiento de este ángulo en un caso específico.The application of the Boundary Element Method (BEM) to the computation of the stress intensity factors (SIF) and the crack propagation angle in orthotropic materials is the aim of this paper. The computer program includes isoparametric linear, quadratic and quarter-pointtraction- singular elements in order to obtain the stress distribution around the crack edges. A multidomain approach is followed in order to avoid the geometrical singularity that appears in the double-node method. Different methods to compute the SIF are compared and severa1 SIFs computed for some cases. Finally, the maximun circunferencial stress approach is used to obtain the crack propagation angle in a mixed-mode propagation problein in an ortliotropic material.Peer Reviewe

Predicting cell behaviour parameters from glioblastoma on a chip images. A deep learning approach

The broad possibilities offered by microfluidic devices in relation to massive data monitoring and acquisition open the door to the use of deep learning technologies in a very promising field: cell culture monitoring. In this work, we develop a methodology for parameter identification in cell culture from fluorescence images using Convolutional Neural Networks (CNN). We apply this methodology to the in vitro study of glioblastoma (GBM), the most common, aggressive and lethal primary brain tumour. In particular, the aim is to predict the three parameters defining the go or grow GBM behaviour, which is determinant for the tumour prognosis and response to treatment. The data used to train the network are obtained from a mathematical model, previously validated with in vitro experimental results. The resulting CNN provides remarkably accurate predictions (Pearson''s ¿ > 0.99 for all the parameters). Besides, it proves to be sound, to filter noise and to generalise. After training and validation with synthetic data, we predict the parameters corresponding to a real image of a microfluidic experiment. The obtained results show good performance of the CNN. The proposed technique may set the first steps towards patient-specific tools, able to predict in real-time the tumour evolution for each particular patient, thanks to a combined in vitro-in silico approach. © 2021 The Author(s

An unsupervised data completion method for physically-based data-driven models

Data-driven methods are an innovative model-free approach for engineering and sciences, still in process of maturation. The idea behind is the combination of data analytics techniques, to handle the huge amount of data derived from continuous monitoring or experimental measurements, and of the constraints imposed by universal physical laws, particular to the field in hands. A well-known problem in the former corresponds to the quality and completeness of the available data that, sometimes, are so poor that make the predictions useless. In data-driven simulation-based engineering and sciences (DDSBES), the intrinsic physical constraints may help in completing the missing data in a more precise manner, by forcing them to remain in the manifold defined by the physical laws. In this work, a suitable imputation method to complete incomplete data that preserves the data context-dependent structure is presented. This is accomplished by enforcing the data to fulfill the set of physical constraints, specific to the problem. For this purpose, a generalization of the weighted mean concept is proposed, where the distance to the admissible points (in a physical sense) is used as a weighting function to get the optimal candidate. The method is evaluated in a classical regression problem, where it is compared with other standard methods, showing better results. Then, its application is illustrated in two data-driven problems, where no filling data procedure has been yet proposed, showing good predictive capability, provided that the data are close enough to the actual system state

A PGD-based multiscale formulation for non-linear solid mechanics under small deformations

Model reduction techniques have became an attractive and a promising field to be applied in multiscale methods. The main objective of this work is to formulate a multiscale procedure for non-linear problems based on parametrized microscale models. The novelty of this work relies in the implementation of the model reduction technique known as Proper Generalized Decomposition for solving the high dimensional parametrized problem resulting from the microscale model. The multiscale framework here proposed is formulated to non-linear problems, specifically to material non-linearities, where material response is governed by a strain dependent evolution law. Two strategies to deal with this kind of problem under small deformations are detailed in this work. Both strategies based on parametrized microscale models solved by PGD have been applied to a problem with a rate-dependent isotropic damage model. First, a procedure where the problem is solved by uncoupling the equilibrium equation to the state variable expression has been explored. In order, to alleviate the parametrized microscale problem, a second strategy for problems with material non-linearity has been proposed, incorporating a parametrized microscale problem at each macroscale increment (FE-PGD). The basis of those procedures are described and compared, highlighting the solution accuracy and computer time consumption in comparison to a traditional finite element analysis

Computational Multiscale Solvers for Continuum Approaches

Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper.Abengoa Researc

Analysis of the parametric correlation in mathematical modeling of in vitro glioblastoma evolution using copulas

Modeling and simulation are essential tools for better understanding complex biological processes, such as cancer evolution. However, the resulting mathematical models are often highly non-linear and include many parameters, which, in many cases, are difficult to estimate and present strong correlations. Therefore, a proper parametric analysis is mandatory. Following a previous work in which we modeled the in vitro evolution of Glioblastoma Multiforme (GBM) under hypoxic conditions, we analyze and solve here the problem found of parametric correlation. With this aim, we develop a methodology based on copulas to approximate the multidimensional probability density function of the correlated parameters. Once the model is defined, we analyze the experimental setting to optimize the utility of each configuration in terms of gathered information. We prove that experimental configurations with oxygen gradient and high cell concentration have the highest utility when we want to separate correlated effects in our experimental design. We demonstrate that copulas are an adequate tool to analyze highly-correlated multiparametric mathematical models such as those appearing in Biology, with the added value of providing key information for the optimal design of experiments, reducing time and cost in in vivo and in vitro experimental campaigns, like those required in microfluidic models of GBM evolution