A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting

[EN] A new stress recovery procedure that provides accurate estimations of the discretization error for linear elastic fracture mechanic problems analyzed with the extended finite element method (XFEM) is presented. The procedure is an adaptation of the superconvergent patch recovery (SPR) technique for the XFEM framework. It is based oil three fundamental aspects: (a) the use of a singular+smooth stress field decomposition technique involving the use of different recovery methods (or each field: standard SPR for the smooth field and reconstruction of the recovered singular field using the stress intensity factor K for the singular field: (b) direct calculation of smoothed stresses at integation points using conjoint polynomial enhancement and (c) assembly of patches with elements intersected by the crack using different stress interpolation polynomials at each side of the crack. The method was validated by testing it oil problems with an exact solution in mode I, mode II, and mixed mode and oil it problem without analytical solution. The results obtained showed the accuracy of the proposed error estimator.This paper was developed within the framework of the research projects DP12007-66773-C02-01 and DPI2007-66995-C03-02 of the Ministerio de Educacion y Ciencia (Spain). Funding was also received from the Generalitat Valenciana and the Universidad Politecnica de Valencia.Ródenas, J.; González-Estrada, O.; Taráncón, J.; Fuenmayor, F. (2008). A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting. International Journal for Numerical Methods in Engineering. 76(4):545-571. https://doi.org/10.1002/nme.2313S54557176

Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

International audienceIn this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator

Direct medical image-based Finite Element modelling for patient-specific simulation of future implants

[EN] In patient specific biomedical simulation, the numerical model is usually created after cumbersome, time consuming procedures which often require highly specialized human work and a great amount of man-hours to be carried out. In order to make numerical simulation available for medical practice, it is of primary importance to reduce the cost associated to these procedures by making them automatic. In this paper a method for the automatic creation of Finite Element (FE) models from medical images is presented. This method is based on the use of a hierarchical structure of nested Cartesian grids in which the medical image is immersed. An efficient h-adaptive procedure conforms the FE model to the image characteristics by refining the mesh on the basis of the distribution of elastic properties associated to the pixel values. As a result, a problem with a reasonable number of degrees of freedom is obtained, skipping the geometry creation stage. All the image information is taken into account during the calculation of the element stiffness matrix, therefore it is straightforward to include the material heterogeneity in the simulation. The proposed method is an adapted version of the Cartesian grid Finite Element Method (cgFEM) for the FE analysis of objects defined by images. cgFEM is an immersed boundary method that uses h-adaptive Cartesian meshes non-conforming to the boundary of the object to be analysed. The proposed methodology, used together with the original geometry-based cgFEM, allows prosthesis geometries to be easily introduced in the model providing a useful tool for evaluating the effect of future implants in a preoperative framework. The potential of this kind of technology is presented by mean of an initial implementation in 2D and 3D for linear elasticity problems.With the support of the European Union Framework Programme (FP7) under grant agreement No. 289361 'Integrating Numerical Simulation and Geometric Design Technology (INSIST)', the Ministerio de Economia y Competitividad of Spain (DPI2010-20542) and the Generalitat Valenciana (PROMETEO/2016/007).Giovannelli, L.; Ródenas, J.; Navarro-Jiménez, J.; Tur Valiente, M. (2017). Direct medical image-based Finite Element modelling for patient-specific simulation of future implants. Finite Elements in Analysis and Design. 136:37-57. https://doi.org/10.1016/j.finel.2017.07.010S375713

Robust h-adaptive meshing strategy considering exact arbitrary CAD geometries in a Cartesian grid framework

[EN] Geometry plays a key role in contact and shape optimization problems in which the accurate representation of the exact geometry and the use of adaptive analysis techniques are crucial to obtaining accurate computationally-efficient Finite Element (FE) simulations. We propose a novel algorithm to generate 3D h-adaptive meshes for an Immersed Boundary Method (IBM) based on Cartesian grids and the so-called NEFEM (NURBS-Enhanced FE Method) integration techniques. To increase the accuracy of the results at the minimum computational cost we seek to keep the efficient Cartesian structure of the mesh during the whole analysis process while considering the exact boundary representation of domains given by NURBS or T-Splines. Within the framework of Cartesian grids, the two significant contributions of this paper are: (a) the methodology used for the mesh-geometry intersection, which represents a considerable challenge due to their independence; and (b) the robust procedure used to generate the integration subdomains that exactly represent the CAD model. The numerical examples given show the proper convergence of the method, its capacity to mesh complex 3D geometries and that Cartesian grid-based IBM can be considered a robust and reliable tool in terms of accuracy and computational cost.The authors wish to thank the Spanish Ministerio de Economia y Competitividad for the financial support received through Project DPI2013-46317-R and the FPI program (BES-2011-044080), also the Generalitat Valenciana for the assistance received through Project PROMETEO/2016/007.Marco, O.; Ródenas, J.; Navarro-Jiménez, J.; Tur Valiente, M. (2017). Robust h-adaptive meshing strategy considering exact arbitrary CAD geometries in a Cartesian grid framework. Computers & Structures. 193:87-109. doi:10.1016/j.compstruc.2017.08.004S8710919

Accurate recovery-based error upper bounds for the extended finite element framework

[EN] This paper introduces a recovery-type error estimator yielding upper bounds of the error in energy norm for linear elastic fracture mechanics problems solved using the extended finite element method (XFEM) The paper can be considered as an extension and enhancement of a previous work in which the upper bounds of the error were developed in a FEM framework The upper bound property requires the recovered solution to be equilibrated and continuous The proposed technique consists of using a recovery technique, especially adapted to the XFEM framework that yields equilibrium at a local level (patch by patch) Then a postprocess based on the partition of unity concept is used to obtain continuity The result is a very accurate but only nearly-statically admissible recovered stress field, with small equilibrium defaults introduced by the postprocess Sharp upper bounds are obtained using a new methodology accounting for the equilibrium defaults, as demonstrated by the numerical testsThis work has been carried out within the framework of the research projects DPI2007-66773-C02-01, DPI2007-66995-C03-02 and DPI2007-62395 of the Ministerio de Educacion y Ciencia (Spain). The financial support of the Generalitat Valenciana and the Universidad Politecnica de Valencia is also acknowledged.Ródenas, J.; Gonzalez-Estrada, O.; Díez, P.; Fuenmayor Fernández, F. (2010). Accurate recovery-based error upper bounds for the extended finite element framework. Computer Methods in Applied Mechanics and Engineering. 199(37-40):2607-2621. https://doi.org/10.1016/j.cma.2010.04.010S2607262119937-4

Metodología jerárquica h adaptativa basada en subdivisión de elementos

[EN] This paper presents a hierarchical h adaptive methodology for Finite Element Analysis based on the hierarchical relations between parent and child elements that come out if these elements are geometrically similar. Under this similarity condition the terms involved in the evaluation of element stiffness matrices of parent and child elements are related by a constant which is a function of the element sizes ratio (scaling factor). These relations have been the basis for the development of a hierarchical h adaptivity methodology based on element subdivision and the use of multipoint-constraints to ensure C0 continuity. The use of a hierarchical data structure significantly reduces the amount of calculations required for the mesh refinement, the evaluation of the global stiffness matrix, element stresses and element error estimation. The data structure also produces a natural reordering of the global stiffness matrix that improves the behaviour of the Cholesky factorization.[ES] En este artículo se presenta una metodología h adaptativa para el Análisis por Elementos Finitos basada en las relaciones jerárquicas entre elementos padre e hijo que surgen si estos elementos son geométricamente similares. Bajo esta condición de similitud, los términos resultantes de la evaluación de las matrices de rigidez de elementos padre e hijo están relacionados por una constante que es una función de la relación de tamaños de elemento (factor de escala). Estas relaciones han sido la base para el desarrollo de una metodología jerárquica h adaptativa basada en la subdivisión de elementos y el uso de restricciones multipunto para asegurar la continuidad C0 . El uso de una estructura de datos jerárquica reduce significativamente la cantidad de cálculos requeridos para el refinamiento de la malla, la evaluación de la matriz de rigidez global, las tensiones de los elementos y la estimación del error del elemento. La estructura de datos también produce un reordenamiento natural de la matriz de rigidez global que mejora el comportamiento de la factorización de Cholesky.The authors wish to thank the Spanish Ministerio de Economía y Competitividad for the fiancial support received through the project DPI2013-46317-R and the Generalitat Valenciana through the project PROMETEO/2016/007. The support of the Universidad Politécnica de Valencia is also acknowledged. The authors also want to thank Ana Ródenas’s help in the translation of this paper.Ródenas, J.; Albelda Vitoria, J.; Tur Valiente, M.; Fuenmayor Fernández, F. (2017). A hierarchical h adaptivity methodology based on element subdivision. Revista UIS Ingenierías. 16(2):263-280. https://doi.org/10.18273/revuin.v16n2-2017024S26328016

3D analysis of the influence of specimen dimensions on fretting stresses

[EN] In this paper, the contact conditions and stresses that arise in a fretting test have been analyzed by means of a three-dimensional finite element model of the contact between a sphere and a flat surface. An h-adaptive process, based on element subdivision, has been used in order to obtain a low discretization error at a reasonable computational cost. The influence of finite dimensions of the specimen in the stress fields has been evaluated. The results have been compared with the classical Cattaneo-Mindlin solution.The authors wish to thank the financial support received from CICYT by means of the project PB97-0696-C02-02.Tur Valiente, M.; Fuenmayor Fernández, F.; J.J. Ródenas; Giner Maravilla, E. (2003). 3D analysis of the influence of specimen dimensions on fretting stresses. Finite Elements in Analysis and Design. 39(10):933-949. https://doi.org/10.1016/S0168-874X(02)00139-7S933949391

Preliminary evaluation of fenugreek (Trigonella foenum-graecum) seed gum as a potential prebiotic for growing rabbits in Tunisia: effects on in vivo faecal digestibility and in vitro fermentation

[EN] This study aims to determine the effect of dietary inclusion of fenugreek seed gum (FSG), rich in galactomannans, on nutrient apparent digestibility and caecal environment, as well as on in vitro caecal fermentation of Tunisian growing rabbits. Three experimental diets were formulated, including 0, 0.25 and 0.5% of FSG (FSG0, FSG0.25 and FSG0.5, respectively) for the in vivo trial and 0, 0.125, 0.25, 0.5 and 100% of FSG (FSG0, FSG0125, FSG0.25, FSG0.5 and FSG100, respectively) for the in vitro trial. In the in vivo trial, 45 weaned rabbits 31 d old (15 per treatment) were housed in individual cages until 94 d of age. Apparent digestibility coefficients were determined at two ages, from 38 to 41 and from 56 to 59 d old, and caecal traits were recorded after slaughtering. In the in vitro trial, the five experimental diets were incubated with a rabbit caecal inoculum. Gas production was measured and modelled until 72 h and the fermentation traits were measured. Apparent faecal digestibility coefficients of main nutrients and main caecal environment traits were not significantly affected by the dietary inclusion of FSG (P>0.05). However, animals fed with FSG showed lower caecal pH (–0.15; P<0.05) values. Regarding the in vitro fermentation, FSG100 increased asymptotic gas production (+11.25, P<0.001), sharpness of the switching characteristic of the profile (+1.98, P<0.001) and the maximum substrate degradation rate (RM) (+0.188, P<0.001), but decreasing the time after incubation at which half of the asymptotic amount of gas has been formed (–5.86, P<0.001) and at which RM occurs (–4.53, P<0.01). Likewise, FSG100 significantly decreased caecal pH (–1.035, P<0.001), lactic acid (–9.51, P<0.069) and N-NH3 concentrations (–12.81, P<0.001). Meanwhile, it increased the total volatile fatty acids (VFA) production (+43.15, P<0.001). Gradual dietary inclusion of FSG from 0 to 0.5% only significantly increased total VFA production in the caecum (+100 mmol/L per percentage point of FSG inclusion; P<0.05). In conclusion, FSG is highly and rapidly in vitro fermented by rabbit caecal bacteria. However, dietary inclusion of FSG up to 0.5%, might be insufficient to affect the apparent digestibility and fermentation profile of growing rabbits to a great extent.This study is supported by the Interministerial Commission for Science and Technology (CICYT) of the Spanish Government (AGL2017-85162-C2-1R), the Universitat Politècnica de València (Project 20180290; Spain), and the Higher School of Agriculture of Mateur of the Carthage University (Tunisia Republic). Grant assistance for Jihed Zemzmi from the Carthage University is also gratefully acknowledged.Zemzmi, J.; Ródenas, L.; Blas, E.; Abdouli, H.; Najar, T.; Pascual, J. (2020). Preliminary evaluation of fenugreek (Trigonella foenum-graecum) seed gum as a potential prebiotic for growing rabbits in Tunisia: effects on in vivo faecal digestibility and in vitro fermentation. World Rabbit Science. 28(3):113-122. https://doi.org/10.4995/wrs.2020.12994OJS113122283Abad-Guamán R., Larrea-Dávalos J.A., Carabaño R., García J., Carro M.D. 2018. Influence of inoculum type (ileal, caecal and faecal) on the in vitro fermentation of different sources of carbohydrates in rabbits. World Rabbit Sci., 26: 227-240. https://doi.org/10.4995/wrs.2018.9726AOAC. 2002. Official methods of analysis of the AOAC International. 17th ed. AOAC International., Gaithersburg, MD USA.Bartley G.B., Hiltry M.D., Andreson B.D., Clairemont A.C., Maschke S.P. 1981. "Maple-syrup" urine odor due to fenugreek ingestion. New Engl. J. Med., 305: 467. https://doi.org/10.1056/NEJM198108203050823Batey I.L. 1982. Starch Analysis Using Thermostable Alpha-Amylases. 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Effect of fibre level reduction and glucooligosaccharide addition on the growth performance and caecal fermentation in the growing rabbit. Anim. Feed Sci. Technol., 56: 253-263. https://doi.org/10.1016/0377-8401(95)00834-9Gidenne T., Licois D. 2005. Effect of a high fibre intake on the resistance of the growing rabbit to an experimental inoculation with an enteropathogenic strain of Escherichia coli. Animal Sci., 80: 281-288. https://doi.org/10.1079/ASC41570281Gómez-Conde M.S., Garcia J., Chamorro S., Eirás P., Rebollar P.G., De Rozas A.P., Badiola I., De Blas C., Carabaño R. 2007. Neutral detergent-soluble fiber improves gut barrier function in twenty-five-day-old weaned rabbits. J. Ani. Sci., 85: 3313-3321. https://doi.org/10.2527/jas.2006-777Gómez-Conde M.S., Pérez de Rozas A., Badiola I., Pérez-Alba L., de Blas C., Carabaño R., García J. 2009. Effect of neutral detergent soluble fibre on digestion, intestinal microbiota and performance in twenty five day old weaned rabbits. 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Direct spectrophotometric determination of ammonia in precipitation. Tellus XVIII., 2. https://doi.org/10.3402/tellusa.v18i2-3.9343Lipinski K., Purwin C., Tywonczuk J., Zdunczyk Z., Wroblewska M., Laniewska-Trokenheim L., Warminska-Radyko L. 2005. Effects of feed additives on nutrient digestibility and the bacterial status of faeces in pigs. J. Anim. Feed Sci., 14: 369-372. https://doi.org/10.22358/jafs/70582/2005Majeed M., Majeed S., Nagabhushanam K., Arumugam S., Natarajan S., Beede K., Furqan A. 2018. Galactomannan from Trigonella foenum-graecum L. Seed: Prebiotic application and its fermentation by prebiotic Bacillus coagulans strain MTCC 5856. Food Sci. Nutr., 6: 666-673. https://doi.org/10.1002/fsn3.606Marten G.C., Barnes R.F. 1980. Prediction of energy digestibility of forages with in vitro rumen fermentation and fungal enzyme systems. In: W.J. Pigden, C.C. Balch, M. Graham (Eds.), In Proc.: The International Workshop on Standardization of Analytical Methodology for Feeds, Int. 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On the need for the use of error-controlled finite element analyses in structural shape optimization processes

This is the peer reviewed version of the following article: Ródenas, J. J., Bugeda, G., Albelda, J. and Oñate, E. (2011), On the need for the use of error-controlled finite element analyses in structural shape optimization processes. Int. J. Numer. Meth. Engng., 87: 1105–1126, which has been published in final form at http://dx.doi.org/10.1002/nme.3155. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.This work analyzes the influence of the discretization error associated with the finite element (FE) analyses of each design configuration proposed by the structural shape optimization algorithms over the behavior of the algorithm. The paper clearly shows that if FE analyses are not accurate enough, the final solution provided by the optimization algorithm will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper proposes the combination of two strategies to reduce the computational cost related to the use of mesh adaptivity in evolutionary optimization algorithms: (a) the use of an algorithm for the mesh generation by projection of the discretization error, which reduces the computational cost associated with the adaptive FE analysis of each geometrical configuration and (b) the successive increase of the required accuracy of the FE analyses in order to obtain a considerable reduction of the computational cost in the early stages of the optimization process.The second author is grateful for the financial support received for the development of this paper through the research project DPI2008-05250 of the Ministerio de Ciencia e Innovacion (Spain).Ródenas, J.; Bugeda Castelltort, G.; Albelda Vitoria, J.; Oñate Ibáñez De Navarra, E. (2011). On the need for the use of error-controlled finite element analyses in structural shape optimization processes. International Journal for Numerical Methods in Engineering. 87(11):1105-1126. https://doi.org/10.1002/nme.3155S11051126871

A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework

[EN] Today industries do not only require fast simulation techniques but also verification techniques for the simulations. The proper generalized decomposition (PGD) has been situated as a suitable tool for fast simulation for many physical phenomena. However, so far, verification tools for the PGD are under development. The PGD approximation error mainly comes from two different sources. The first one is related with the truncation of the PGD approximation and the second one is related with the discretization error of the underlying numerical technique. In this work we propose a fast error indicator technique based on recovery techniques, for the discretization error of the numerical technique used by the PGD technique, for refinement purposes.Authors 5 and 6 thank the financial support of the research Project DPI2013-46317-R of the Ministerio de Economia y Competitividad (Spain). The funding from Universitat Politecnica de Valencia and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged. These authors also thank the support of the Framework Programme 7 Initial Training Network Funding under Grant number 289361 "Integrating Numerical Simulation and Geometric Design Technology".Nadal, E.; Leygue, A.; Chinesta, F.; Beringhier, M.; Ródenas, J.; Fuenmayor Fernández, FJ. (2015). A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework. Computational Mechanics. 55(2):251-266. https://doi.org/10.1007/s00466-014-1097-yS251266552Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. 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