Contact problem modelling using the Cartesian grid Finite Element Method

Tesis por compendio[ES] La interacción de contacto entre sólidos deformables es uno de los fenómenos más complejos en el ámbito de la mecánica computacional. La resolución de este problema requiere de algoritmos robustos para el tratamiento de no linealidades geométricas. El Método de Elementos Finitos (MEF) es uno de los más utilizados para el diseño de componentes mecánicos, incluyendo la solución de problemas de contacto. En este método el coste asociado al proceso de discretización (generación de malla) está directamente vinculado a la definición del contorno a modelar, lo cual dificulta la introducción en la simulación de superficies complejas, como las superficies NURBS, cada vez más utilizadas en el diseño de componentes. Esta tesis está basada en el "Cartesian grid Finite Element Method" (cgFEM). En esta metodología, encuadrada en la categoría de métodos "Immersed Boundary", se extiende el problema a un dominio de aproximación (cuyo mallado es sencillo de generar) que contiene al dominio de análisis completamente en su interior. Al desvincular la discretización de la definición del contorno del problema se reduce drásticamente el coste de generación de malla. Es por ello que el método cgFEM es una herramienta adecuada para la resolución de problemas en los que es necesario modificar la geometría múltiples veces, como el problema de optimización de forma o la simulación de desgaste. El método cgFEM permite también crear de manera automática y eficiente modelos de Elementos Finitos a partir de imágenes médicas. La introducción de restricciones de contacto habilitaría la posibilidad de considerar los diferentes estados de integración implante-tejido en procesos de optimización personalizada de implantes. Así, en esta tesis se desarrolla una formulación para resolver problemas de contacto 3D con el método cgFEM, considerando tanto modelos de contacto sin fricción como problemas con rozamiento de Coulomb. La ausencia de nodos en el contorno en cgFEM impide la aplicación de métodos tradicionales para imponer las restricciones de contacto, por lo que se ha desarrollado una formulación estabilizada que hace uso de un campo de tensiones recuperado para asegurar la estabilidad del método. Para una mayor precisión de la solución, se ha introducido la definición analítica de las superficies en contacto en la formulación propuesta. Además, se propone la mejora de la robustez de la metodología cgFEM en dos aspectos: el control del mal condicionamiento del problema numérico mediante un método estabilizado, y la mejora del campo de tensiones recuperado, utilizado en el proceso de estimación de error. La metodología propuesta se ha validado a través de diversos ejemplos numéricos presentados en la tesis, mostrando el gran potencial de cgFEM en este tipo de problemas.[CA] La interacció de contacte entre sòlids deformables és un dels fenòmens més complexos en l'àmbit de la mecànica computacional. La resolució d'este problema requerix d'algoritmes robustos per al tractament de no linealitats geomètriques. El Mètode dels Elements Finits (MEF) és un dels més utilitzats per al disseny de components mecànics, incloent la solució de problemes de contacte. En este mètode el cost associat al procés de discretització (generació de malla) està directament vinculat a la definició del contorn a modelar, la qual cosa dificulta la introducció en la simulació de superfícies complexes, com les superfícies NURBS, cada vegada més utilitzades en el disseny de components. Esta tesi està basada en el "Cartesian grid Finite Element Method" (cgFEM). En esta metodologia, enquadrada en la categoria de mètodes "Immersed Boundary", s'estén el problema a un domini d'aproximació (el mallat del qual és senzill de generar) que conté al domini d'anàlisi completament en el seu interior. Al desvincular la discretització de la definició del contorn del problema es reduïx dràsticament el cost de generació de malla. És per això que el mètode cgFEM és una ferramenta adequada per a la resolució de problemes en què és necessari modificar la geometria múltiples vegades, com el problema d'optimització de forma o la simulació de desgast. El mètode cgFEM permet també crear de manera automàtica i eficient models d'Elements Finits a partir d'imatges mèdiques. La introducció de restriccions de contacte habilitaria la possibilitat de considerar els diferents estats d'integració implant-teixit en processos d'optimització personalitzada d'implants. Així, en esta tesi es desenvolupa una formulació per a resoldre problemes de contacte 3D amb el mètode cgFEM, considerant tant models de contacte sense fricció com a problemes amb fregament de Coulomb. L'absència de nodes en el contorn en cgFEM impedix l'aplicació de mètodes tradicionals per a imposar les restriccions de contacte, per la qual cosa s'ha desenvolupat una formulació estabilitzada que fa ús d'un camp de tensions recuperat per a assegurar l'estabilitat del mètode. Per a una millor precisió de la solució, s'ha introduït la definició analítica de les superfícies en contacte en la formulació proposada. A més, es proposa la millora de la robustesa de la metodologia cgFEM en dos aspectes: el control del mal condicionament del problema numèric per mitjà d'un mètode estabilitzat, i la millora del camp de tensions recuperat, utilitzat en el procés d'estimació d'error. La metodologia proposada s'ha validat a través de diversos exemples numèrics presentats en la tesi, mostrant el gran potencial de cgFEM en este tipus de problemes.[EN] The contact interaction between elastic solids is one of the most complex phenomena in the computational mechanics research field. The solution of such problem requires robust algorithms to treat the geometrical non-linearities characteristic of the contact constrains. The Finite Element Method (FE) has become one of the most popular options for the mechanical components design, including the solution of contact problems. In this method the computational cost of the generation of the discretization (mesh generation) is directly related to the complexity of the analysis domain, namely its boundary. This complicates the introduction in the numerical simulations of complex surfaces (for example NURBS), which are being increasingly used in the CAD industry. This thesis is grounded on the Cartesian grid Finite Element Method (cgFEM). In this methodology, which belongs to the family of Immersed Boundary methods, the problem at hand is extended to an approximation domain which completely embeds the analysis domain, and its meshing is straightforward. The decoupling of the boundary definition and the discretization mesh results in a great reduction of the mesh generation's computational cost. Is for this reason that the cgFEM is a suitable tool for the solution of problems that require multiple geometry modifications, such as shape optimization problems or wear simulations. The cgFEM is also capable of automatically generating FE models from medical images without the intermediate step of generating CAD entities. The introduction of the contact interaction would open the possibility to consider different states of the union between implant and living tissue for the design of optimized implants, even in a patient-specific process. Hence, in this thesis a formulation for solving 3D contact problems with the cgFEM is presented, considering both frictionless and Coulomb's friction problems. The absence of nodes along the boundary in cgFEM prevents the enforcement of the contact constrains using the standard procedures. Thus, we develop a stabilized formulation that makes use of a recovered stress field, which ensures the stability of the method. The analytical definition of the contact surfaces (by means of NURBS) has been included in the proposed formulation in order to increase the accuracy of the solution. In addition, the robustness of the cgFEM methodology is increased in this thesis in two different aspects: the control of the numerical problem's ill-conditioning by means of a stabilized method, and the enhancement of the stress recovered field, which is used in the error estimation procedure. The proposed methodology has been validated through several numerical examples, showing the great potential of the cgFEM in these type of problems.Navarro Jiménez, JM. (2019). Contact problem modelling using the Cartesian grid Finite Element Method [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/124348TESISCompendi

Superconvergent patch recovery with constraints for three-dimensional contact problems within the Cartesian grid Finite Element Method

"This is the peer reviewed version of the following article: Navarro-Jiménez, José M., Héctor Navarro-García, Manuel Tur, and Juan J. Ródenas. 2019. Superconvergent Patch Recovery with Constraints for Three-dimensional Contact Problems within the Cartesian Grid Finite Element Method. International Journal for Numerical Methods in Engineering 121 (6). Wiley: 1297 1313. doi:10.1002/nme.6266, which has been published in final form at https://doi.org/10.1002/nme.6266. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] The superconvergent patch recovery technique with constraints (SPR-C) consists in improving the accuracy of the recovered stresses obtained with the original SPR technique by considering known information about the exact solution, like the internal equilibrium equation, the compatibility equation or the Neumann boundary conditions, during the recovery process. In this paper the SPR-C is extended to consider the equilibrium around the contact area when solving contact problems with the Cartesian grid Finite Element Method. In the proposed method, the Finite Element stress fields of both bodies in contact are considered during the recovery process and the equilibrium is enforced by means of the continuity of tractions along the contact surface.The authors would like to thank Generalitat Valenciana (PROMETEO/2016/007), the Spanish Ministerio de Economía, Industria y Competitividad (DPI2017-89816-R), the Spanish Ministerio de Ciencia, Innovación y Universidades (FPU17/03993), and Universitat Politècnica de València (FPI2015) for the financial support to this work.Navarro-Jiménez, J.; Navarro-García, H.; Tur Valiente, M.; Ródenas, JJ. (2020). Superconvergent patch recovery with constraints for three-dimensional contact problems within the Cartesian grid Finite Element Method. International Journal for Numerical Methods in Engineering. 121(6):1297-1313. https://doi.org/10.1002/nme.6266S129713131216Wriggers, P. (2006). Computational Contact Mechanics. doi:10.1007/978-3-540-32609-0Marco, O., Sevilla, R., Zhang, Y., Ródenas, J. J., & Tur, M. (2015). Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry. International Journal for Numerical Methods in Engineering, 103(6), 445-468. doi:10.1002/nme.4914Navarro-Jiménez, J. M., Tur, M., Albelda, J., & Ródenas, J. J. (2018). Large deformation frictional contact analysis with immersed boundary method. Computational Mechanics, 62(4), 853-870. doi:10.1007/s00466-017-1533-xMarco, O., Ródenas, J. J., Navarro-Jiménez, J. M., & Tur, 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.2017.08.004Ródenas, J. J., Tur, M., Fuenmayor, F. J., & Vercher, A. (2007). Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. International Journal for Numerical Methods in Engineering, 70(6), 705-727. doi:10.1002/nme.1903Zienkiewicz, O. C., & Zhu, J. Z. (1992). The superconvergent patch recovery (SPR) and adaptive finite element refinement. Computer Methods in Applied Mechanics and Engineering, 101(1-3), 207-224. doi:10.1016/0045-7825(92)90023-dRódenas, J. J., González-Estrada, O. A., Díez, P., & Fuenmayor, F. J. (2010). Accurate recovery-based upper error bounds for the extended finite element framework. Computer Methods in Applied Mechanics and Engineering, 199(37-40), 2607-2621. doi:10.1016/j.cma.2010.04.010Blacker, T., & Belytschko, T. (1994). Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. International Journal for Numerical Methods in Engineering, 37(3), 517-536. doi:10.1002/nme.1620370309Díez, P., José Ródenas, J., & Zienkiewicz, O. C. (2007). Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error. International Journal for Numerical Methods in Engineering, 69(10), 2075-2098. doi:10.1002/nme.1837Nadal, E., Díez, P., Ródenas, J. J., Tur, M., & Fuenmayor, F. J. (2015). A recovery-explicit error estimator in energy norm for linear elasticity. Computer Methods in Applied Mechanics and Engineering, 287, 172-190. doi:10.1016/j.cma.2015.01.013Badia, S., Verdugo, F., & Martín, A. F. (2018). The aggregated unfitted finite element method for elliptic problems. Computer Methods in Applied Mechanics and Engineering, 336, 533-553. doi:10.1016/j.cma.2018.03.022Zienkiewicz, O. C., Zhu, J. Z., & Wu, J. (1993). Superconvergent patch recovery techniques - some further tests. Communications in Numerical Methods in Engineering, 9(3), 251-258. doi:10.1002/cnm.1640090309FUENMAYOR, F. J., & OLIVER, J. L. (1996). CRITERIA TO ACHIEVE NEARLY OPTIMAL MESHES IN THEh-ADAPTIVE FINITE ELEMENT METHOD. International Journal for Numerical Methods in Engineering, 39(23), 4039-4061. doi:10.1002/(sici)1097-0207(19961215)39:233.0.co;2-cBabuška, I., Strouboulis, T., & Upadhyay, C. . (1994). A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles. Computer Methods in Applied Mechanics and Engineering, 114(3-4), 307-378. doi:10.1016/0045-7825(94)90177-

Real-time motor rotation frequency detection with event-based visual and spike-based auditory AER sensory integration for FPGA

Multisensory integration is commonly used in various robotic areas to collect more environmental information using different and complementary types of sensors. Neuromorphic engineers mimics biological systems behavior to improve systems performance in solving engineering problems with low power consumption. This work presents a neuromorphic sensory integration scenario for measuring the rotation frequency of a motor using an AER DVS128 retina chip (Dynamic Vision Sensor) and a stereo auditory system on a FPGA completely event-based. Both of them transmit information with Address-Event-Representation (AER). This integration system uses a new AER monitor hardware interface, based on a Spartan-6 FPGA that allows two operational modes: real-time (up to 5 Mevps through USB2.0) and data logger mode (up to 20Mevps for 33.5Mev stored in onboard DDR RAM). The sensory integration allows reducing prediction error of the rotation speed of the motor since audio processing offers a concrete range of rpm, while DVS can be much more accurate.Ministerio de Economía y Competitividad TEC2012-37868-C04-02/0

Live Demonstration: Real-time motor rotation frequency detection by spike-based visual and auditory AER sensory integration for FPGA

Multisensory integration is commonly used in various robotic areas to collect much more information from an environment using different and complementary types of sensors. This demonstration presents a scenario where the motor rotation frequency is obtained using an AER DVS128 retina chip (Dynamic Vision Sensor) and a frequency decomposer auditory system on a FPGA that mimics a biological cochlea. Both of them are spike-based sensors with Address-Event-Representation (AER) outputs. A new AER monitor hardware interface, based on a Spartan-6 FPGA, allows two operational modes: real-time (up to 5 Mevps through USB2.0) and off-line mode (up to 20Mevps and 33.5Mev stored in DDR RAM). The sensory integration allows the bio-inspired cochlea limit to provide a concrete range of rpm approaches, which are obtained by the silicon retina.Ministerio de Economía y Competitividad TEC2012-37868-C04-02/0

Funcionamiento de una escala de intensidad de apoyos en niños y adolescentes con Tea en edad escolar

[ES] Los constructos de apoyo y necesidades de apoyo han constituido uno de los ejes de desarrollo en investigación y aplicación de acciones destinadas a mejorar la calidad de vida de las personas con discapacidad intelectual o del desarrollo. La evaluación de las necesidades de apoyo y de la intensidad de estos apoyos resulta una estrategia crucial tanto en personas adultas con discapacidad intelectual, como en escolares. En la investigación que se presenta, se exponen los resultados de una evaluación de las necesidades de apoyo y su intensidad, en escolares con Trastorno del Espectro del Autismo (TEA) del territorio español. Se comparan los resultados en intensidad de necesidad de apoyo con otros grupos con discapacidad intelectual, pero sin TEA, además de presentar unos primeros análisis de las necesidades de apoyo de escolares con TEA de alto funcionamiento o sin discapacidad intelectual. ´ El método utilizado ha sido la administración de una escala de intensidad de apoyos (SIS-C) en su primera adaptación al contexto español. La escala cuenta con dos secciones: (1) necesidades excepcionales de apoyo (médicas y conductuales) y (2) escala de necesidades de apoyo en actividades representativas, agrupadas en siete factores, vida en el hogar, vida en la comunidad, participación escolar, aprendizaje escolar, salud y seguridad, actividades sociales y defensa o autorrepresentación. Se evalúa la intensidad de apoyo a través de tres parámetros: tipo de apoyo, frecuencia de apoyo y tiempo de apoyo diario. Hemos evaluado 249 escolares con TEA y discapacidad intelectual, así como en 44 niños y adolescentes con TEA sin discapacidad intelectual de entre 5 a 16 años edad. Se han comparado los valores medios obtenidos con una muestra de 565 niños y adolescentes con discapacidad intelectual sin TEA de España. Las medias obtenidas han mostrado diferencias significativas en intensidad de de apoyo, entre los niños y adolescentes con discapacidad intelectual sin TEA y con TEA; y también cuando se contrastan los valores de los grupos de edad: 5-10 años y 11-16 años. En todas las actividades representativas de la escala, la muestra con TEA presenta necesidades de apoyo más intensas. La muestra con TEA sin discapacidad intelectual ha presentado necesidades de apoyo en diversas áreas de apoyo, especialmente en actividades sociales, defensa (autorrepresentación) y aprendizaje escolar. Algunas conclusiones presentadas en la tesis van en la línea de explicitar que, la escala SIS-C es un instrumento útil para evaluar las necesidades de apoyo en actividades de la vida diaria en escolares con TEA y discapacidad intelectual. Los datos sugieren que la intensidad de necesidades de apoyo de los escolares con TEA es mayor que la mostrada por otros escolares con discapacidad intelectual y que no presentan TEA. Existen actividades en las que la intensidad de apoyo es significativamente diferente para el grupo con TEA, lo que puede resultar de interés para los procesos de: (1) reflexión y planificación de apoyos individuales, (2) organización de recursos y servicios y (3) para el desarrollo de estrategias de la administración educativa

Optimization of a finite element code implemented in MATLAB. On the use of GPUs for High Performance Computing

[EN] The Department of Mechanical and Materials Engineering has developed a 2D Finite Element code based on geometry independent Cartesian grids (cgFEM) capable of solving shape optimization problems as well as making patient-specific analyses using medical images. A similar code in 3D (FEAVox) is currently under development. Both codes are implemented in MATLAB, a simple and intuitive programming language but with a higher computational cost than compiled languages such as C++ or FORTRAN. The objective of this Thesis is to develop programming procedures to improve the performance of the existing and the currently under development software. Among other optimization techniques this Thesis will focus on the use of Graphics Processing Units (GPU) for high performance computing. The use of these techniques has led to a software that, despite being implemented with MATLAB, improves the computational efficiency of commercial software which is developed using compiled programming languages.[ES] El Departamento de Ingeniería Mecánica y de Materiales ha desarrollado un código de Elementos Finitos 2D basado en mallados Cartesianos independientes de la geometría (cgFEM) capaz de resolver problemas de optimización topológica y de realizar análisis específicos de paciente a partir de imágenes médicas. Se está desarrollando actualmente un código similar 3D (FEAVox). Ambos códigos están implementados en MATLAB, un lenguaje de programación sencillo e intuitivo pero menos eficiente computacionalmente que otros lenguajes compilados como C++ o FORTRAN. El objetivo de este Trabajo Fin de Máster es desarrollar procedimientos de programación que permitan aumentar el rendimiento computacional del software que ha sido o está siendo desarrollado en el Departamento. De entre las técnicas de optimización disponibles, se hará hincapié en el uso de tarjetas gráficas (GPU) como medio de computación de alto rendimiento. La utilización de estas técnicas ha permitido obtener un software de EF que, pese a estar implementado en MATLAB, mejora el rendimiento computacional de software comercial desarrollado con lenguajes de programación compilados[CA] El Departament d'Enginyeria Mecànica i de Materials ha desenvolupat un codi d'Elements Finits 2D basat en mallats Cartesians independents de la geometria (cgFEM) capaç de resoldre problemes d'optimització topològica i de realitzar anàlisis específics de pacient a partir d'imatges mèdiques. Actualment s'està treballant en un codi similar 3D (FEAVox). Ambdós codis estan implementats en MATLAB, un llenguatge de programació senzill i intuitiu però menys eficient computacionalment que altres llenguatges compil·lats com C++ o FORTRAN. Aquest Treball Fi de Màster té com a objectiu desenvolupar procediments de programació que permeten millorar el rendiment computacional del software que ha sigut o està sent desenvolupat al Departament. De les tècniques d'optimització disponibles, aquest Treball es centrarà en l'utilització de targetes gràfiques (GPU) com a mitjà de computació d'alt rendiment. L'ús d'aquestes tècniques ha permés obtindre un software d'EF que, a pesar d'estar implementat en MATLAB, millora el rendiment computacional del software comercial elaborat amb llenguatges de programació compil·lats.Navarro Jiménez, JM. (2014). Optimization of a finite element code implemented in MATLAB. On the use of GPUs for High Performance Computing. http://hdl.handle.net/10251/53393Archivo delegad

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

Large deformation frictional contact analysis with immersed boundary method

[EN] This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method.The authors wish to thank the Spanish Ministerio de Economia y Competitividad the Generalitat Valenciana and the Universitat Politecnica de Valencia for their financial support received through the projects DPI2013-46317-R, Prometeo 2016/007 and the FPI2015 program.Navarro-Jiménez, J.; Tur Valiente, M.; Albelda Vitoria, J.; Ródenas, JJ. (2018). Large deformation frictional contact analysis with immersed boundary method. Computational Mechanics. 62(4):853-870. https://doi.org/10.1007/s00466-017-1533-xS853870624ANSYS$$^{\textregistered }$$® Academic Research Mechanical, Release 16.2Alart P, Curnier A (1991) A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput Methods Appl Mech Eng 92(3):353–375. https://doi.org/10.1016/0045-7825(91)90022-XAnnavarapu C, Hautefeuille M, Dolbow JE (2012) Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods. Int J Numer Methods Eng 92(June):206–228. https://doi.org/10.1002/nme.4343Annavarapu C, Hautefeuille M, Dolbow JE (2014) A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: single interface. Comput Methods Appl Mech Eng 268:417–436. https://doi.org/10.1016/j.cma.2013.09.002Annavarapu C, Settgast RR, Johnson SM, Fu P, Herbold EB (2015) A weighted nitsche stabilized method for small-sliding contact on frictional surfaces. Comput Methods Appl Mech Eng 283:763–781. https://doi.org/10.1016/j.cma.2014.09.030Baiges J, Codina R, Henke F, Shahmiri S, Wall WA (2012) A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes. Int J Numer Methods Eng 90(5):636–658. https://doi.org/10.1002/nme.3339Béchet É, Moës N, Wohlmuth B (2009) A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. Int J Numer Methods Eng 78(8):931–954. https://doi.org/10.1002/nme.2515Béchet E, Moës N, Wohlmuth B (2009) A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. Int J Numer Methods Eng 78:931–954. https://doi.org/10.1002/nme.2515Belgacem F, Hild P, Laborde P (1998) The mortar finite element method for contact problems. Math Comput Model 28(4–8):263–271. https://doi.org/10.1016/S0895-7177(98)00121-6De Lorenzis L, Wriggers P, Zavarise G (2012) A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method. Comput Mech 49(1):1–20. https://doi.org/10.1007/s00466-011-0623-4Dittmann M, Franke M, Temizer I, Hesch C (2014) Isogeometric Analysis and thermomechanical Mortar contact problems. Comput Methods Appl Mech Eng 274:192–212. https://doi.org/10.1016/j.cma.2014.02.012Dolbow J, Moës N, Belytschko T (2001) An extended finite element method for modeling crack growth with frictional contact. Comput Methods Appl Mech Eng 190:6825–6846. https://doi.org/10.1016/S0045-7825(01)00260-2Dolbow JE, Devan a (2004) Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test. Int J Numer Methods Eng 59(1):47–67. https://doi.org/10.1002/nme.862Fischer KA, Wriggers P (2006) Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Comput Methods Appl Mech Eng 195(37–40):5020–5036. https://doi.org/10.1016/j.cma.2005.09.025Giovannelli L, Ródenas J, Navarro-Jiménez J, Tur M (2017) Direct medical image-based Finite Element modelling for patient-specific simulation of future implants. Finite Elem Anal Des. https://doi.org/10.1016/j.finel.2017.07.010Gitterle M, Popp A, Gee MW, Wall WA (2010) Finite deformation frictional mortar contact using a semi-smooth Newton method with consistent linearization. Int J Numer Methods Eng. https://doi.org/10.1002/nme.2907Hammer ME (2013) Frictional mortar contact for finite deformation problems with synthetic contact kinematics. Comput Mech 51(6):975–998. https://doi.org/10.1007/s00466-012-0780-0Hansbo P, Rashid A, Salomonsson K (2015) Least-squares stabilized augmented Lagrangian multiplier method for elastic contact. Finite Elem Anal Des 116:32–37. https://doi.org/10.1016/j.finel.2016.03.005Haslinger J, Renard Y (2009) A new fictitious domain approach inspired by the extended finite element method. SIAM J Numer Anal 47(2):1474–1499. https://doi.org/10.1137/070704435Hautefeuille M, Annavarapu C, Dolbow JE (2012) Robust imposition of Dirichlet boundary conditions on embedded surfaces. Int J Numer Methods Eng 90:40–64. https://doi.org/10.1002/nme.3306Heintz P, Hansbo P (2006) Stabilized Lagrange multiplier methods for bilateral elastic contact with friction. Comput Methods Appl Mech Eng 195(33–36):4323–4333. https://doi.org/10.1016/j.cma.2005.09.008Hughes T, Cottrell J, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39–41):4135–4195. https://doi.org/10.1016/j.cma.2004.10.008Laursen T (2003) Computational contact and impact mechanics: fundamentals of modelling interfacial phenomena in nonlinear finite element analysis. Springer, BerlinLiu F, Borja RI (2008) A contact algorithm for frictional crack propagation with the extended finite element method. Int J Numer Methods Eng 76(June):1489–1512. https://doi.org/10.1002/nme.2376Liu F, Borja RI (2010) Stabilized low-order finite elements for frictional contact with the extended finite element method. Comput Methods Appl Mech Eng 199(37–40):2456–2471. https://doi.org/10.1016/j.cma.2010.03.030Marco O, Sevilla R, Zhang Y, Ródenas JJ, Tur M (2015) Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry. Int J Numer Methods Eng 103(6):445–468. https://doi.org/10.1002/nme.4914Nadal E, Ródenas JJ, Albelda J, Tur M, Tarancón JE, Fuenmayor FJ (2013) Efficient finite element methodology based on cartesian grids: application to structural shape optimization. Abstr Appl Anal 2013:1–19. https://doi.org/10.1155/2013/953786Neto D, Oliveira M, Menezes L, Alves J (2016) A contact smoothing method for arbitrary surface meshes using nagata patches. Comput Methods Appl Mech Eng 299:283–315. https://doi.org/10.1016/j.cma.2015.11.011Nistor I, Guiton MLE, Massin P, Moës N, Géniaut S (2009) An X-FEM approach for large sliding contact along discontinuities. Int J Numer Methods Eng 78:1407–1435. https://doi.org/10.1002/nme.2532Oliver J, Hartmann S, Cante JC, Weyler R, Hernández JA (2009) A contact domain method for large deformation frictional contact problems. Part 1: theoretical basis. Comput Methods Appl Mech Eng 198:2591–2606. https://doi.org/10.1016/j.cma.2009.03.006Piegl L, Tiller W (1995) The NURBS Book. Springer, BerlinPietrzak G, Curnier A (1999) Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment. Comput Methods Appl Mech Eng 177(3–4):351–381. https://doi.org/10.1016/S0045-7825(98)00388-0Poulios K, Renard Y (2015) An unconstrained integral approximation of large sliding frictional contact between deformable solids. Comput Struct 153:75–90. https://doi.org/10.1016/j.compstruc.2015.02.027Puso MA, Laursen TA (2004) A mortar segment-to-segment frictional contact method for large deformations. Comput Methods Appl Mech Eng 193(45–47):4891–4913. https://doi.org/10.1016/j.cma.2004.06.001Renard Y (2013) Generalized Newton’s methods for the approximation and resolution of frictional contact problems in elasticity. Comput Methods Appl Mech Eng 256:38–55. https://doi.org/10.1016/j.cma.2012.12.008Ribeaucourt R, Baietto-Dubourg MC, Gravouil A (2007) A new fatigue frictional contact crack propagation model with the coupled X-FEM/LATIN method. Comput Methods Appl Mech Eng 196:3230–3247. https://doi.org/10.1016/j.cma.2007.03.004Ródenas JJ, Tur M, Fuenmayor FJ, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint equations: The SPR-C technique. Int J Numer Methods Eng 70:705–727. https://doi.org/10.1002/nme.1903Rogers DF (2001) An introduction to NURBS: with historical perspective. Elsevier, AmsterdamTemizer I, Wriggers P, Hughes TJR (2012) Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 209–212:115–128. https://doi.org/10.1016/j.cma.2011.10.014Tur M, Albelda J, Marco O, Ródenas JJ (2015) Stabilized method of imposing Dirichlet boundary conditions using a recovered stress field. Comput Methods Appl Mech Eng 296:352–375. https://doi.org/10.1016/j.cma.2015.08.001Tur M, Albelda J, Navarro-Jimenez JM, Rodenas JJ (2015) A modified perturbed Lagrangian formulation for contact problems. Comput Mech. https://doi.org/10.1007/s00466-015-1133-6Tur M, Fuenmayor FJ, Wriggers P (2009) A mortar-based frictional contact formulation for large deformations using Lagrange multipliers. Comput Methods Appl Mech Eng 198(37–40):2860–2873. https://doi.org/10.1016/j.cma.2009.04.007Tur M, Giner E, Fuenmayor F, Wriggers P (2012) 2d contact smooth formulation based on the mortar method. Comput Methods Appl Mech Eng 247–248:1–14. https://doi.org/10.1016/j.cma.2012.08.002Wriggers P (2006) Computational contact mechanics. Springer, BerlinWriggers P (2008) Nonlinear finite element methods. Springer, Berlin. https://doi.org/10.1007/978-3-540-71001-1Yang B, Laursen TA, Meng X (2005) Two dimensional mortar contact methods for large deformation frictional sliding. Int J Numer Methods Eng 62(9):1183–1225. https://doi.org/10.1002/nme.1222Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. Int J Numer Methods. https://doi.org/10.1002/nme.162033070