Articles de revista
http://hdl.handle.net/2117/6145
2016-05-05T22:23:32ZFast r-adaptivity for multiple queries of heterogeneous stochastic material fields
http://hdl.handle.net/2117/86637
Fast r-adaptivity for multiple queries of heterogeneous stochastic material fields
Cottereau, Régis; Díez, Pedro
We present an r-adaptivity approach for boundary value problems with randomly fluctuating material parameters solved through the Monte Carlo or stochastic collocation methods. This approach tailors a specific mesh for each sample of the problem. It only requires the computation of the solution of a single deterministic problem with the same geometry and the average parameter, whose numerical cost becomes marginal for large number of samples. Starting from the mesh used to solve that deterministic problem, the nodes are moved depending on the particular sample of mechanical parameter field. The reduction in the error is small for each sample but sums up to reduce the overall bias on the statistics estimated through the Monte Carlo scheme. Several numerical examples in 2D are presented.
2016-05-05T12:08:08ZCottereau, RégisDíez, PedroWe present an r-adaptivity approach for boundary value problems with randomly fluctuating material parameters solved through the Monte Carlo or stochastic collocation methods. This approach tailors a specific mesh for each sample of the problem. It only requires the computation of the solution of a single deterministic problem with the same geometry and the average parameter, whose numerical cost becomes marginal for large number of samples. Starting from the mesh used to solve that deterministic problem, the nodes are moved depending on the particular sample of mechanical parameter field. The reduction in the error is small for each sample but sums up to reduce the overall bias on the statistics estimated through the Monte Carlo scheme. Several numerical examples in 2D are presented.AAR-based decomposition method for lower-bound limit analysis
http://hdl.handle.net/2117/86620
AAR-based decomposition method for lower-bound limit analysis
Muñoz Romero, José; Rabiei, Syednima
Despite the recent progress in optimisation techniques, finite-element stability analysis of realistic three-dimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive de-remeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but non-linear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other well-known decomposition algorithms.
2016-05-05T08:50:31ZMuñoz Romero, JoséRabiei, SyednimaDespite the recent progress in optimisation techniques, finite-element stability analysis of realistic three-dimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive de-remeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but non-linear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other well-known decomposition algorithms.Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators
http://hdl.handle.net/2117/86474
Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators
Abdollahi Hosnijeh, Amir; Arias Vicente, Irene
Flexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and symmetry. Flexoelectricity is generally perceived as a small effect noticeable only at the nanoscale. Since ferroelectric ceramics have a particularly high flexoelectric coefficient, however, it may play a significant role as piezoelectric transducers shrink to the submicrometer scale. We examine this issue with a continuum model self-consistently treating piezo- and flexoelectricity. We show that in piezoelectric device configurations that induce strain gradients and at small but technologically relevant scales, the electromechanical coupling may be dominated by flexoelectricity. More importantly, depending on the device design flexoelectricity may enhance or reduce the effective piezoelectric effect. Focusing on bimorph configurations, we show that configurations that are equivalent at large scales exhibit dramatically different behavior for thicknesses below 100¿nm for typical piezoelectric materials. Our results suggest flexoelectric-aware designs for small-scale piezoelectric bimorph transducers.
2016-05-02T12:12:55ZAbdollahi Hosnijeh, AmirArias Vicente, IreneFlexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and symmetry. Flexoelectricity is generally perceived as a small effect noticeable only at the nanoscale. Since ferroelectric ceramics have a particularly high flexoelectric coefficient, however, it may play a significant role as piezoelectric transducers shrink to the submicrometer scale. We examine this issue with a continuum model self-consistently treating piezo- and flexoelectricity. We show that in piezoelectric device configurations that induce strain gradients and at small but technologically relevant scales, the electromechanical coupling may be dominated by flexoelectricity. More importantly, depending on the device design flexoelectricity may enhance or reduce the effective piezoelectric effect. Focusing on bimorph configurations, we show that configurations that are equivalent at large scales exhibit dramatically different behavior for thicknesses below 100¿nm for typical piezoelectric materials. Our results suggest flexoelectric-aware designs for small-scale piezoelectric bimorph transducers.Cell-centred model for the simulation of curved cellular monolayers
http://hdl.handle.net/2117/86189
Cell-centred model for the simulation of curved cellular monolayers
Mosafa, Payman; Asadipour, Nina; Millán, Raúl Daniel; Rodríguez Ferran, Antonio; Muñoz Romero, José
This paper presents a cell-centred model for the simulation of planar and curved multicellular soft tissues. We propose a computational model that includes stress relaxation due to cell reorganisation (intercellular connectivity changes) and cytoskeleton remodelling (intracellular changes). Cells are represented by their cell centres, and their mechanical interaction is modelled through active non-linear elastic laws with a dynamically changing resting length. Special attention is paid to the handling of connectivity changes between cells, and the relaxation that the tissues exhibit under these topological changes. Cell--cell connectivity is computed by resorting to a Delaunay triangulation, which is combined with a mapping technique in order to obtain triangulations on curved manifolds. Our numerical results show that even a linear elastic cell--cell interaction model may induce a global non-linear response due to the reorganisation of the cell connectivity. This plastic-like behaviour is combined with a non-linear rheological law where the resting length depends on the elastic strain, mimicking the global visco-elastic response of tissues. The model is applied to simulate the elongation of planar and curved monolayers.
2016-04-26T10:28:30ZMosafa, PaymanAsadipour, NinaMillán, Raúl DanielRodríguez Ferran, AntonioMuñoz Romero, JoséThis paper presents a cell-centred model for the simulation of planar and curved multicellular soft tissues. We propose a computational model that includes stress relaxation due to cell reorganisation (intercellular connectivity changes) and cytoskeleton remodelling (intracellular changes). Cells are represented by their cell centres, and their mechanical interaction is modelled through active non-linear elastic laws with a dynamically changing resting length. Special attention is paid to the handling of connectivity changes between cells, and the relaxation that the tissues exhibit under these topological changes. Cell--cell connectivity is computed by resorting to a Delaunay triangulation, which is combined with a mapping technique in order to obtain triangulations on curved manifolds. Our numerical results show that even a linear elastic cell--cell interaction model may induce a global non-linear response due to the reorganisation of the cell connectivity. This plastic-like behaviour is combined with a non-linear rheological law where the resting length depends on the elastic strain, mimicking the global visco-elastic response of tissues. The model is applied to simulate the elongation of planar and curved monolayers.Size-preserving size functions and smoothing procedures for adaptive quadrilateral mesh generation
http://hdl.handle.net/2117/85220
Size-preserving size functions and smoothing procedures for adaptive quadrilateral mesh generation
Ruiz-Gironés, Eloi; Roca Navarro, Xevi; Sarrate Ramos, Josep
The generation of meshes that correctly reproduce a prescribed size function is crucial for quadrilateral meshing due to two reasons. First, quadrilateral meshes are difficult to adapt to a given size field by refining or coarsening the elements without compromising the element quality. Second, after the meshing algorithm is finished, it may be necessary to apply a smoothing algorithm to improve the global quality. This smoothing step may modify the element size and the final mesh will not reproduce the prescribed element size. To solve these issues, we propose to combine the size-preserving method with a smoothing technique that takes into account both the element shape and size. The size-preserving technique allows directly generating a quadrilateral mesh that reproduces the size function, while the proposed smoother allows obtaining a high-quality mesh while maintaining the element size. In adaptive processes, the proposed approach may reduce the number of iterations to achieve convergence, since at each iteration the background mesh is properly reproduced. In addition, we detail new theoretical results that provide more insight to size-preserving size functions. Specifically, we prove that the maximum gradient of a one-dimensional size-preserving size function is bounded. Finally, several applications that show the benefits of applying the proposed techniques are presented.
2016-04-05T14:58:27ZRuiz-Gironés, EloiRoca Navarro, XeviSarrate Ramos, JosepThe generation of meshes that correctly reproduce a prescribed size function is crucial for quadrilateral meshing due to two reasons. First, quadrilateral meshes are difficult to adapt to a given size field by refining or coarsening the elements without compromising the element quality. Second, after the meshing algorithm is finished, it may be necessary to apply a smoothing algorithm to improve the global quality. This smoothing step may modify the element size and the final mesh will not reproduce the prescribed element size. To solve these issues, we propose to combine the size-preserving method with a smoothing technique that takes into account both the element shape and size. The size-preserving technique allows directly generating a quadrilateral mesh that reproduces the size function, while the proposed smoother allows obtaining a high-quality mesh while maintaining the element size. In adaptive processes, the proposed approach may reduce the number of iterations to achieve convergence, since at each iteration the background mesh is properly reproduced. In addition, we detail new theoretical results that provide more insight to size-preserving size functions. Specifically, we prove that the maximum gradient of a one-dimensional size-preserving size function is bounded. Finally, several applications that show the benefits of applying the proposed techniques are presented.Mapping forces and kinematics during collective cell migration
http://hdl.handle.net/2117/84622
Mapping forces and kinematics during collective cell migration
Serra-Picamal, Xavier; Conte, Vito; Sunyer, Raimon; Muñoz Romero, José; Trepat, Xavier
Fundamental biological processes including morphogenesis and tissue repair require cells to migrate collectively. In these processes, epithelial or endothelial cells move in a cooperative manner coupled by intercellular junctions. Ultimately, the movement of these multicellular systems occurs through the generation of cellular forces, exerted either on the substrate via focal adhesions (cell–substrate forces) or on neighboring cells through cell–cell junctions (cell–cell forces). Quantitative measurements of multicellular forces and kinematics with cellular or subcellular resolution have become possible only in recent years. In this chapter, we describe some of these techniques, which include particle image velocimetry to map cell velocities, traction force microscopy to map forces exerted by cells on the substrate, and monolayer stress microscopy to map forces within and between cells. We also describe experimental protocols to perform these measurements. The combination of these techniques with high-resolution imaging tools and molecular perturbations will lead to a better understanding of the mechanisms underlying collective cell migration in health and disease.
2016-03-17T13:29:47ZSerra-Picamal, XavierConte, VitoSunyer, RaimonMuñoz Romero, JoséTrepat, XavierFundamental biological processes including morphogenesis and tissue repair require cells to migrate collectively. In these processes, epithelial or endothelial cells move in a cooperative manner coupled by intercellular junctions. Ultimately, the movement of these multicellular systems occurs through the generation of cellular forces, exerted either on the substrate via focal adhesions (cell–substrate forces) or on neighboring cells through cell–cell junctions (cell–cell forces). Quantitative measurements of multicellular forces and kinematics with cellular or subcellular resolution have become possible only in recent years. In this chapter, we describe some of these techniques, which include particle image velocimetry to map cell velocities, traction force microscopy to map forces exerted by cells on the substrate, and monolayer stress microscopy to map forces within and between cells. We also describe experimental protocols to perform these measurements. The combination of these techniques with high-resolution imaging tools and molecular perturbations will lead to a better understanding of the mechanisms underlying collective cell migration in health and disease.High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation
http://hdl.handle.net/2117/84601
High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation
Ruiz-Gironés, Eloi; Roca Navarro, Xevi; Sarrate Ramos, Josep
We propose a 3D mesh curving method that converts a straight-sided mesh to an optimal-quality curved high-order mesh that interpolates a CAD boundary representation. The main application of this method is the generation of discrete approximations of curved domains that are valid for simulation analysis with unstructured high-order methods. We devise the method as follows. First, the boundary of a straight-sided high-order mesh is curved to match the curves and surfaces of a CAD model. Second, the method minimizes the volume mesh distortion with respect to the coordinates of the inner nodes and the parametric coordinates of the curve and surface nodes. The proposed minimization features untangling capabilities and therefore, it repairs the invalid elements that may arise from the initial curving step. Compared with other mesh curving methods, the only goal of the proposed residual system is to minimize the volume mesh distortion. Furthermore, it is less constrained since the boundary nodes are free to slide on the CAD curves and surfaces. Hence, the proposed method is well suited to generate curved high-order meshes of optimal quality from CAD models that contain thin parts or high-curvature entities. To illustrate these capabilities, we generate several curved high-order meshes from CAD models with the implementation detailed in this work. Specifically, we detail a node-by-node non-linear iterative solver that minimizes the proposed objective function in a block Gauss-Seidel manner.
2016-03-17T11:04:42ZRuiz-Gironés, EloiRoca Navarro, XeviSarrate Ramos, JosepWe propose a 3D mesh curving method that converts a straight-sided mesh to an optimal-quality curved high-order mesh that interpolates a CAD boundary representation. The main application of this method is the generation of discrete approximations of curved domains that are valid for simulation analysis with unstructured high-order methods. We devise the method as follows. First, the boundary of a straight-sided high-order mesh is curved to match the curves and surfaces of a CAD model. Second, the method minimizes the volume mesh distortion with respect to the coordinates of the inner nodes and the parametric coordinates of the curve and surface nodes. The proposed minimization features untangling capabilities and therefore, it repairs the invalid elements that may arise from the initial curving step. Compared with other mesh curving methods, the only goal of the proposed residual system is to minimize the volume mesh distortion. Furthermore, it is less constrained since the boundary nodes are free to slide on the CAD curves and surfaces. Hence, the proposed method is well suited to generate curved high-order meshes of optimal quality from CAD models that contain thin parts or high-curvature entities. To illustrate these capabilities, we generate several curved high-order meshes from CAD models with the implementation detailed in this work. Specifically, we detail a node-by-node non-linear iterative solver that minimizes the proposed objective function in a block Gauss-Seidel manner.The receding front method applied to hexahedral mesh generation of exterior domains
http://hdl.handle.net/2117/84598
The receding front method applied to hexahedral mesh generation of exterior domains
Ruiz-Gironés, Eloi; Roca Navarro, Francisco Javier; Sarrate Ramos, Josep
Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.; Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.
2016-03-17T10:50:31ZRuiz-Gironés, EloiRoca Navarro, Francisco JavierSarrate Ramos, JosepTwo of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.
Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.Cell-based maximum entropy approximants
http://hdl.handle.net/2117/84277
Cell-based maximum entropy approximants
Millán, Raúl Daniel; Sukumar, N; Arroyo Balaguer, Marino
In this paper, we devise cell-based maximum-entropy (max-ent) basis functions that are used in a Galerkin method for the solution of partial differential equations. The motivation behind this work is the construction of smooth approximants with controllable support on unstructured meshes. In the variational scheme to obtain max-ent basis functions, the nodal prior weight function is constructed from an approximate distance function to a polygonal curve in R2. More precisely, we take powers of the composition of R-functions via Boolean operations. The basis functions so constructed are nonnegative, smooth, linearly complete, and compactly-supported in a neighbor-ring of segments that enclose each node. The smoothness is controlled by two positive integer parameters: the normalization order of the approximation of the distance function and the power to which it is raised. The properties and mathematical foundations of the new compactly-supported approximants are described, and its use to solve two-dimensional elliptic boundary-value problems (Poisson equation and linear elasticity) is demonstrated. The sound accuracy and the optimal rates of convergence of the method in Sobolev norms are established.
2016-03-14T09:26:39ZMillán, Raúl DanielSukumar, NArroyo Balaguer, MarinoIn this paper, we devise cell-based maximum-entropy (max-ent) basis functions that are used in a Galerkin method for the solution of partial differential equations. The motivation behind this work is the construction of smooth approximants with controllable support on unstructured meshes. In the variational scheme to obtain max-ent basis functions, the nodal prior weight function is constructed from an approximate distance function to a polygonal curve in R2. More precisely, we take powers of the composition of R-functions via Boolean operations. The basis functions so constructed are nonnegative, smooth, linearly complete, and compactly-supported in a neighbor-ring of segments that enclose each node. The smoothness is controlled by two positive integer parameters: the normalization order of the approximation of the distance function and the power to which it is raised. The properties and mathematical foundations of the new compactly-supported approximants are described, and its use to solve two-dimensional elliptic boundary-value problems (Poisson equation and linear elasticity) is demonstrated. The sound accuracy and the optimal rates of convergence of the method in Sobolev norms are established.An efficient and general approach for implementing thermodynamic phase equilibria information in geophysical and geodynamic studies
http://hdl.handle.net/2117/84276
An efficient and general approach for implementing thermodynamic phase equilibria information in geophysical and geodynamic studies
Afonso, Juan Carlos; Zlotnik, Sergio; Díez, Pedro
We present a flexible, general, and efficient approach for implementing thermodynamic phase equilibria information (in the form of sets of physical parameters) into geophysical and geodynamic studies. The approach is based on Tensor Rank Decomposition methods, which transform the original multidimensional discrete information into a separated representation that contains significantly fewer terms, thus drastically reducing the amount of information to be stored in memory during a numerical simulation or geophysical inversion. Accordingly, the amount and resolution of the thermodynamic information that can be used in a simulation or inversion increases substantially. In addition, the method is independent of the actual software used to obtain the primary thermodynamic information, and therefore, it can be used in conjunction with any thermodynamic modeling program and/or database. Also, the errors associated with the decomposition procedure are readily controlled by the user, depending on her/his actual needs (e.g., preliminary runs versus full resolution runs). We illustrate the benefits, generality, and applicability of our approach with several examples of practical interest for both geodynamic modeling and geophysical inversion/modeling. Our results demonstrate that the proposed method is a competitive and attractive candidate for implementing thermodynamic constraints into a broad range of geophysical and geodynamic studies. MATLAB implementations of the method and examples are provided as supporting information and can be downloaded from the journal's website.
2016-03-14T09:21:16ZAfonso, Juan CarlosZlotnik, SergioDíez, PedroWe present a flexible, general, and efficient approach for implementing thermodynamic phase equilibria information (in the form of sets of physical parameters) into geophysical and geodynamic studies. The approach is based on Tensor Rank Decomposition methods, which transform the original multidimensional discrete information into a separated representation that contains significantly fewer terms, thus drastically reducing the amount of information to be stored in memory during a numerical simulation or geophysical inversion. Accordingly, the amount and resolution of the thermodynamic information that can be used in a simulation or inversion increases substantially. In addition, the method is independent of the actual software used to obtain the primary thermodynamic information, and therefore, it can be used in conjunction with any thermodynamic modeling program and/or database. Also, the errors associated with the decomposition procedure are readily controlled by the user, depending on her/his actual needs (e.g., preliminary runs versus full resolution runs). We illustrate the benefits, generality, and applicability of our approach with several examples of practical interest for both geodynamic modeling and geophysical inversion/modeling. Our results demonstrate that the proposed method is a competitive and attractive candidate for implementing thermodynamic constraints into a broad range of geophysical and geodynamic studies. MATLAB implementations of the method and examples are provided as supporting information and can be downloaded from the journal's website.