Articles de revista
http://hdl.handle.net/2117/6145
Fri, 23 Feb 2018 01:06:18 GMT2018-02-23T01:06:18ZGeometric derivation of the microscopic stress: a covariant central force decomposition
http://hdl.handle.net/2117/113657
Geometric derivation of the microscopic stress: a covariant central force decomposition
Torres Sánchez, Alejandro; Vanegas, Juan Manuel; Arroyo Balaguer, Marino
We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle-Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving-Kirkwood-Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.
Fri, 02 Feb 2018 18:10:15 GMThttp://hdl.handle.net/2117/1136572018-02-02T18:10:15ZTorres Sánchez, AlejandroVanegas, Juan ManuelArroyo Balaguer, MarinoWe revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle-Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving-Kirkwood-Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations
http://hdl.handle.net/2117/113279
An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations
Giacomini, Matteo
The certified descent algorithm (CDA) is a gradient-based method for shape optimization which certifies that the direction computed using the shape gradient is a genuine descent direction for the objective functional under analysis. It relies on the computation of an upper bound of the error introduced by the finite element approximation of the shape gradient. In this paper, we present a goal-oriented error estimator which depends solely on local quantities and is fully-computable. By means of the equilibrated fluxes approach, we construct a unified strategy valid for both conforming finite element approximations and discontinuous Galerkin discretizations. The new variant of the CDA is tested on the inverse identification problem of electrical impedance tomography: both its ability to identify a genuine descent direction at each iteration and its reliable stopping criterion are confirmed.
Fri, 26 Jan 2018 15:40:29 GMThttp://hdl.handle.net/2117/1132792018-01-26T15:40:29ZGiacomini, MatteoThe certified descent algorithm (CDA) is a gradient-based method for shape optimization which certifies that the direction computed using the shape gradient is a genuine descent direction for the objective functional under analysis. It relies on the computation of an upper bound of the error introduced by the finite element approximation of the shape gradient. In this paper, we present a goal-oriented error estimator which depends solely on local quantities and is fully-computable. By means of the equilibrated fluxes approach, we construct a unified strategy valid for both conforming finite element approximations and discontinuous Galerkin discretizations. The new variant of the CDA is tested on the inverse identification problem of electrical impedance tomography: both its ability to identify a genuine descent direction at each iteration and its reliable stopping criterion are confirmed.Towards the modelling of ageing and atherosclerosis effects in ApoE-/- mice aortic tissue
http://hdl.handle.net/2117/113143
Towards the modelling of ageing and atherosclerosis effects in ApoE-/- mice aortic tissue
Waffenschmidt, T., Tobias; Cilla, Myriam; Sáez Viñas, Pablo; Pérez, Marta M.; Menzel, Andreas; Peña, E.
The goal of this work consists in a quantitative analysis and constitutive modelling of ageing processes associated to plaque formation in mice arteries. Reliable information on the characteristic evolution of pressure–stretch curves due to the ageing effects is extracted from previous inflation test experiments. Furthermore, characteristic age-dependent material parameters are identified on the basis of a continuum-mechanics-based parameter optimisation technique. The results indicate that the aorta-stiffness of the healthy control mice remains basically constant irrespective of the diet-time and age. In contrast, significant differences exist within the material response and in consequence within the material parameters between the and the control mice as well as for the different locations over the aorta which is underlined by our experimental observations. With regard to the temporal evolution of the material parameters, we observe that the material parameters for the mice aortas exhibit a saturation-type increase with respect to age.
Wed, 24 Jan 2018 12:37:36 GMThttp://hdl.handle.net/2117/1131432018-01-24T12:37:36ZWaffenschmidt, T., TobiasCilla, MyriamSáez Viñas, PabloPérez, Marta M.Menzel, AndreasPeña, E.The goal of this work consists in a quantitative analysis and constitutive modelling of ageing processes associated to plaque formation in mice arteries. Reliable information on the characteristic evolution of pressure–stretch curves due to the ageing effects is extracted from previous inflation test experiments. Furthermore, characteristic age-dependent material parameters are identified on the basis of a continuum-mechanics-based parameter optimisation technique. The results indicate that the aorta-stiffness of the healthy control mice remains basically constant irrespective of the diet-time and age. In contrast, significant differences exist within the material response and in consequence within the material parameters between the and the control mice as well as for the different locations over the aorta which is underlined by our experimental observations. With regard to the temporal evolution of the material parameters, we observe that the material parameters for the mice aortas exhibit a saturation-type increase with respect to age.Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures
http://hdl.handle.net/2117/113137
Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures
Ruiz Gironès, Eloi; Oliver Serra, Albert; Socorro Marrero, Guillermo Valentín; Cascón Barbero, José Manuel; Escobar Sánchez, José M.; Montenegro Armas, Rafael; Sarrate Ramos, Josep
In this paper, we present a new method for inserting several triangulated surfaces into an existing tetrahedral mesh generated by the meccano method. The result is a conformal mesh where each inserted surface is approximated by a set of faces of the final tetrahedral mesh. First, the tetrahedral mesh is refined around the inserted surfaces to capture their geometric features. Second, each immersed surface is approximated by a set of faces from the tetrahedral mesh. Third, following a novel approach, the nodes of the approximated surfaces are mapped to the corresponding immersed surface. Fourth, we untangle and smooth the mesh by optimizing a regularized shape distortion measure for tetrahedral elements in which we move all the nodes of the mesh, restricting the movement of the edge and surface nodes along the corresponding entity they belong to. The refining process allows approximating the immersed surface for any initial meccano tetrahedral mesh. Moreover, the proposed projection method avoids computational expensive geometric projections. Finally, the applied simultaneous untangling and smoothing process delivers a high-quality mesh and ensures that the immersed surfaces are interpolated. Several examples are presented to assess the properties of the proposed method.
This is the peer reviewed version of the following article: Ruiz Gironès , E., Oliver , A., Socorro, G., Cascón, J., Escobar, J.M., Montenegro, R., Sarrate, J. Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures. "International journal for numerical methods in engineering", 2018, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5706/pdf. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Wed, 24 Jan 2018 12:17:46 GMThttp://hdl.handle.net/2117/1131372018-01-24T12:17:46ZRuiz Gironès, EloiOliver Serra, AlbertSocorro Marrero, Guillermo ValentínCascón Barbero, José ManuelEscobar Sánchez, José M.Montenegro Armas, RafaelSarrate Ramos, JosepIn this paper, we present a new method for inserting several triangulated surfaces into an existing tetrahedral mesh generated by the meccano method. The result is a conformal mesh where each inserted surface is approximated by a set of faces of the final tetrahedral mesh. First, the tetrahedral mesh is refined around the inserted surfaces to capture their geometric features. Second, each immersed surface is approximated by a set of faces from the tetrahedral mesh. Third, following a novel approach, the nodes of the approximated surfaces are mapped to the corresponding immersed surface. Fourth, we untangle and smooth the mesh by optimizing a regularized shape distortion measure for tetrahedral elements in which we move all the nodes of the mesh, restricting the movement of the edge and surface nodes along the corresponding entity they belong to. The refining process allows approximating the immersed surface for any initial meccano tetrahedral mesh. Moreover, the proposed projection method avoids computational expensive geometric projections. Finally, the applied simultaneous untangling and smoothing process delivers a high-quality mesh and ensures that the immersed surfaces are interpolated. Several examples are presented to assess the properties of the proposed method.A non-intrusive proper generalized decomposition scheme with application in biomechanics
http://hdl.handle.net/2117/111374
A non-intrusive proper generalized decomposition scheme with application in biomechanics
Zou, Xi; Conti, Michele; Díez, Pedro; Auricchio, Ferdinando
Proper generalized decomposition (PGD) is often used for multiquery and fast-response simulations. It is a powerful tool alleviating the curse of dimensionality affecting multiparametric partial differential equations. Most implementations of PGD are intrusive extensions based on in-house developed FE solvers. In this work, we propose a nonintrusive PGD scheme using off-the-shelf FE codes (such as certified commercial software) as an external solver. The scheme is implemented and monitored by in-house flow-control codes. A typical implementation is provided with downloadable codes. Moreover, a novel parametric separation strategy for the PGD resolution is presented. The parametric space is split into two- or three-dimensional subspaces, to allow PGD technique solving problems with constrained parametric spaces, achieving higher convergence ratio. Numerical examples are provided. In particular, a practical example in biomechanics is included, with potential application to patient-specific simulation.
This is the peer reviewed version of the following article: Zou, X., Conti, M., Diez, P., Auricchio, F. A non-intrusive proper generalized decomposition scheme with application in biomechanics. "International journal for numerical methods in engineering", 7 Setembre 2017., which has been published in final form at http://dx.doi.org/10.1002/nme.5610. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Thu, 30 Nov 2017 12:27:31 GMThttp://hdl.handle.net/2117/1113742017-11-30T12:27:31ZZou, XiConti, MicheleDíez, PedroAuricchio, FerdinandoProper generalized decomposition (PGD) is often used for multiquery and fast-response simulations. It is a powerful tool alleviating the curse of dimensionality affecting multiparametric partial differential equations. Most implementations of PGD are intrusive extensions based on in-house developed FE solvers. In this work, we propose a nonintrusive PGD scheme using off-the-shelf FE codes (such as certified commercial software) as an external solver. The scheme is implemented and monitored by in-house flow-control codes. A typical implementation is provided with downloadable codes. Moreover, a novel parametric separation strategy for the PGD resolution is presented. The parametric space is split into two- or three-dimensional subspaces, to allow PGD technique solving problems with constrained parametric spaces, achieving higher convergence ratio. Numerical examples are provided. In particular, a practical example in biomechanics is included, with potential application to patient-specific simulation.Generalized parametric solutions in Stokes flow
http://hdl.handle.net/2117/111372
Generalized parametric solutions in Stokes flow
Díez, Pedro; Zlotnik, Sergio; Huerta, Antonio
Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized Decomposition (PGD) provides a separable solution, a computational vademecum explicitly dependent on the parameters, efficiently computed with a greedy algorithm combined with an alternated directions scheme and compactly stored. This strategy has been successfully employed in many problems in computational mechanics. The application to problems with saddle point structure raises some difficulties requiring further attention. This article proposes a PGD formulation of the Stokes problem. Various possibilities of the separated forms of the PGD solutions are discussed and analyzed, selecting the more viable option. The efficacy of the proposed methodology is demonstrated in numerical examples for both Stokes and Brinkman models.
The final publication is available at Springer via https://doi.org/10.1016/j.cma.2017.07.016
Thu, 30 Nov 2017 11:59:32 GMThttp://hdl.handle.net/2117/1113722017-11-30T11:59:32ZDíez, PedroZlotnik, SergioHuerta, AntonioDesign optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized Decomposition (PGD) provides a separable solution, a computational vademecum explicitly dependent on the parameters, efficiently computed with a greedy algorithm combined with an alternated directions scheme and compactly stored. This strategy has been successfully employed in many problems in computational mechanics. The application to problems with saddle point structure raises some difficulties requiring further attention. This article proposes a PGD formulation of the Stokes problem. Various possibilities of the separated forms of the PGD solutions are discussed and analyzed, selecting the more viable option. The efficacy of the proposed methodology is demonstrated in numerical examples for both Stokes and Brinkman models.Numerical modelling of multi-phase multi-component reactive transport in the Earth's interior
http://hdl.handle.net/2117/111365
Numerical modelling of multi-phase multi-component reactive transport in the Earth's interior
Oliveira, Beñat; Afonso, Juan Carlos; Zlotnik, Sergio; Díez, Pedro
We present a conceptual and numerical approach to model processes in the Earth's interior that involve multiple phases that simultaneously interact thermally, mechanically and chemically. The approach is truly multiphase in the sense that each dynamic phase is explicitly modelled with an individual set of mass, momentum, energy and chemical mass balance equations coupled via interfacial interaction terms. It is also truly multi-component in the sense that the compositions of the system and its constituent thermodynamic phases are expressed by a full set of fundamental chemical components (e.g. SiO$_2$, Al$_2$O$_3$, MgO, etc) rather than proxies. In contrast to previous approaches these chemical components evolve, react with, and partition into, different phases with different physical properties according to an internally-consistent thermodynamic model. This enables a thermodynamically-consistent coupling of the governing set of balance equations. Interfacial processes such as surface tensions and/or surface energy contributions to the dynamics and energetics of the system are also taken into account. The model presented here describes the evolution of systems governed by Multi-Phase Multi-Component Reactive Transport (MPMCRT) based on Ensemble Averaging and Classical Irreversible Thermodynamics principles. This novel approach provides a flexible platform to study the dynamics and non-linear feedbacks occurring within various natural systems at different scales. This notably includes major-and trace-element transport, diffusion-controlled trace-element re-equilibration or rheological changes associated with melt generation and migration in the Earth's mantle.
This is a pre-copyedited, author-produced PDF of an article accepted for publication in
Geophysical journal international following peer review. The version of record Oliveira, B.,
Afonso, J., Zlotnik, S., Diez, P. Numerical modelling of multi-phase multi-component reactive transport in the Earth's interior. "Geophysical journal international", 1 Gener 2018, vol. 212, núm. 1, p. 345-388 is available online at: https://doi.org/10.1093/gji/ggx399.
Thu, 30 Nov 2017 11:12:12 GMThttp://hdl.handle.net/2117/1113652017-11-30T11:12:12ZOliveira, BeñatAfonso, Juan CarlosZlotnik, SergioDíez, PedroWe present a conceptual and numerical approach to model processes in the Earth's interior that involve multiple phases that simultaneously interact thermally, mechanically and chemically. The approach is truly multiphase in the sense that each dynamic phase is explicitly modelled with an individual set of mass, momentum, energy and chemical mass balance equations coupled via interfacial interaction terms. It is also truly multi-component in the sense that the compositions of the system and its constituent thermodynamic phases are expressed by a full set of fundamental chemical components (e.g. SiO$_2$, Al$_2$O$_3$, MgO, etc) rather than proxies. In contrast to previous approaches these chemical components evolve, react with, and partition into, different phases with different physical properties according to an internally-consistent thermodynamic model. This enables a thermodynamically-consistent coupling of the governing set of balance equations. Interfacial processes such as surface tensions and/or surface energy contributions to the dynamics and energetics of the system are also taken into account. The model presented here describes the evolution of systems governed by Multi-Phase Multi-Component Reactive Transport (MPMCRT) based on Ensemble Averaging and Classical Irreversible Thermodynamics principles. This novel approach provides a flexible platform to study the dynamics and non-linear feedbacks occurring within various natural systems at different scales. This notably includes major-and trace-element transport, diffusion-controlled trace-element re-equilibration or rheological changes associated with melt generation and migration in the Earth's mantle.AAR-based decomposition method for lower bound limit analysis
http://hdl.handle.net/2117/108908
AAR-based decomposition method for lower bound limit analysis
Muñoz Romero, José; Rabiei, Nima
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.
Fri, 20 Oct 2017 10:53:50 GMThttp://hdl.handle.net/2117/1089082017-10-20T10:53:50ZMuñoz Romero, JoséRabiei, NimaDespite 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.Ferroelectrics as smart mechanical materials
http://hdl.handle.net/2117/108844
Ferroelectrics as smart mechanical materials
Cordero Edwards, Kumara; Domingo Marimon, Neus; Abdollahi Hosnijeh, Amir; Sort Viñas, Jordi; Catalan, Gustau
The mechanical properties of materials are insensitive to space inversion, even when they are crystallographically asymmetric. In practice, this means that turning a piezoelectric crystal upside down or switching the polarization of a ferroelectric should not change its mechanical response. Strain gradients, however, introduce an additional source of asymmetry that has mechanical consequences. Using nanoindentation and contact-resonance force microscopy, this study demonstrates that the mechanical response to indentation of a uniaxial ferroelectric (LiNbO3) does change when its polarity is switched, and use this mechanical asymmetry both to quantify its flexoelectricity and to mechanically read the sign of its ferroelectric domains.
This is the peer reviewed version of the following article: Cordero, K., Domingo Marimon, Neus, Abdollahi, A., Sort Viñas, Jordi, Catalan, G. Ferroelectrics as smart mechanical materials. "Advanced materials", 21 Juliol 2017, vol. 29, núm. 37, p. 1-6, which has been published in final form at DOI: 10.1002/adma.201702210. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Thu, 19 Oct 2017 08:43:20 GMThttp://hdl.handle.net/2117/1088442017-10-19T08:43:20ZCordero Edwards, KumaraDomingo Marimon, NeusAbdollahi Hosnijeh, AmirSort Viñas, JordiCatalan, GustauThe mechanical properties of materials are insensitive to space inversion, even when they are crystallographically asymmetric. In practice, this means that turning a piezoelectric crystal upside down or switching the polarization of a ferroelectric should not change its mechanical response. Strain gradients, however, introduce an additional source of asymmetry that has mechanical consequences. Using nanoindentation and contact-resonance force microscopy, this study demonstrates that the mechanical response to indentation of a uniaxial ferroelectric (LiNbO3) does change when its polarity is switched, and use this mechanical asymmetry both to quantify its flexoelectricity and to mechanically read the sign of its ferroelectric domains.Coexistence of wrinkles and blisters in supported graphene
http://hdl.handle.net/2117/108583
Coexistence of wrinkles and blisters in supported graphene
Zang, Kuan; Arroyo Balaguer, Marino
Blisters induced by gas trapped in the interstitial space between supported graphene and the substrate are commonly observed. These blisters are often quasi-spherical with a circular rim, but polygonal blisters are also common and coexist with wrinkles emanating from their vertices. Here, we show that these different blister morphologies can be understood mechanically in terms of free energy minimization of the supported graphene sheet for a given mass of trapped gas and for a given lateral strain. Using a nonlinear continuum model for supported graphene closely reproducing experimental images of blisters, we build a morphological diagram as a function of strain and trapped mass. We show that the transition from quasi-spherical to polygonal of blisters as compressive strain is increased is a process of stretching energy relaxation and focusing, as many other crumpling events in thin sheets. Furthermore, to characterize this transition, we theoretically examine the onset of nucleation of short wrinkles in the periphery of a quasi-spherical blister. Our results are experimentally testable and provide a framework to control complex out-of-plane motifs in supported graphene combining blisters and wrinkles for strain engineering of graphene.
Tue, 10 Oct 2017 10:43:11 GMThttp://hdl.handle.net/2117/1085832017-10-10T10:43:11ZZang, KuanArroyo Balaguer, MarinoBlisters induced by gas trapped in the interstitial space between supported graphene and the substrate are commonly observed. These blisters are often quasi-spherical with a circular rim, but polygonal blisters are also common and coexist with wrinkles emanating from their vertices. Here, we show that these different blister morphologies can be understood mechanically in terms of free energy minimization of the supported graphene sheet for a given mass of trapped gas and for a given lateral strain. Using a nonlinear continuum model for supported graphene closely reproducing experimental images of blisters, we build a morphological diagram as a function of strain and trapped mass. We show that the transition from quasi-spherical to polygonal of blisters as compressive strain is increased is a process of stretching energy relaxation and focusing, as many other crumpling events in thin sheets. Furthermore, to characterize this transition, we theoretically examine the onset of nucleation of short wrinkles in the periphery of a quasi-spherical blister. Our results are experimentally testable and provide a framework to control complex out-of-plane motifs in supported graphene combining blisters and wrinkles for strain engineering of graphene.