77 research outputs found
Locally adaptive phase-field models and transition to fracture
This thesis proposes a new computational model for the efficient simulation of crack propagation, through the combination of a phase-field model in small subdomains around crack tips and a discontinuous model in the rest of the domain. The combined model inherits the advantages of both approaches. The phase-field model determines crack propagation at crack tips, and the discontinuous model explicitly describes the crack elsewhere, enabling to use a coarser discretization and thus reducing the computational cost.
In crack-tip subdomains, the discretization is refined to capture the phase-field solution, while in the discontinuous part, sharp cracks are incorporated into the coarse background discretization by the eXtended Finite Element Method (XFEM). As crack-tip subdomains move with crack growth, the discretization is automatically updated and phase-field bands are replaced by sharp cracks in the wake of cracks.
The first step is the development of an adaptive refinement strategy for phase-field models. To this end, two alternatives are proposed. Both of them consider two types of elements, standard and refined, which are mapped into a fixed background mesh. In refined elements, the space of approximation is uniformly -refined. Continuity between elements of different type is imposed in weak form to handle the non-conformal approximations in a natural way, without spreading of refinement nor having to deal with hanging nodes, leading to a very local refinement along cracks.
The first adaptive strategy relies on a Hybridizable Discontinuous Galerkin (HDG) formulation of the problem, in which continuity between elements is imposed in weak form. The second one is based on a more efficient Continuous Galerkin (CG) formulation; a continuous FEM approximation is used in the standard and refined regions and, then, continuity on the interface between regions is imposed in weak form by Nitsche's method.
The proposed strategies robustly refine the discretization as cracks propagate and can be easily incorporated into a working code for phase-field models. However, the computational cost can be further reduced by transitioning to the discontinuous in the combined model. In the wake of crack tips, the phase-field diffuse cracks are replaced by XFEM discontinuous cracks and elements are derefined. The combined model is studied within the adaptive CG formulation. Numerical experiments include branching and coalescence of cracks, and a fully 3D test.En aquesta tesi es proposa un nou model computacional per a simular la propagaciĂł de fractures de manera eficient, a partir de la combinaciĂł d’un model de camp de fase en petits subdominis al voltant dels extrems de les fissures, i d’un model discontinu a la resta del domini. El model combinat mantĂ© els avantatges de tots dos tipus de model. El model continu determina la propagaciĂł de la fissura, i el model discontinu descriu explĂcitament la fissura en gairebĂ© tot del domini, amb una discretitzaciĂł mĂ©s grollera i el conseqĂĽent estalvi en cost computacional. Als subdominis de camp de fase, la discretitzaciĂł es refina per tal d’aproximar bĂ© la soluciĂł, mentre que a la part discontĂnua, les fissures s’incorporen a la discretitzaciĂł grollera a partir de l’eXtended Finite Element Method (XFEM). A mesura que les fissures es propaguen pel domini, la discretitzaciĂł s’actualitza automĂ ticament i, lluny dels extrems, la representaciĂł suavitzada de les fissures a partir del camp de fase es reemplaça per una representaciĂł discontĂnua. El primer pas Ă©s definir una estratègia de refinament adaptatiu pels models continus de camp de fase. En aquesta tesi es proposen dues alternatives diferents. Totes dues consideren dos tipus d’elements, estĂ ndards i refinats, que es mapen a la malla inicial. Als elements refinats, l’espai d’aproximaciĂł es refina uniformement. La continuĂŻtat entre elements de tipus diferent s’imposa en forma feble per facilitar el tractament de les aproximacions no conformes, sense que s’escampi el refinament ni haver d’imposar restriccions als nodes de la interfĂcie, donant lloc a un refinament molt localitzat. La primera estratègia adaptativa es basa en una formulaciĂł Hybridizable Discontinuous Galerkin (HDG) del problema, que imposa continuĂŻtat entre elements en forma feble. La segona es basa en una formulaciĂł contĂnua mĂ©s eficient; es fa servir una aproximaciĂł contĂnua del Mètode dels Elements Finits a les regions estĂ ndards i refinades i, aleshores, a la interfĂcie entre les dues regions s’imposa la continuĂŻtat en forma feble amb el mètode de Nitsche. Les estratègies adaptatives refinen la discretitzaciĂł a mesura que les fissures es propaguen, i es poden afegir a un codi per a models de camp de fase de manera senzilla. No obstant, el cost computacional es pot reduir encara mĂ©s fent servir el model combinat. Lluny dels extrems de les fissures, la representaciĂł suavitzada del camp de fase es substitueix per discontinuĂŻtats en una discretitzaciĂł de XFEM, i els elements es desrefinen. El model combinat es formula a partir de l’estratègia adaptativa contĂnua. Els exemples numèrics inclouen bifurcaciĂł i coalescència de fissures, i un exemple en 3D
Nonlinear dimensionality reduction for parametric problems: a kernel proper orthogonal decomposition
This is the peer reviewed version of the following article: Diez, P. [et al.]. Nonlinear dimensionality reduction for parametric problems: a kernel proper orthogonal decomposition. "International journal for numerical methods in engineering", 30 Desembre 2021, vol. 122, nĂşm. 24, p. 7306-7327, which has been published in final form at DOI: 10.1002/nme.6831. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with dimension equal to the number of independent parameters) embedded in a large-dimensional space (dimension equal to the number of degrees of freedom of the full-order discrete model). A posteriori model reduction is based on constructing a basis from a family of snapshots (solutions of the full-order model computed offline), and then use this new basis to solve the subsequent instances online. Proper orthogonal decomposition (POD) reduces the problem into a linear subspace of lower dimension, eliminating redundancies in the family of snapshots. The strategy proposed here is to use a nonlinear dimensionality reduction technique, namely, the kernel principal component analysis (kPCA), in order to find a nonlinear manifold, with an expected much lower dimension, and to solve the problem in this low-dimensional manifold. Guided by this paradigm, the methodology devised here introduces different novel ideas, namely, 1) characterizing the nonlinear manifold using local tangent spaces, where the reduced-order problem is linear and based on the neighboring snapshots, 2) the approximation space is enriched with the cross-products of the snapshots, introducing a quadratic description, 3) the kernel for kPCA is defined ad hoc, based on physical considerations, and 4) the iterations in the reduced-dimensional space are performed using an algorithm based on a Delaunay tessellation of the cloud of snapshots in the reduced space. The resulting computational strategy is performing outstandingly in the numerical tests, alleviating many of the problems associated with POD and improving the numerical accuracy.Generalitat de Catalunya, 2017-SGR-1278; Ministerio de Ciencia e InnovaciĂłn, CEX2018-000797-S; PID2020-113463RB-C32; PID2020-113463RB-C33Peer ReviewedPostprint (published version
A hybridizable discontinuous Galerkin phase-field model for brittle fracture
Phase-field models for brittle fracture consider smeared representations of cracks, which are described by a continuous field that varies abruptly in the transition zone between unbroken and broken states. Computationally, meshes have to be fine locally near the crack to capture the solution. We present an HDG formulation for a quasi-static phase-field model, based on a staggered approach to solve the system. The use of HDG for this model is motivated by the suitability of the method for spatial adaptivity.Peer ReviewedPostprint (author's final draft
Cuerpos performativos en el ​voguing. Una etnografĂa sobre la casa Ubetta y la escena ​ballroom​ en Barcelona
MĂ ster Oficial en Antropologia i Etnografia, Departament d'Antropologia, Facultat Geografia i Història, Universitat de Barcelona, Curs: 2019-2020, Director: Jordi Mas GrauEsta etnografĂa ahonda en la relaciĂłn entre cuerpo, gĂ©nero y danza teniendo en cuenta las posibilidades de transformaciĂłn y recreaciĂłn que derivan de esta conexiĂłn socio-cultural. El voguing y​ sus bailarines serán el hilo conductor para profundizar en la potencialidad creadora de la danza y del cuerpo: rompiendo los lĂmites de las normatividades inscritas en el aprendizaje corporal e incidiendo en las trayectorias identitarias y subjetivas de los bailarines y ​performers.​ Para ello, he considerado imprescindible tomar en cuenta los estudios realizados desde la antropologĂa sobre cuatro ejes analĂticos interrelacionados: la danza, el cuerpo, el gĂ©nero y la performance
A hybridizable discontinuous Galerkin phase-field model for brittle fracture with adaptive refinement
This is the peer reviewed version of the following article: Muixi, A.; Rodriguez-Ferran, A.; Fernandez, S. A hybridizable discontinuous Galerkin phase-field model for brittle fracture with adaptive refinement. "International journal for numerical methods in engineering", 30 Març 2020, vol. 121, núm. 6, p. 1147-1169, which has been published in final form at DOI: 10.1002/nme.6260. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this paper, we propose an adaptive refinement strategy for phase-field models of brittle fracture, which is based on a novel hybridizable discontinuous Galerkin (HDG) formulation of the problem. The adaptive procedure considers standard elements and only one type of h-refined elements, dynamically located along the propagating cracks. Thanks to the weak imposition of interelement continuity in HDG methods, and in contrast with other existing adaptive approaches, hanging nodes or special transition elements are not needed, which simplifies the implementation. Various numerical experiments, including one branching test, show the accuracy, robustness, and applicability of the presented approach to quasistatic phase-field simulations.Peer ReviewedPostprint (author's final draft
Adaptive refinement for phase-field models of brittle fracture based on Nitsche's method
“This is a post-peer-review, pre-copyedit version of an article published in Computational mechanics. The final authenticated version is available online at:
http://dx.doi.org/10.1007/s00466-020-01841-1”.A new adaptive refinement strategy for phase-field models of brittle fracture is proposed. The approach provides a computationally efficient solution to the high demand in spatial resolution of phase-field models. The strategy is based on considering two types of elements: h-refined elements along cracks, where more accuracy is needed to capture the solution, and standard elements in the rest of the domain. Continuity between adjacent elements of different type is imposed in weak form by means of Nitsche's method. The weakly imposition of continuity leads to a very local refinement in a simple way, for any degree of approximation and both in 2D and 3D. The performance of the strategy is assessed for several scenarios in the quasi-static regime, including coalescence and branching of cracks in 2D and a twisting crack in 3D.Peer ReviewedPostprint (author's final draft
Equacions de difusiĂł no local: laplaciĂ fraccionari i operadors convolutius
L objectiu d aquest treball de fi de grau Ă©s estudiar dues generalitzacions de l equaciĂł de la calor, la primera enlloc d un laplaciĂ tĂ© un laplaciĂ fraccionari i la segona un operador de la forma Lu = J ∗ u − u, i determinar certes hipòtesis sota les quals les seves solucions es comporten com les de l equaciĂł clĂ ssica de la calor. Obtenim els dos operadors generalitzant el laplaciĂ i estudiem algunes de les seves propietats, que aplicarem en els capĂtols principals del treball. El resultat mĂ©s important parla del comportament asimptòtic de les solucions del model convolutiu, i afirma que la seva decaiguda Ă©s la mateixa que la de les solucions de l equaciĂł de difusiĂł fraccionĂ ria. TambĂ© estudiem la Γ-convergència dels funcionals que ens defineixen aquestes equacions per tal de demostrar que el seu lĂmit coincideix en alguns casos
A combined XFEM phase-field computational model for crack growth without remeshing
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-020-01929-8This paper presents an adaptive strategy for phase-field simulations with transition to fracture. The phase-field equations are solved only in small subdomains around crack tips to determine propagation, while an XFEM discretization is used in the rest of the domain to represent sharp cracks, enabling to use a coarser discretization and therefore reducing the computational cost. Crack-tip subdomains move as cracks propagate in a fully automatic process. The same computational mesh is used during all the simulation, with an h-refined approximation in the elements in the crack-tip subdomains. Continuity of the displacement between the refined subdomains and the XFEM region is imposed in weak form via Nitsche’s method. The robustness of the strategy is shown for some numerical examples in 2D and 3D, including branching and coalescence tests.Peer ReviewedPostprint (author's final draft
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