86,987 research outputs found
Adaptive mesh refinement for the phase field method: A FEniCS implementation
No full textThis paper reports insightful implementation details of the global adaptive refinement procedure for the phase-field method recently published in Freddi and Mingazzi (2022). Phase field approaches reproduce cracks within solids in a smeared manner. The small transition zone between broken and unbroken material, whose width is controlled by an internal scale length parameter, permits to precisely replicate complex sharp crack topologies only if an extremely fine mesh is adopted. Starting from a coarse mesh, the proposed refinement process utilizes an energetic criterion to selectively refine the elements on which cracks may propagate. In fully broken areas, where the phase field is no longer evolving, a specific refinement is adopted to capture the high displacement gradient. The implementation is performed within the open-source finite element software FEniCS (ver. 19.1.0) which provides a framework for automated solutions of partial differential equations. The fundamental aspects of the code are described starting from the functional definition to the various steps of the refinement technique. A representative example is illustrated to supply further information on the code functionality. The code can be downloaded from https://github.com/LorenzoMingazzi/AGu-AGal and be used to easily apply the proposed refinement strategy to different problems or as a starting point for more sophisticated formulations
Numerical aspects in the SGBEM solution of softening cohesive interface problems
No full textAbstractSome numerical aspects of a new symmetric Galerkin boundary integral formulation presented in [A. Salvadori, A symmetric boundary integral formulation for cohesive interface problems, Comput. Mech. 32 (2003) 381–391] connected with a like arc-length technique for softening cohesive interface problems introduced in [F. Freddi, Cohesive interface analysis via boundary integral equations, Ph.D. thesis, University of Bologna, Italy, 2004] are here investigated. Further, if the problem is invariant with respect to a finite group G of congruences of the Euclidean space R2, we propose to reduce the computational cost of the symmetric Galerkin boundary element method (SGBEM) matrix evaluation and linear system solution using suitable restriction matrices strictly related to a system of irreducible matrix representation of G. Some numerical simulations are presented and discussed
Rivista italiana di Politiche Pubbliche
No full textLa Rivista Italiana di Politiche Pubbliche (RIPP), prima e unica rivista in Italia interamente dedicata all’analisi delle politiche pubbliche, è stata fondata nel 2001 da Giorgio Freddi – che tuttora la dirige - e raccoglie nel Comitato direttivo i principali esperti, italiani e stranieri, dello studio politologico dei programmi di intervento pubblico e degli apparati amministrativi in Italia e in prospettiva comparata.
La Rivista, ad impronta fortemente multidisciplinare, è interessata ad articoli di carattere teorico-interpretativo e a presentazioni di ricerche empiriche che abbiano come oggetto:
a) gli elementi costitutivi delle politiche pubbliche (attori, istituzioni, idee, reti relazionali);
b) l’interazione tra il sistema politico e la società nel policy making;
c) l'impatto della competizione partitica e degli assetti politico-istituzionali sui programmi di politica pubblica;
d) le relazioni tra le proprietà organizzative delle strutture politico-amministrative e le politiche pubbliche;
e) l’analisi di politiche settoriali, sviluppata sia in relazione a singoli casi sia mediante comparazioni;
f) lo studio delle politiche europee e della loro interazione con gli ambiti nazionali;
g) gli strumenti e le strategie di regolazione;
h) il management strategico delle politiche pubbliche;
i) i problemi teorici ed operativi del cambiamento delle politiche;
j) i metodi per lo studio delle politiche pubbliche
Phase-field modelling of failure in hybrid laminates
No full textIn this paper, the complex failure process of unidirectional hybrid laminates under uniaxial loading condition is reproduced and investigated by a one-dimensional phase-field model. The key ingredients of the approach, describing the mechanical response of a hybrid composite made of two different layers, are: (i) a phase-field method, based on a variational formulation of brittle fracture with regularised approximation of discontinuities for the two layers, (ii) cohesive law for the adhesive interface that connects the layers and (iii) robust and consolidated numerical strategy for the solution of the non-linear discretised problem. Explicit and well detailed simulations are shown for four peculiar failure mechanisms and the outcomes validated against experimental results available in literature. The model is able to discriminate among these different failure mechanisms according to the geometrical and mechanical properties of the hybrid composite. Both delamination of the adhesive interface is followed and crack patterns within the materials are fully determined. Finally, the proposed approach opens new perspective studies in higher dimension settings
Analysis of FRP–concrete debonding via boundary integral equations
No full textThe problem of debonding of FRP plates glued over a concrete element is studied making use of boundary integral
equations. Mode II cohesive crack model is adopted for the interface, whereas linear elasticity is used for the two materials outside the process zone. Symmetric Galerkin boundary element method is used, adopting the arc-length technique to follow the equilibrium path beyond its critical point. It is shown that, due to the presence of a softening branch in shear stress slip law, the behavior of a specimen undergoing debonding may be strongly non-linear, and is associated with a very brittle failure mechanism. For bond lengths longer than minimum anchorage length, a snap-back branch typically occurs after the attainment of the maximum force. Two different test setups have been numerically simulated and results in good agreement with experimental tests are found
Fracture energy in phase field models
No full textThe phase field approach to brittle fracture is based on smeared energetic representation of sharp fracture into surface. The passage between damaged and undamaged zones is influenced by an internal length scale parameter. In the present paper the approximation of fracture energy in phase field models is studied. Firstly, the diffusion equation of the phase field is numerically investigated. It is demonstrated through simple paradigmatic 2d and 3d cases that the fracture energy during crack initiation and propagation phenomena, such as crack branching and bifurcation, is strictly correlated with the internal length parameter. Moreover, it is shown that for finite value of the internal length parameter the dissipated energy does not depend only on the crack extension but on the geometrical configuration of fracture differently from the Griffith sharp approach. In particular, it is demonstrated that 3d cracks with same area may be characterized by different values of approximated fracture energy
Mortar Joints Influence in Debonding of Masonry Element Strengthened with FRP
No full textThe effects of mortars joints in masonry substrate reinforced with FRP is investigated from the numerical point of view. The analysis has been conducted by means of a new interface model specifically developed to reproduce the debonding process occurring between an elastic thin body in adhesion with a cohesive support material, as concrete or masonry. The model accounts for mode I and mode II of failure, considering the effect of the in-plane deformation of the interface, i.e. the possible elongation or confinement of the material constituting the interface. Numerical results are compared with experimental evidences showing the good performances of the proposed model in investigating the transferring phenomena in heterogeneous interfaces and, in particular, in studying the influence of the presence of mortar joints in the masonry texture in the debonding process
Local and Global Response Parameters in Seismic Risk Assessment of RC Frames Retrofitted by BRBs
No full textThis paper deals with the seismic performance and risk assessment of existing reinforced concrete (RC) buildings with limited ductility retrofitted by means of buckling restrained braces (BRBs). Two different approaches for evaluating the seismic vulnerability and risk before and after retrofit are introduced and analyzed. These approaches involve the use of different categories of engineering demand parameters (EDPs) for the system response assessment: global EDPs, that permit to obtain a synthetic description of the system behavior at a reduced computational cost, and local EDPs, more accurate in describing the response of the frame elements and of the BRBs, though more demanding from a computational point of view.
A probabilistic methodology is first introduced that permits to evaluate and compare the vulnerabilities of the frame before and after the retrofit (Freddi et al. 2012). This methodology, similarly to other methodologies present in the literature (e.g., Hueste and Bai 2006, Ramamoorthy et al. 2006, Özel and Güneyisi 2012), is based on the development of system fragility curves before and after the retrofit. However, differently from the others, it employs local rather than global EDPs to monitor the structural seismic response. This approach allows to capture accurately the modifications of the frame components’ response induced by the added bracing system. Successively, the effects of the EDPs choice on the seismic risk assessment and risk-based design of the retrofit of existing RC frames with dissipative braces is investigated by considering and analyzing a specific case study. This consists of an existing RC frame with low ductility capacity retrofitted by inserting a system of BRBs with elasto-plastic behaviour. The braces are designed by applying a widespread method based on an equivalent nonlinear SDOF approximation (Dall'Asta et al. 2009) and by considering different values of the shear capacity of the bracing system.
The importance of using local EDPs in the probabilistic evaluation of the retrofit effectiveness for the type of system analyzed in this paper is demonstrated by comparing both the fragility curves and the risk estimates under different hazard scenarios. It is shown that the use of global EDPs may result in a significant overestimation of the retrofit effectiveness in terms of both vulnerability and risk reduction. Consequently, if a risk-based design is carried out for the retrofit system, the dimension of the braces evaluated by using global EDPs for vulnerability assessment are significantly lower with respect to the corresponding dimensions obtained by using local EDPs. Larger differences are observed for the hazard scenarios with higher intensity
Mesh refinement procedures for the phase field approach to brittle fracture
No full textTwo refinement procedures for phase field approach are proposed and their numerical performances are investigated in the solution of fracture problems. Starting from a coarse discretization of the domain, an energetic criterion is used to determine the active zones where damage initiates, evolves and mesh refinement is mandatory to accurately approximate crack topology. Moreover, the extension of the refined regions is strictly correlated with the size of the process zone defined by the optimal profile. Global and global/local refinement strategies are investigated. In particular, the global/local technique solves the displacement and phase field problems on a local mesh dynamically updated and adaptively refined during the computation. Once the solutions of the local problems are obtained, the phase field is interpolated back onto the original mesh, adequately refined where a damage threshold is exceeded. The performances of the refinement techniques are analyzed and compared in representative examples with stable and brutal crack propagation
Introduzione Giuseppe di Federico e le ricerche sul sistema giudiziario: un caso di navigazione in mari molto nebbiosi
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