Umberto Perego | Politecnico di Milano (original) (raw)

Papers by Umberto Perego

$Research paper thumbnail of Higher order phase-field modeling of brittle fracture via isogeometric analysis$

Engineering with computers, Mar 14, 2024

The evolution of brittle fracture in a material can be conveniently investigated by means of the ... more The evolution of brittle fracture in a material can be conveniently investigated by means of the phase-field technique introducing a smooth crack density functional. Following Borden et al. (2014), two distinct types of phase-field functional are considered: (i) a second-order model and (ii) a fourth-order one. The latter approach involves the bi-Laplacian of the phase field and therefore the resulting Galerkin form requires continuously differentiable basis functions: a condition we easily fulfill via Isogeometric Analysis. In this work, we provide an extensive comparison of the considered formulations performing several tests that progressively increase the complexity of the crack patterns. To measure the fracture length necessary in our accuracy evaluations, we propose an image-based algorithm that features an automatic skeletonization technique able to track complex fracture patterns. In all numerical results, damage irreversibility is handled in a straightforward and rigorous manner using the Projected Successive Over-Relaxation algorithm that is suitable to be adopted for both phase-field formulations since it can be used in combination with higher continuity isogeometric discretizations. Based on our results, the fourth-order approach provides higher rates of convergence and a greater accuracy. Moreover, we observe that fourthand second-order models exhibit a comparable accuracy when the former methods employ a mesh-size approximately two times larger, entailing a substantial reduction of the computational effort.

Euromech Colloquium 592, DEFORMATION AND DAMAGE MECHANISMS OF WOODFIBRE NETWORK- MATERIALS AND STRUCTURES, 2017

Paperboard and paperboard products, such as carton packages, generally present a layered structur... more Paperboard and paperboard products, such as carton packages, generally present a layered structure. Paperboard is often produced in the form of multiplies, with coatings, decor layers and possible layers of other materials, such as aluminum layers for food protection. Delamination between any of these layers is a common problem during the different phases of the converting process. Ink-tack delamination [1] can e.g. occur during printing, while delamination is intentionally induced during creasing and folding [2,3]. Delamination is also frequent in the converting of corrugated boards, particularly in the die-cutting of multiply materials. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Archivio istituzionale della ricerca-Politecnico di Milano

IAMMC2017 - Interaction of Applied Mathematics and Mechanics Conference, 2017

This work is devoted to the formulation of a new cohesive law for the modelling of mixed mode del... more This work is devoted to the formulation of a new cohesive law for the modelling of mixed mode delamination. The proposed model is based on the physical observation that the failure of many interfaces is characterized by the competition between different mechanisms under dominant shear or tensile stresses, which is not usually taken explicitly into account in damage cohesive models (see e.g. [1-4]). A notable exception is e.g. the work in [5], where a multiscale frictional model is proposed, accounting for friction under normal tensile tractions and shear at the microscale. In the proposed cohesive model, internal friction is accounted for at the macroscale with a phenomenological approach, based on the definition of two damage modes. A three-surface activation criterion, characterized by an internal friction angle (figure 1), is defined in the normal and shear tractions plane: each one of the three normals to the domain defines a distinct damage mode. A decomposition of the strain energy release rate in terms of the three damage modes is achieved in a natural way by projecting the cohesive tractions onto the three normals. The mixed-mode fracture energy is the result of the interaction among modes, without the need to define an empirical law for its evolution with mode mixity. Several numerical examples are simulated in order to validate the proposed interface law in both pure mode and mixed-mode delamination problems. In particular, the comparison between the numerical results and the experimental data of Mixed-Mode Bending (MMB) tests [6] is shown. Fig 1 Three-surfaces activation domain in tractions compenents space.

VI ECCOMAS Thematic Conference on the Mechanical Response of Composites, 2017

This work deals with the formulation of a thermodynamically consistent, isotropic damage cohesive... more This work deals with the formulation of a thermodynamically consistent, isotropic damage cohesive model for mixed-mode delamination under variable mode ratio. The proposed model is based on the introduction of an internal friction angle in the tensile case, that allows for an accurate modelling of the interaction between normal and shear openings.

Interface elements based on cohesive formulations provide an effective numerical tool for the sim... more Interface elements based on cohesive formulations provide an effective numerical tool for the simulation of the decohesion processes occurring during delamination and debonding phenomena. Although a large number of cohesive models has been proposed in the literature, many of them exhibit limitations or drawbacks in dealing with mixed-mode loading conditions with variable mode ratios. Accurately predicting the delamination growth requires the cohesive law to respect some basic thermodynamic requirements, such as producing a positive dissipation under any loading path, to properly describe the mode interaction, and to correctly reproduce the experimentally measured dissipated energy under any loading path. Several experimental studies point out that the fracture energy significantly increases in passing from pure Mode I to pure Mode II [1]. A new cohesive model, specifically conceived for the description of mixed-mode delamination and based on an isotropic damage formulation, is propo...

Delamination, i.e. the decohesion between layers, is one of the main failure modes in composite m... more Delamination, i.e. the decohesion between layers, is one of the main failure modes in composite materials. Making use of robust and accurate numerical tools is fundamental to reliably predict the delamination growth. The finite element simulation of these problems is often dealt with by the insertion between adjacent layers of interface elements, whose constitutive behavior is described by a cohesive model in terms of a traction-opening displacement law. In the literature, there exists a variety of works devoted to the formulation of cohesive laws (see [1] for a comparative review of some models), although many of them exhibit a number of shortcomings, such as the need of strong assumptions on the loading path and on the mixed-mode failure properties, or the lack of thermodynamic consistency. Real-life delamination processes are indeed often characterized by mixed-mode loading conditions with varying mode ratio. In addition, several experimental results show that the fracture energy...

In questo lavoro viene presentata una strategia numerica dedicata alla simulazione agli elementi ... more In questo lavoro viene presentata una strategia numerica dedicata alla simulazione agli elementi finiti di fenomeni di taglio e delaminazione in strutture sottili a uno o più strati. Sebbene lo studio di queste due problematiche sia di interesse in molteplici settori ingegneristici, l’applicazione che ha motivato lo sviluppo del codice di simulazione riguarda laminati impiegati nell’industria del packaging alimentare.

Delamination is among the most frequent failure mechanism in laminated composite materials, often... more Delamination is among the most frequent failure mechanism in laminated composite materials, often characterized by mixed-mode loading conditions. As underlined in [1, 2], classical cohesive models, formulated under the hypothesis of small openings, are not able to describe the delamination growth either in the presence of extensive fiber-bridging phenomena or when large relative displacements are involved. As shown by a number of DCB tests performed on fiber-reinforced composites, large-scale fiber bridging causes an increment in the fracture energy, typically expressed by an R-curve in which the toughness gradually increases until a steady-state value is reached. In this work the cohesive model proposed in [3] for the simulation of mixed-mode delamination problems under the assumption of small openings is extended to handle the transition between small and large openings and to account for large-scale bridging or interfacial fibrilation. Consistently with the fact that fiber bridgi...

Computer Methods in Applied Mechanics and Engineering, 2020

We present a Lagrangian nodal integration method for the simulation of Newtonian and non-Newtonia... more We present a Lagrangian nodal integration method for the simulation of Newtonian and non-Newtonian free-surface fluid flows. The proposed nodal Lagrangian method uses a finite element mesh to discretize the computational domain and to define the (linear) shape functions for the unknown nodal variables, as in the standard Particle Finite Element Method (PFEM). In this approach, however, the integrals are performed over nodal patches and not over elements, and strains/stresses are defined at nodes and not at Gauss points. This allows to limit the drawbacks associated with the remeshing and leads to a more accurate stress computation than in the classical elemental PFEM. Several numerical tests, in 2D and in 3D, are presented to validate the proposed nodal PFEM. In all cases, the method has shown a very good agreement with analytical solutions and with experimental and numerical results from the literature. A thorough comparison between nodal and elemental PFEMs is also presented, focusing on crucial issues, such as solution accuracy, convergence, mass conservation and sensitivity to mesh distortion. c

Advanced Structured Materials, 2019

Paperboard is one of the most widely used materials in industrial processes, notably for packagin... more Paperboard is one of the most widely used materials in industrial processes, notably for packaging purposes. Packages are obtained through a continuous forming process, in which a flat laminated sheet is converted into the final 3-D solid. In the package forming process, it is common practice to score the paperboard laminate with crease lines, in order to obtain folds with sharp edges and to minimize the initiation and propagation of flaws during the subsequent folding procedures. In this work, a constitutive model for the mechanical response of crease lines is proposed and validated on the basis of experimental tests available in the literature.

Advanced Structured Materials, 2014

I principj ed i metodi generali esposti dal sommo Lagrange nella Meccanica Analitica vennero in m... more I principj ed i metodi generali esposti dal sommo Lagrange nella Meccanica Analitica vennero in molta parte abbandonati dai geometri che dopo di lui trattarono questioni di Matematica applicata. L’essere alcuni di quei principj, o non dimostrati, o dimostrati incompletamente, pare sia la cagione principale di quell’abbandono, e ne abbiamo quasi una prova nel vedere adoperate tuttora le formole date da Lagrange nella Sezione IV della seconda parte, le quali, appunto perche rigorosamente dimostrate, non vennero lasciate in disparte anche dopo i lavori di Hamilton e di Jacobi sullo stesso argomento. Fra questi principj il piu importante per le applicazioni e certamente quello indicato dall’autore nella Sezione II, ed esposto con maggior chiarezza nella Sezione IV della prima parte della M. A., intorno al modo di introdurre l’effetto delle forze interne nella equazione generale per l’equilibrio e pel moto, e che il difetto di dimostrazione rese quasi sterile pei successori di Lagrange.

Journal of Applied Mechanics, 1989

In beams with full-end constraints, loaded transversely by short pressure pulses, the effect of e... more In beams with full-end constraints, loaded transversely by short pressure pulses, the effect of extensional plastic deformation is to make possible instabilities related to snap buckling in the elastic-plastic recovery after the first peak displacement (Symonds and Yu, 1985). In the present paper we make use of a damped, Shanley-type model to study the calculation of the final displacement, reached asymptotically. We show that plots of the elastic strain energy and of the total energy as functions of the displacement help to guide thinking. They provide clarification of previously observed phenomena (Genna and Symonds, 1988) that appear complex at small damping, and lead to lower and upper bounds on the load parameter such that anomalous responses are observed. The response is calculable with the usual accuracy in problems where bifurcations are concerned.

Journal of Applied Mechanics, 1988

DISCUSSION/AUTHORS CLOSURE "this problem has been solved previously in a more general form" by Kn... more DISCUSSION/AUTHORS CLOSURE "this problem has been solved previously in a more general form" by Knapp is not correct. Even if the strong nature of some of the assumptions in Knapp's treatment is overlooked, one cannot lose sight of the fact that his analysis applies only in the two extreme cases of cables with either rigid or perfectly incompressible core; i.e., when p = 0.5. In contrast, our treatment does not suffer from this limitation and applies to any general linear material having an arbitrary v. We concur with the assertion that for each a 2 , there are, in general, two solutions for a 3 that cause the cable to be "nonrotating." This characteristic is also evident from Fig. 4 in our paper. Regarding the convention followed in presenting the helix angles, it has been stated in the first paragraph under the heading-Results and Discussion. Accordingly, "... for each of the layers with left lay, its helix angle a, must be replaced by the corresponding obtuse angle w-a,-.. . " This convention has been adhered to throughout the paper. In Fig. 4, from the context of the discussion, it is understood that the two layers have opposite lays (see first paragraph under subheading "Nonrotating Rope"); however, to avoid any possible ambiguities, it might have been better to have the ordinate read as w-a 3 in place of a 3. With this change, the apparent inconsistencies would disappear. Chaotic Motion of an Elastic-Plastic Beam 3 P. S. Symonds 4 , G. Borino 5 , and U. Perego 6. The authors looked for evidence of chaotic behavior both under impulsive loading and under periodic excitation, in the pin ended elastic-plastic Shanley model. Their results and conclusions in the impulsive loading ("free vibration") case disagree with ours, in recent studies. The disagreement seems to arise from the different ways of treating damping. Here we demonstrate this briefly. Details are given in a forthcoming paper by Borino et al. (1988). The authors purport to show in their Figs. 3 and 4 how certain initial conditions lead to final displacements of negative sign-i.e., in the opposite direction to the loading ("anomalous"). In these figures a dot is entered if the prediction is for a negative value, and a blank for a positive outcome. Figure 3 shows a complex pattern. Figure 4 shows a portion of this to expanded scales, and is equally complex. This suggests a fine structure, with possible resemblance to fractal boundaries between attracting basins. They observe that the "slightest change in initial conditions can cause a drastic change in the response, and attempts at obtaining detailed numerical solutions to the problem are meaningless". Our work on the response due to short pulse loading in the presence of damping (Genna and Symonds (1988); Borino et al. (1988)) leads to the opposite conclusion. For any value of damping ratio f, there are regions in the initial condition space such that the final displacement is negative, and outside of which it is positive. For the value f =0.1 used by the authors, there are two bands that are loci of pairs (a 0 , a 0) leading to

Le Journal de Physique IV, 1997

The purpose of the present work was to compare the well-documented results of experiments on stee... more The purpose of the present work was to compare the well-documented results of experiments on steel rectangular plates subjected to blast loading, carried out by Jones, Uran and Tekin [I], with the explicit fmite element analysis (ABAQUSJExplicit [2]) and the simplified analytical solution, based on a kinematic approach. This study was undertaken in order to establish the conclusions concerning the possible application of the simplified approach, and evaluate the capacity of material modelling in ABAQUSExplicit in a case of extremely high velocities of deformation. Resume. L'objectif du present travail etait la comparaison des rksultats des experimentations pour les plaques rectangulaires en acier chargees d'explosion, realisees par Jones, Uran et Tekin [I] a I'analyse par la mtthode des Cltments finis (programme ABAQUSIExplicit 121) de merne qu'a la solution analytique simplifiqe. Ces recherche Ctaient entreprises afin d'obtenir les conclusions concernant I'utilisation eventuelle de la jonction simplifiee de meme que de prkciser I'efficacite du modele materiel employe dans le programme ABAQUS/Explicit dans le cas d'une tres grande vitesse de deformation.

The problem of inception and growth of a damaging-cohesive crack in an elastic bar is considered.... more The problem of inception and growth of a damaging-cohesive crack in an elastic bar is considered. It is shown that the position where the crack actually forms can the obtained from the minimality conditions of an energy functional, including the bulk energy and the surface energy, while the equilibrium of the system is obtained from the stationarity conditions. The progressive damage of the cohesive interface is taken into account by means of a step by step procedure. The finite step solution is also shown to make stationary a functional defined for each step.