Optimization algorithms for the solution of the frictionless normal contact between rough surfaces

This paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half-plane using the boundary element method (BEM). After recasting the resulting Linear Complementarity Problem (LCP) as a convex quadratic program (QP) with nonnegative constraints, different optimization algorithms are compared for its solution: (i) a Greedy method, based on different solvers for the unconstrained linear system (Conjugate Gradient CG, Gauss-Seidel, Cholesky factorization), (ii) a constrained CG algorithm, (iii) the Alternating Direction Method of Multipliers (ADMM), and ($iv$) the Non-Negative Least Squares (NNLS) algorithm, possibly warm-started by accelerated gradient projection steps or taking advantage of a loading history. The latter method is two orders of magnitude faster than the Greedy CG method and one order of magnitude faster than the constrained CG algorithm. Finally, we propose another type of warm start based on a refined criterion for the identification of the initial trial contact domain that can be used in conjunction with all the previous optimization algorithms. This method, called Cascade Multi-Resolution (CMR), takes advantage of physical considerations regarding the scaling of the contact predictions by changing the surface resolution. The method is very efficient and accurate when applied to real or numerically generated rough surfaces, provided that their power spectral density function is of power-law type, as in case of self-similar fractal surfaces.Comment: 38 pages, 11 figure

Node-to-segment and node-to-surface interface finite elements for fracture mechanics

The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets (in 3D) belonging to the opposite crack faces and enforce the cohesive traction-separation relation. In the present work we propose a novel type of interface element for fracture mechanics sharing some analogies with the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact elements. The displacement gap of a node belonging to the finite element discretization of one crack face with respect to its projected point on the opposite face is used to determine the cohesive tractions, the residual vector and its consistent linearization for an implicit solution scheme. The following advantages with respect to classical interface finite elements are demonstrated: (i) non-matching finite element discretizations of the opposite crack faces is possible; (ii) easy modelling of cohesive cracks with non-propagating crack tips; (iii) the internal rotational equilibrium of the interface element is assured. Detailed examples are provided to show the usefulness of the proposed approach in nonlinear fracture mechanics problems.Comment: 37 pages, 17 figure

A consistent interface element formulation for geometrical and material nonlinearities

Decohesion undergoing large displacements takes place in a wide range of applications. In these problems, interface element formulations for large displacements should be used to accurately deal with coupled material and geometrical nonlinearities. The present work proposes a consistent derivation of a new interface element for large deformation analyses. The resulting compact derivation leads to a operational formulation that enables the accommodation of any order of kinematic interpolation and constitutive behavior of the interface. The derived interface element has been implemented into the finite element codes FEAP and ABAQUS by means of user-defined routines. The interplay between geometrical and material nonlinearities is investigated by considering two different constitutive models for the interface (tension cut-off and polynomial cohesive zone models) and small or finite deformation for the continuum. Numerical examples are proposed to assess the mesh independency of the new interface element and to demonstrate the robustness of the formulation. A comparison with experimental results for peeling confirms the predictive capabilities of the formulation.Comment: 14 pages, 11 figure

X-ray Photons in the CO 2-1 'Lacuna' of NGC 2110

A recent ALMA study of the Seyfert 2 Active Galactic Nucleus (AGN) NGC 2110 by Rosario et al. (2019) has reported a remarkable lack of CO 2-1 emission from the circumnuclear region, where optical lines and H2 emission are observed, leading to the suggestion of excitation of the molecular clouds by the AGN. Since interaction with X-ray photons could be the cause of this excitation, we have searched the archival Chandra data for corroborating evidence. We report an extra-nuclear ~1'' (~170 pc) feature found in the soft (<1.0 keV) Chandra data of the Seyfert 2 Active Galactic Nucleus (AGN) NGC 2110. This feature is elongated to the north of the nucleus and its shape matches well that of the optical lines and H2 emission observed in this region, which is devoid of CO 2-1 emission. The Chandra image completes the emerging picture of a multi-phase circumnuclear medium excited by the X-rays from the AGN, with dense warm molecular clouds emitting in H2 but depleted of CO 2-1 emission.Comment: ApJ Letters - in pres

An Analysis of the Italian Lockdown in Retrospective Using Particle Swarm Optimization in Machine Learning Applied to an Epidemiological Model

A critical analysis of the open data provided by the Italian Civil Protection Centre during phase 1 of Covid-19 epidemic&mdash;the so-called Italian lockdown&mdash;is herein proposed in relation to four of the most affected Italian regions, namely Lombardy, Reggio Emilia, Valle d&rsquo;Aosta, and Veneto. A possible bias in the data induced by the extent in the use of medical swabs is found in relation to Valle d&rsquo;Aosta and Veneto. Observed data are then interpreted using a Susceptible-Infectious-Recovered (SIR) epidemiological model enhanced with asymptomatic (infected and recovered) compartments, including lockdown effects through time-dependent model parameters. The initial number of susceptible individuals for each region is also considered as a parameter to be identified. The issue of parameters identification is herein addressed by a robust machine learning approach based on particle swarm optimization. Model predictions provide relevant information for policymakers in terms of the effect of lockdown measures in the different regions. The number of susceptible individuals involved in the epidemic, important for a safe release of lockdown during the next phases, is predicted to be around 10% of the population for Lombardy, 16% for Reggio Emilia, 18% for Veneto, and 40% for Valle d&rsquo;Aosta

Fatigue degradation and electric recovery in Silicon solar cells embedded in photovoltaic modules

Cracking in Silicon solar cells is an important factor for the electrical power-loss of photovoltaic modules. Simple geometrical criteria identifying the amount of inactive cell areas depending on the position of cracks with respect to the main electric conductors have been proposed in the literature to predict worst case scenarios. Here we present an experimental study based on the electroluminescence (EL) technique showing that crack propagation in monocrystalline Silicon cells embedded in photovoltaic (PV) modules is a much more complex phenomenon. In spite of the very brittle nature of Silicon, due to the action of the encapsulating polymer and residual thermo-elastic stresses, cracked regions can recover the electric conductivity during mechanical unloading due to crack closure. During cyclic bending, fatigue degradation is reported. This pinpoints the importance of reducing cyclic stresses caused by vibrations due to transportation and use, in order to limit the effect of cracking in Silicon cells