Crack propagation in honeycomb cellular materials: a computational approach

Computational models based on the finite element method and linear or nonlinear fracture mechanics are herein proposed to study the mechanical response of functionally designed cellular components. It is demonstrated that, via a suitable tailoring of the properties of interfaces present in the meso- and micro-structures, the tensile strength can be substantially increased as compared to that of a standard polycrystalline material. Moreover, numerical examples regarding the structural response of these components when subjected to loading conditions typical of cutting operations are provided. As a general trend, the occurrence of tortuous crack paths is highly favorable: stable crack propagation can be achieved in case of critical crack growth, whereas an increased fatigue life can be obtained for a sub-critical crack propagation

Structural integrity of hierarchical composites

Interface mechanical problems are of paramount importance in engineering and materials science. Traditionally, due to the complexity of modelling their mechanical behaviour, interfaces are often treated as defects and their features are not explored. In this study, a different approach is illustrated, where the interfaces play an active role in the design of innovative hierarchical composites and are fundamental for their structural integrity. Numerical examples regarding cutting tools made of hierarchical cellular polycrystalline materials are proposed, showing that tailoring of interface properties at the different scales is the way to achieve superior mechanical responses that cannot be obtained using standard material

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

Flavor revolution at ICECUBE horizons?

Recently (May-November 2013) highest energy neutrino events have been presented by ICECUBE. Most (21) of all these (28) events are cascades shower whose flux exhibits a sharp hardening respect other lower energy atmospheric neutrino component, events suggesting an injection of extraterrestrial neutrino, mostly nu e, nu tau, making cascades. ICECUBE claimed that a component (10:6+5:0 3:6), a third, of these events must be a trace of expected downward muons and-or atmospheric neutrinos (muon track dominated): The probability that this scenario occurs is very poor, about 0.1- 0.5%. The paradox might be mitigate as we suggest if nearly all of the 28 events are originated by extraterrestrial sources arriving to us in de-coherent states. At first sight also a partial solution may rise if highest energy events at E nu > 60 TeV ( 17 showering versus 4 muon tracks) are mostly of extraterrestrial nature. However this solution leaves problematic the earlier 30 - 60 TeV energy region, whose 8 showers versus 3 tracks is in tension with most nearby atmospheric neutrino signals, by a sharp difference at TeV energy ruled (as shown in Deep Core) by ten over one neutrino (muon) events over showers. This puzzling (fast) flavor transition from atmospheric nu muon flux at TeV to tens TeV showers and muon neutrino absence has deep consequences. Few cascades shower events in Antares might also test the nu flavor changes above TeVs up to a rare one at few tens TeV signal. Higher energy EeV tau air-shower induced by UHE nu tau within mountains or Earth skin while skimming terrestrial ground as AUGER arrays might be still rare, but the correlated horizontal upward PeVs tau air-shower may soon shine into ASHRA crown telescopes at mountain edges by their Cherenkov flashes.Comment: 5 pages, 6 figures; major editorial corrections and comments; we caution to not be blazed by a recent apparent brillant solution, arXiv:1402.6678, "The Glashow resonance in neutrino-photon scattering", because it is based on a very tuned ad hoc large Time asimmetry, (in disagreement with recent observations (PRL 109, 211801 (2012)

Influence of the intermediate material on the singular stress field in tri-material junctions

According to the mathematical formalism of the eigenfunction expansion method, the problem of stress-singularities arising from multi-material junctions is addressed. The wedges are composed of isotropic homogeneous materials and are in a condition of plane stress or strain. The order of the stress-singularity is provided for tri-material junctions, paying special attention to the role played by Mode-I and Mode-II deformation. The effect of cracks inside either the softer or the stiffer material is also investigated. Numerical results can be profitably used for establishing optimum material configurations

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

Topological characterization of antireflective and hydrophobic rough surfaces: are random process theory and fractal modeling applicable?

The random process theory (RPT) has been widely applied to predict the joint probability distribution functions (PDFs) of asperity heights and curvatures of rough surfaces. A check of the predictions of RPT against the actual statistics of numerically generated random fractal surfaces and of real rough surfaces has been only partially undertaken. The present experimental and numerical study provides a deep critical comparison on this matter, providing some insight into the capabilities and limitations in applying RPT and fractal modeling to antireflective and hydrophobic rough surfaces, two important types of textured surfaces. A multi-resolution experimental campaign by using a confocal profilometer with different lenses is carried out and a comprehensive software for the statistical description of rough surfaces is developed. It is found that the topology of the analyzed textured surfaces cannot be fully described according to RPT and fractal modeling. The following complexities emerge: (i) the presence of cut-offs or bi-fractality in the power-law power-spectral density (PSD) functions; (ii) a more pronounced shift of the PSD by changing resolution as compared to what expected from fractal modeling; (iii) inaccuracy of the RPT in describing the joint PDFs of asperity heights and curvatures of textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured surfaces in case of special surface treatments, not accounted by fractal modeling.Comment: 21 pages, 13 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

Theoretical and numerical investigation on internal instability phenomena in composite materials

Instability phenomena occurring in the microstructure of composite materials are investigated. To this aim, a complete description of the mechanical behavior of bi-material interfaces in composite materials requires the definition of both a cohesive law involving damage for the debonding stage, and a contact model during the closure of the interface. Both formulations are herein presented and implemented in the FE code FEAP. Numerical examples showing the transition from a snap-back instability to a stable mechanical response are presented