Fast statistical homogenization procedure (FSHP) for particle random composites using virtual element method

Mechanical behaviour of particle composite materials is growing of interest to engineering applications. A computational homogenization procedure in conjunction with a statistical approach have been successfully adopted for the definition of the representative volume element (RVE) size, that in random media is an unknown of the problem, and of the related equivalent elastic moduli. Drawback of such a statistical approach to homogenization is the high computational cost, which prevents the possibility to perform series of parametric analyses. In this work, we propose a so-called fast statistical homogenization procedure (FSHP) developed within an integrated framework that automates all the steps to perform. Furthermore within the FSHP, we adopt the numerical framework of the virtual element method for numerical simulations to reduce the computational burden. The computational strategies and the discretization adopted allow us to efficiently solve the series (hundreds) of simulations and to rapidly converge to the RVE size detection

Am J Prev Med

CC999999/Intramural CDC HHS/United States2017-02-19T00:00:00Z26456878PMC531651

Micromechanical estimates of the interaction energy for shape memory alloys based on a two-phases microstructure

The interaction energy is a fundamental ingredient in the modeling of Shape Memory Alloys (SMA) and several micromechanical estimates are available in the literature Some of the models describe SMA by Multi-Variant Microstructures (MVM) made of a mixture of Austenite and several variants (or groups of variants) of Martensite. Others, rely upon Two-Phase Microstructures(TPM) in which only one type of Martensite arises. Besides the different approaches there is a common issue to most micromechanical estimates: they tend to largely overestimate the values of the interaction energy. In this work the quantitative relevance of the overestimation of the interaction energy is evaluated, in a sample case, showing that some models based on TPM may lead to violations of the second law of thermodynamics. While various solutions to this problem have been proposed in the framework of MVM by enriching the description of the microstructure, it seems that similar remedies are not yet available in the two-phases setting. In a previous work it was shown that, for SMA modeled by TPM, any estimate of the effective compliance immediately lead to a corresponding estimate of the interaction energy. Among the several estimates available in the literature, Dvorak's Average Field Approximation (AFA) turns out to be very useful in this context. In this micromechanical scheme mechanical concentration tensors are approximated by embedding inclusions in a comparison material subject to a suitable stress field that models, in an indirect way, the interaction between phases. The use of this scheme in the framework of leads to estimates of the interaction energy that depend on the elastic properties of the comparison material. While in the composite materials applications of the AFA scheme the comparison material is used to model the interactions between the phases, here the idea is to model, in an overall and indirect way, the secondary accommodation phenomena that take place during phase transformations by a comparison material less stiff than parent phase. This might be interpreted also as a kind of effective microscale damage occurring around the product phase regions. The elastic properties of the comparison material may thus be tuned in order to model the reduction of stiffness induced by the, otherwise unspecified, secondary accommodation phenomena. Finally, it is shown that this gives rise to physically plausible values of the interaction energy consistent with the thermodynamical bounds

Non-Gaussian solution for random rocking of slender rigid block

This paper adopts a random vibration approach to study the response of the slender rigid block to seismic action. The problem is strongly non-linear because of (i) the restoring term and (ii) the quadratic dissipation of energy due to the inelastic impacts, modeled as an impulsive process. The excitation process is firstly assumed to be a Gaussian white noise; secondly, a non-stationary filtered Gaussian white noise is assumed to simulate seismic shaking more accurately. The solution of the associated Fokker-Planck equation in terms of moments of the response is obtained by means of a non-Gaussian closure technique, that enables the complete statistical definition of the approximated transient response process to be achieved. The mean upcrossing rates and the response spectra in terms of displacement are evaluated. The reliability of the solutions derived is assessed by comparing them with Monte Carlo simulations

ANCIENT AND MODERN RESTORATIONS FOR THE COLUMN OF MARCUS AURELIUS IN ROME

In 1589, on the occasion of a complex intervention on the Column of Marcus Aurelius, Domenico Fontana reconstructed an entire corner of the abacus resorting to a wise joint of blocks, the stability of which was simply guaranteed by their shape. The same corner was over again restored in 1987 by Antonino Giuffre because it was feared that the decay and fracturing of the material inserted during the 16th-century intervention could compromise the safety of the abacus. Despite the seemingly unbridgeable distance that separates them, the two restorations share an undeniable affinity of method in which an essential role is played by the need not only of recovering the cultural and technical continuity with the historical architecture but also of correlating the different specialist contributions available within a unified approach. With respect to the latter aspect, both restorations discussed in this work constitute a suggestion for the current culture that, breathlessly running after the detail, often risks losing sight of the entirety