Andrea Panteghini

Latent hardening size effect in small-scale plasticity

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

On the existence of a unique class of yield and failure criteria comprising Tresca, von Mises, Drucker–Prager, Mohr–Coulomb, Galileo–Rankine, Matsuoka–Nakai and Lade–Duncan

In this paper, it is mathematically demonstrated that classical yield and failure criteria such as Tresca, von Mises, Drucker–Prager, Mohr–Coulomb, Matsuoka–Nakai and Lade–Duncan are all defined by the same equation. This can be seen as one of the three solutions of a cubic equation of the principal stresses and suggests that all such criteria belong to a more general class of non-convex formulations which also comprises a recent generalization of the Galileo–Rankine criterion. The derived equation is always convex and can also provide a smooth approximation of continuity of at least class C2 of the original Tresca and Mohr–Coulomb criteria. It is therefore free from all the limitations which restrain the use of some of them in numerical analyses. The mathematical structure of the presented equation is based on a separate definition of the meridional and deviatoric sections of the graphical representation of the criteria. This enables the use of an efficient implicit integration algorithm which results in a very short machine runtime even when demanding boundary value problems are analysed.

Design of perforated panels for low frequency acoustic correction of rooms for listening to music

The acoustic design of rooms for listening to music or recording is a very difficult subject: in order to improve the acoustic performance of these confined rooms, it may be necessary to absorb noise energy; sometimes all audible frequencies of the spectrum, sometimes at some specific frequencies. The design is especially difficult at low frequencies, where both resonance modes and standing waves are present. For the correction of problems of this kind, a resonance cavity perforated panel can be used. In the technical literature, there are some theoretical models describing the behavior of such a panel, but the results given are scarcely informative. Here we try to develop a simple but accurate approach for the design of these devices. On the basis of a reference FEM simulation of a drilled panel which was discussed in a previous paper [4], an engineering analytical model, which can be simply implemented either in few lines of FORTRAN code or by means of free engineering software tools like OpenOffice.org, has been developed. The dependency of the panels behavior on the design parameters is here discussed.