A three-dimensional constitutive model for shape memory alloys

Shape memory alloys (SMAs) are materials that, among other characteristics, have the ability to present high deformation levels when subjected to mechanical loading, returning to their original form after a temperature change. Literature presents numerous constitutive models that describe the phenomenological features of the thermomechanical behavior of SMAs. The present paper introduces a novel three-dimensional constitutive model that describes the martensitic phase transformations within the scope of standard generalized materials. The model is capable of describing the main features of the thermomechanical behavior of SMAs by considering four macroscopic phases associated with austenitic phase and three variants of martensite. A numerical procedure is proposed to deal with the nonlinearities of the model. Numerical simulations are carried out dealing with uniaxial and multiaxial single-point tests showing the capability of the introduced model to describe the general behavior of SMAs. Specifically, uniaxial tests show pseudoelasticity, shape memory effect, phase transformation due to temperature change and internal subloops due to incomplete phase transformations. Concerning multiaxial tests, the pure shear stress and hydrostatic tests are discussed showing qualitatively coherent results. Moreover, other tensile–shear tests are conducted modeling the general three-dimensional behavior of SMAs. It is shown that the multiaxial results are qualitative coherent with the related data presented in the literature.     

Quantum metrology: dynamics versus entanglement

A parameter whose coupling to a quantum probe of n constituents includes all two-body interactions between the constituents can be measured with an uncertainty that scales as 1/n3/2, even when the constituents are initially unentangled. We devise a protocol that achieves the 1/n3/2 scaling without generating any entanglement among the constituents, and we suggest that the protocol might be implemented in a two-component Bose-Einstein condensate.     

Genus Four Superstring Measures

A main issue in superstring theory are the superstring measures. D’Hoker and Phong showed that for genus two these reduce to measures on the moduli space of curves which are the product of modular forms of weight eight and the bosonic measure. They also suggested a generalisation to higher genus. We showed that their approach works, with a minor modification, in genus three and we announced a positive result also in genus four. Here we give the modular form in genus four explicitly. Recently, S. Grushevsky published this result as part of a more general approach.     

A guide on FIB preparation of samples containing stress corrosion crack tips for TEM and atom-probe analysis

The preparation of samples containing stress corrosion crack tips for 3D atom-probe tomography and transmission electron microscopy is of ultimate importance for understanding the mechanisms controlling crack propagation. In this paper, it will be shown that a focused ion beam machine equipped with an in situ micromanipulator is an ideal tool to systematically prepare such demanding samples. The methodology is described and discussed in detail, and several results are presented to demonstrate the potential of the technique.     

On the Stability of a Class of Modified Gravitational Models

Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting is investigated. Specifically, after revisiting the f(R) case, R being the Ricci curvature, we present a stability condition around a de Sitter solution valid for modified gravitational models of generalized type F(R,G,Q), G and Q being the Gauss-Bonnet and quadratic Riemann invariants respectively. A generalization to higher order invariants is presented.     

Mixed analytical–numerical relaxation in finite single-slip crystal plasticity

The modeling of the finite elastoplastic behaviour of single crystals with one active slip system leads to a nonconvex variational problem, whose minimization produces fine structures. The computation of the quasiconvex envelope of the energy density involves the solution of a nonconvex optimization problem and faces severe numerical difficulties from the presence of many local minima. In this paper, we consider a standard model problem in two dimensions and, by exploiting analytical relaxation results for limiting cases and the special structure of the problem at hand, we obtain a fast and efficient numerical relaxation algorithm. The effectiveness of our algorithm is demonstrated with numerical examples. The precision of the results is assessed by lower bounds from polyconvexity.      

The Probabilistic Feynman–Kac Formula for an Infinite-Dimensional Schrödinger Equation with Exponential and Singular Potentials

Using the probabilistic Feynman–Kac formula, the existence of solutions of the Schrödinger equation on an infinite dimensional space E is proven. This theorem is valid for a large class of potentials with exponential growth at infinity as well as for singular potentials. The solution of the Schrödinger equation is local with respect to time and space variables. The space E can be a Hilbert space or other more general infinite dimensional spaces, like Banach and locally convex spaces (continuous functions, test functions, distributions). The specific choice of the infinite dimensional space corresponds to the smoothness of the fields to which the Schrödinger equation refers. The results also express an infinite-dimensional Heisenberg uncertainty principle: increasing of the field smoothness implies increasing of divergence of the momentum part of the quantum field Hamiltonian.     

Peroxide-Induced Synthesis of Maleic Anhydride-Grafted Poly(butylene succinate) and Its Compatibilizing Effect on Poly(butylene succinate)/Pistachio Shell Flour Composites

Framing the Circular Bioeconomy, the use of reactive compatibilizers was applied in order to increase the interfacial adhesion and, hence, the physical properties and applications of green composites based on biopolymers and food waste derived lignocellulosic fillers. In this study, poly(butylene succinate) grafted with maleic anhydride (PBS-g-MAH) was successfully synthetized by a reactive melt-mixing process using poly(butylene succinate) (PBS) and maleic anhydride (MAH) that was induced with dicumyl peroxide (DCP) as a radical initiator and based on the formation of macroradicals derived from the hydrogen abstraction of the biopolymer backbone. Then, PBS-g-MAH was used as reactive compatibilizer for PBS filled with different contents of pistachio shell flour (PSF) during melt extrusion. As confirmed by Fourier transform infrared (FTIR), PBS-g-MAH acted as a bridge between the two composite phases since it was readily soluble in PBS and could successfully form new esters by reaction of its multiple MAH groups with the hydroxyl (–OH) groups present in cellulose or lignin of PSF and the end ones in PBS. The resultant compatibilized green composites were, thereafter, shaped by injection molding into 4-mm thick pieces with a wood-like color. Results showed significant increases in the mechanical and thermomechanical rigidity and hardness, meanwhile variations on the thermal stability were negligible. The enhancement observed was related to the good dispersion and the improved filler-matrix interfacial interactions achieved by PBS-g-MAH and also to the PSF nucleating effect that increased the PBS’s crystallinity. Furthermore, water uptake of the pieces progressively increased as a function of the filler content, whereas the disintegration in controlled compost soil was limited due to their large thickness.