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We propose a new discrete FFT-based method for computational homogenization of micromechanics on a regular grid that is simple, fast and robust. The discretization scheme is based on a tetrahedral stencil that displays three crucial properties. First, and most importantly, the Fourier representation of the associated Green operator is defined for any finite q-vector generated by the periodic boundary conditions and that does not belong to the Reciprocal Lattice of the discrete grids. As shown in the paper, this property guaranties that, for any elastic contrats, even infinite, mechanical equilibrium is always mathematically stable, i.e. free of any unphysical patterns, such as oscillations, ringing or checkerboarding, a property which is not shared by the original Moulinec-Suquet method \cite{moulinec1994fast,moulinec1998numerical} nor by the rotated scheme proposed by Willot \cite{willot2015fourier}. Second, the components of tensorial quantities are all defined on the same location, which permits the use of any elastic anisotropy and any spatial variation of the material fields. Third, convergence to equilibrium using the simplest iterative scheme, the "basic scheme", is fast and the number of iterates stabilizes at high contrasts, so that infinite contrast is obtained without additional computational cost., Comment: 34 pages, 10 figures

The assessment of myocardial fiber disarray is of major interest for the study of the progression of myocardial disease. However, time-resolved imaging of the myocardial structure remains unavailable in clinical practice. In this study, we introduce 3D Backscatter Tensor Imaging (3D-BTI), an entirely novel ultrasound-based imaging technique that can map the myocardial fibers orientation and its dynamics with a temporal resolution of 10 ms during a single cardiac cycle, non-invasively and in vivo in entire volumes. 3D-BTI is based on ultrafast volumetric ultrasound acquisitions, which are used to quantify the spatial coherence of backscattered echoes at each point of the volume. The capability of 3D-BTI to map the fibers orientation was evaluated in vitro in 5 myocardial samples. The helicoidal transmural variation of fiber angles was in good agreement with the one obtained by histological analysis. 3D-BTI was then performed to map the fiber orientation dynamics in vivo in the beating heart of an open-chest sheep at a volume rate of 90 volumes/s. Finally, the clinical feasibility of 3D-BTI was shown on a healthy volunteer. These initial results indicate that 3D-BTI could become a fully non-invasive technique to assess myocardial disarray at the bedside of patients.

Between 2017 and 2022, Oxfam examined aid to DRM from multiple donors provided to multiple low- and middle-income countries. This synthesis report seeks to draw lessons across these studies. The key issues examined include tradeoffs between efficiency and effectiveness in generating revenues on the one hand, and equity on the other; whether donors support direct or indirect taxation; the progressivity of instruments supported; whether aid to DRM explicitly links revenues to poverty reduction (health, education, social protection); whether aid supports country ownership; and whether aid explicitly seeks to advance gender equality.

The objectives were to develop a novel three-dimensional technology for imaging naturally occurring shear wave (SW) propagation, demonstrate feasibility on human volunteers and quantify SW velocity in different propagation directions. Imaging of natural SWs generated by valve closures has emerged to obtain a direct measurement of cardiac stiffness. Recently, natural SW velocity was assessed in two dimensions on parasternal long axis view under the assumption of a propagation direction along the septum. However, in this approach the source localization and the complex three-dimensional propagation wave path was neglected making the speed estimation unreliable. High volume rate transthoracic acquisitions of the human left ventricle (1100 volume/s) was performed with a 4D ultrafast echocardiographic scanner. Four-dimensional tissue velocity cineloops enabled visualization of aortic and mitral valve closure waves. Energy and time of flight mapping allowed propagation path visualization and source localization, respectively. Velocities were quantified along different directions. Aortic and mitral valve closure SW velocities were assessed for the three volunteers with low standard deviation. Anisotropic propagation was also found suggesting the necessity of using a three-dimensional imaging approach. Different velocities were estimated for the three directions for the aortic (3.4$\pm$0.1 m/s, 3.5$\pm$0.3 m/s, 5.4$\pm$0.7 m/s) and the mitral (2.8$\pm$0.5 m/s, 2.9$\pm$0.3 m/s, 4.6$\pm$0.7 m/s) valve SWs. 4D ultrafast ultrasound alleviates the limitations of 2D ultrafast ultrasound for cardiac SW imaging based on natural SW propagations and enables a comprehensive measurement of cardiac stiffness. This technique could provide stiffness mapping of the left ventricle.

Titanium and its alloys undergo temperature-driven martensitic phase transformation leading to the development of complex microstructures at mesoscale. Optimizing the mechanical properties of these materials requires an understanding of the correlations between the processing parameters and the mechanisms involved in the microstructure formation and evolution. In this work, we study the temperature-induced phase transition from BCC to HCP in pure titanium by atomistic modeling and investigate the influence of local stress conditions on the final martensite morphology. We simulate the transition under different stress conditions and carry a detailed analysis of the microstructural evolution during transition using a deformation gradient map that characterizes the local lattice distortion. The analysis of final martensite morphologies shows how mechanical constraints influence the number of selected variants and the number/type of defects in the final microstructure. We give insight on the origin and structure of different interfaces experimentally observed, such as inter-variant boundaries and antiphase defects. In particular, we show how antiphase defects originate from the two-fold degeneracy shuffling displacement arriving during the transition and how the triple junction formation drives the texture evolution when local stresses prevent a free shape change of the matrix surrounding the growing martensite nuclei.

Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve the continuous character of the theory. We present here a new formulation, which is intrinsically discrete, in which the interfaces are resolved with essentially one grid point with no pinning on the grid and an accurate rotational invariance, improving drastically the numerical capabilities of the method. We show that interfacial kinetic properties are reproduced with a high accuracy. Finally, we apply the model to a situation where conserved and non-conserved fields are coupled.

Because of the enormous range of time and space scales involved in dislocation dynamics, plastic modeling at macroscale requires a continuous formulation. In this paper, we present a rigorous formulation of the transition between the discrete, where plastic flow is resolved at the scale of individual dislocations, and the continuum, where dislocations are represented by densities. First, we focus on the underlying coarse-graining procedure and show that the emerging correlation-induced stresses are scale-dependent. Each of these stresses can be expanded into the sum of two components. The first one depends on the local values of the dislocation densities and always opposes the sum of the applied stress and long-range mean field stress generated by the geometrically necessary dislocation (GND) density; this stress acts as a friction stress. The second component depends on the local gradients of the dislocation densities and is inherently associated to a translation of the elastic domain; therefore, it acts as a back-stress. We also show that these friction and back- stresses contain symmetry-breaking components that make the local stress experienced by dislocations to depend on the sign of their Burgers vector.

Shape memory alloys inherit their macroscopic properties from their mesoscale microstructure originated from the martensitic phase transformation. In a cubic to orthorhombic transition, a single variant of marten- site can have a compatible (exact) interface with the austenite for some special lattice parameters in contrast to conventional austenite/twinned martensite interface with a transition layer. Experimentally, the phase compat- ibility results in a dramatic drop in thermal hysteresis and gives rise to very stable functional properties over cycling. Here, we investigate the microstructures observed in Ti50Ni50-xPdx alloys that undergo a cubic to orthorhombic martensitic transformation using a three dimensional phase field approach. We will show that the simulation results are in very good agreement with transmission electron microscopy observations. However, the understanding of the drop in thermal hysteresis requires the coupling of phase transformation with plastic activity. We will discuss this point within the framework of thermoelasticity, which is a generic feature of the martensitic transformation., Comment: Accepted for publication in in Journal of Applied Physics

The origin of stabilization of complex microstructures along macrotwin boundaries in martensites is explained by comparing two models based on Ginzburg-Landau theory. The first model incorporates a geometrically nonlinear strain tensor to ensure that the Landau energy is invariant under rigid body rotations, while the second model uses a linearized strain tensor under the assumption that deformations and rotations are small. We show that the approximation in the second model does not always hold for martensites and that the experimental observations along macrotwin boundaries can only be reproduced by the geometrically nonlinear (exact) theory.

Within a phase field approach which takes the strain-induced elasticity into account, the kinetics of the coherent order-disorder transition is investigated for the specific case of $Al_3 Zr$ alloy. It is shown that a microstructure with cubic $L1_2$ precipitates appears as a transient state during the decomposition of a homogeneous disordered solid solution into a microstructure with tetragonal $DO_{23}$ precipitates embedded into a disordered matrix. At low enough temperature, favored by a weak internal stress, only $L1_2$ precipitates grow in the transient microstructure preceding nucleation of the $DO_{23}$ precipitates that occurs exclusively at the interface of the solid solution with the $L1_2$ precipitates. Analysis of microstructures at nanoscopic scale shows a characteristic rod shape for the $DO_{23}$ precipitates due to the combination of their tetragonal symmetry and their large internal stress., Comment: 2 postscript figures and 1 JPG page

We present a general formalism for incorporating dislocations in Phase Field methods. This formalism is based on the elastic equivalence between a dislocation loop and a platelet inclusion of specific stress-free strain related to the loop Burgers vector and normal. Dislocations are thus treated as platelet inclusions and may be coupled dynamically to any other field such as a concentration field. The method is illustrated through the simulation of a Frank-Read source and of the shrinkage of a loop in presence of a concentration field., Comment: 6 pages, submitted to the Proceedings of MRS Fall 2000