Collisions in shape memory alloys

We present here a model for instantaneous collisions in a solid made of shape memory alloys (SMA) by means of a predictive theory which is based on the introduction not only of macroscopic velocities and temperature, but also of microscopic velocities responsible of the austenite-martensites phase changes. Assuming time discontinuities for velocities, volume fractions and temperature, and applying the principles of thermodynamics for non-smooth evolutions together with constitutive laws typical of SMA, we end up with a system of nonlinearly coupled elliptic equations for which we prove an existence and uniqueness result in the 2 and 3 D cases. Finally, we also present numerical results for a SMA 2D solid subject to an external percussion by an hammer stroke

A first order phase transition with non-constant density

AbstractWe introduce a new model for first order phase transitions accounting for non-constant densities of the phases during the process. The resulting initial and boundary value problem for a PDE system is recovered by thermodynamical principles. The resulting system presents some singularities and strong nonlinearities accounting for internal constraints, ensuring in particular the positivity of the pressure and the temperature. Physical consistency for the order parameter comes from a maximum principle argument. Existence of a weak solution is proved by a regularization-passage to the limit procedure

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Large deformations in terms of stretch and rotation and global solution to the quasi-stationary problem

In this paper we derive a new model for visco-elasticity with large deformations where the independent variables are the stretch and the rotation tensors which intervene with second gradients terms accounting for physical properties in the principle of virtual power. Another basic feature of our model is that there is conditional compatibility, entering the model as kinematic constraint and depending on the magnitude of an internal force associated to dislocations. Moreover, due to the kinematic constraint, the virtual velocities depend on the solutions of the problem. As a consequence, the variational formulation of the problem and the related mathematical analysis are neither standard nor straightforward. We adopt the strategy to invert the kinematic constraints through Green propagators, obtaining a system of integro-differential coupled equations. As a first mathematical step, we develop the analysis of the model in a simplified setting, i.e. considering the quasi-stationary version of the full system where we neglect inertia. In this context, we prove the existence of a global in time strong solution in three space dimensions for the system, employing techniques from PDEs and convex analysis, thus obtaining a novel contribution in the field of three dimensional finite visco-elasticity described in terms of the stretch and rotation variables. We also study a limit problem, letting the magnitude of the internal force associated to dislocations tend to zero, in which case the deformation becomes incompatible and the equations takes the form of a coupled system of PDEs. For the limit problem we obtain global existence, uniqueness and continuous dependence from data in three space dimensions

Global existence of a solution to a phase field model for supercooling

In this work, we will derive a macroscopic model of phase field type for supercooling. The phase transition process is described by the evolution of the temperature and the volume fraction of the liquid phase. This phase field model can also be interpreted as the approximation of some generalized Stefan problem. We will prove the existence of solutions to an initial--boundary value problem for the resulting system by using a time discrete scheme

Collision of four balls aligned

The collision of four balls aligned is analyzed in this paper. This study is based on the fundamental idea that a system formed by rigid bodies is deformable, since its shape changes because the relative distances of the different bodies change. A simple linear constitutive law, described by a pseudo-potential of dissipation completed by the condition of the impenetrability between the balls, is used. we consider the case where three balls falls on a very massive obstacle. The first ball, considered of very light mass, bounces with a velocity extensively superior to its fall velocity. This is sometimes called the superball phenomenon. This phenomenon is produced according to different cases such as the interaction between the first ball and the massive obstacle must be presented. Introducing an interaction between the first ball and the massive obstacle through the second or the third ball, the superball phenomenon is produced for all cases of evolutions after the collision. For every cases of evolutions of the balls after the collision, has been investigated the relations on the physical parameters which insure the superball phenomenon. These relations are obtained on the basis of the fundamental hypothesis: the mass of the first ball is very small whereas the mass of the massive obstacle is very large.

Numerical approach to a model for quasistatic damage with spatial BV-regularization

We address a model for rate-independent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BV-regularization. Discrete solutions are obtained using an alternate time-discrete scheme and the Variable-ADMM algorithm to solve the constrained nonsmooth optimization problem that determines the damage variable at each time step. We prove convergence of the method and show that discrete solutions approximate a semistable energetic solution of the rate-independent system. Moreover, we present our numerical results for two benchmark problems

Type I interferon-mediated autoinflammation due to DNase II deficiency

Microbial nucleic acid recognition serves as the major stimulus to an antiviral response, implying a requirement to limit the misrepresentation of self nucleic acids as non-self and the induction of autoinflammation. By systematic screening using a panel of interferon-stimulated genes we identify two siblings and a singleton variably demonstrating severe neonatal anemia, membranoproliferative glomerulonephritis, liver fibrosis, deforming arthropathy and increased anti-DNA antibodies. In both families we identify biallelic mutations in DNASE2, associated with a loss of DNase II endonuclease activity. We record increased interferon alpha protein levels using digital ELISA, enhanced interferon signaling by RNA-Seq analysis and constitutive upregulation of phosphorylated STAT1 and STAT3 in patient lymphocytes and monocytes. A hematological disease transcriptomic signature and increased numbers of erythroblasts are recorded in patient peripheral blood, suggesting that interferon might have a particular effect on hematopoiesis. These data define a type I interferonopathy due to DNase II deficiency in humans