A rate-independent model for the isothermal quasi-static evolution of shape-memory materials

This note addresses a three-dimensional model for isothermal stress-induced transformation in shape-memory polycrystalline materials. We treat the problem within the framework of the energetic formulation of rate-independent processes and investigate existence and continuous dependence issues at both the constitutive relation and quasi-static evolution level. Moreover, we focus on time and space approximation as well as on regularization and parameter asymptotics.Comment: 33 pages, 3 figure

Accurate prediction of melt pool shapes in laser powder bed fusion by the non-linear temperature equation including phase changes - isotropic versus anisotropic conductivity

In this contribution, we validate a physical model based on a transient temperature equation (including latent heat) w.r.t. the experimental set AMB2018-02 provided within the additive manufacturing benchmark series, established at the National Institute of Standards and Technology, USA. We aim at predicting the following quantities of interest: width, depth, and length of the melt pool by numerical simulation and report also on the obtainable numerical results of the cooling rate. We first assume the laser to posses a double ellipsoidal shape and demonstrate that a well calibrated, purely thermal model based on isotropic thermal conductivity is able to predict all the quantities of interest, up to a deviation of maximum 7.3\% from the experimentally measured values. However, it is interesting to observe that if we directly introduce, whenever available, the measured laser profile in the model (instead of the double ellipsoidal shape) the investigated model returns a deviation of 19.3\% from the experimental values. This motivates a model update by introducing anisotropic conductivity, which is intended to be a simplistic model for heat material convection inside the melt pool. Such an anisotropic model enables the prediction of all quantities of interest mentioned above with a maximum deviation from the experimental values of 6.5\%. We note that, although more predictive, the anisotropic model induces only a marginal increase in computational complexity

PLoS One

BackgroundInsecticide treated nets (ITNs) and indoor residual spraying (IRS) have been scaled up for malaria prevention in sub-Saharan Africa. However, there are few studies on the benefit of implementing IRS in areas with moderate to high coverage of ITNs. We evaluated the impact of an IRS program on malaria related outcomes in western Kenya, an area of intense perennial malaria transmission and moderate ITN coverage (55\ue2\u20ac\u201c65% use of any net the previous night).MethodsThe Kenya Division of Malaria Control, with support from the US President\ue2\u20ac\u2122s Malaria Initiative, conducted IRS in one lowland endemic district with moderate coverage of ITNs. Surveys were conducted in the IRS district and a neighboring district before IRS, after one round of IRS in July-Sept 2008 and after a second round of IRS in April-May 2009. IRS was conducted with pyrethroid insecticides. At each survey, 30 clusters were selected for sampling and within each cluster, 12 compounds were randomly selected. The primary outcomes measured in all residents of selected compounds included malaria parasitemia, clinical malaria (P. falciparum infection plus history of fever) and anemia (Hb<8) of all residents in randomly selected compounds. At each survey round, individuals from the IRS district were matched to those from the non-IRS district using propensity scores and multivariate logistic regression models were constructed based on the matched dataset.ResultsAt baseline and after one round of IRS, there were no differences between the two districts in the prevalence of malaria parasitemia, clinical malaria or anemia. After two rounds of IRS, the prevalence of malaria parasitemia was 6.4% in the IRS district compared to 16.7% in the comparison district (OR = 0.36, 95% CI = 0.22\ue2\u20ac\u201c0.59, p<0.001). The prevalence of clinical malaria was also lower in the IRS district (1.8% vs. 4.9%, OR = 0.37, 95% CI = 0.20\ue2\u20ac\u201c0.68, p = 0.001). The prevalence of anemia was lower in the IRS district but only in children under 5 years of age (2.8% vs. 9.3%, OR = 0.30, 95% CI = 0.13\ue2\u20ac\u201c0.71, p = 0.006). Multivariate models incorporating both IRS and ITNs indicated that both had an impact on malaria parasitemia and clinical malaria but the independent effect of ITNs was reduced in the district that had received two rounds of IRS. There was no statistically significant independent effect of ITNs on the prevalence of anemia in any age group.ConclusionsBoth IRS and ITNs are effective tools for reducing malaria burden and when implemented in an area of moderate to high transmission with moderate ITN coverage, there may be an added benefit of IRS. The value of adding ITNs to IRS is less clear as their benefits may be masked by IRS. Additional monitoring of malaria control programs that implement ITNs and IRS concurrently is encouraged to better understand how to maximize the benefits of both interventions, particularly in the context of increasing pyrethroid resistance.26731524PMC470119

Numerical simulation of Nitinol peripheral stents: from laser-cutting to deployment in a patient specific anatomy

The current clinical trend is to use percutaneous techniques, exploiting Nitinol self-expanding stents, to treat peripheral occluded vessels such as carotid or superficial femoral arteries. Although this class of stents addresses the biomechanical requirements (i.e. flexibility, kink resistance, etc.), it has been observed that many of these stents implanted in peripheral vessels are fractured. Numerical simulations have shown to be very useful in the investigation and optimization of stents and also to provide novel insights into fatigue/fracture mechanics. To date most finite element based stent simulations are performed in a straight simplified anatomy and neglect the actual deployment process; consequently there is a need for more realistic simulations taking into account the different stages of the stent design process and the insertion in the target anatomy into account. This study proposes a virtual framework to analyze numerically Nitinol stents from the laser-cutting stage to the deployment in a (patient specific) tortuous anatomy

Explicit parametric solutions of lattice structures with proper generalized decomposition (PGD): applications to the design of 3D-printed architectured materials

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-017-1534-9Architectured materials (or metamaterials) are constituted by a unit-cell with a complex structural design repeated periodically forming a bulk material with emergent mechanical properties. One may obtain specific macro-scale (or bulk) properties in the resulting architectured material by properly designing the unit-cell. Typically, this is stated as an optimal design problem in which the parameters describing the shape and mechanical properties of the unit-cell are selected in order to produce the desired bulk characteristics. This is especially pertinent due to the ease manufacturing of these complex structures with 3D printers. The proper generalized decomposition provides explicit parametic solutions of parametric PDEs. Here, the same ideas are used to obtain parametric solutions of the algebraic equations arising from lattice structural models. Once the explicit parametric solution is available, the optimal design problem is a simple post-process. The same strategy is applied in the numerical illustrations, first to a unit-cell (and then homogenized with periodicity conditions), and in a second phase to the complete structure of a lattice material specimen.Peer ReviewedPostprint (author's final draft

A finite strain kinematic hardening constitutive model based on Hencky strain: general framework, solution algorithm and application to shape memory alloys

The logarithmic or Hencky strain measure is a favored measure of strain due to its remarkable properties in large deformation problems. Compared with other strain measures, e.g., the commonly used Green–Lagrange measure, logarithmic strain is a more physical measure of strain. In this paper, we present a Hencky-based phenomenological finite strain kinematic hardening, non-associated constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The derivation is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, and on the use of the isotropic property of the Helmholtz strain energy function. We also use the fact that the corotational rate of the Eulerian Hencky strain associated with the socalled logarithmic spin is equal to the strain rate tensor (symmetric part of the velocity gradient tensor). Satisfying the second law of thermodynamics in the Clausius–Duhem inequality form, we derive a thermodynamically-consistent constitutive model in a Lagrangian form. In comparison with the available finite strain models in which the unsymmetric Mandel stress appears in the equations, the proposed constitutive model includes only symmetric variables. Introducing a logarithmic mapping, we also present an appropriate form of the proposed constitutive equations in the time-discrete frame. We then apply the developed constitutive model to shape memory alloys and propose a well-defined, non-singular definition for model variables. In addition, we present a nucleation-completion condition in constructing the solution algorithm. We finally solve several boundary value problems to demonstrate the proposed model features as well as the numerical counterpart capabilities

Trends to equilibrium for a nonlocal Fokker-Planck equation

We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance, towards the steady profile characterized by uniform spreading over a finite interval of the line. The result follows by combining entropy methods for quantifying the decay of the solution towards its quasi-stationary distribution, with the properties of the quasi-stationary profile

A rate-independent model for the isothermal quasi-static evolution of shape-memory materials

This note addresses a three-dimensional model for isothermal stress-induced transformation in shape-memory polycrystalline materials. We treat the problem within the framework of the energetic formulation of rate-independent processes and investigate existence and continuous dependence issues at both the constitutive relation and quasi-static evolution level. Moreover, we focus on time and space approximation as well as on regularization and parameter asymptotics