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

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

Local Manufacturing Multiplier and Human Capital in Italian Local Labor Markets

This paper quantifies the effect of a local labor demand shock in the tradable sector on the employment in the non-tradable sector for Italy. Following Moretti (2010) and Moretti and Thulin (2013) we analyse for Italy\u2019s case the effect on the employment in tradable and nontradable sector due to an exogenous shift in the number of jobs in the tradable sector in local labor market area. Using Italian census data at LLM level for 1981, 1991, 2001 and 2011, evidences suggest that, on average, the effect of an exogenous shift in local tradable employment upon non-tradable employment is zero. We believe that in this baseline model the absence of evidence of a positive impact of new jobs in the tradable sectors on the remaining parts of the local economy can be explained in particular focusing on excess of regulation, on labor mobility, on the lack of variability of wages, on the rigidity of housing supply and on the Italian familistic welfare system. In addition to the baseline model, we account for the technology level of the manufacturing sector using the EUROSTAT classification. We want to test if the jobs multiplier effect in the high-tech sector is significantly different/higher than for almost any other sector. High-tech workers, with their high opportunity cost of time, are expected to be net buyers of non-tradable goods. Accounting for the technology level, as Moretti, Moretti and Thulin predict, we find evidence that high-tech jobs have a positive and significant local employment multiplier of 0.7 additional jobs. These results bear important implications for the Italian growth path and its regional divide, in terms both of labor market and industry competitiveness

Reptile species composition in the Middle Gurguéia and comparison with inventories in the eastern Parnaíba River Basin, State of Piauí, Brazil

The reptile diversity of the Middle Gurguéia River Basin in southern Piauí, Brazil, is little known. The rapid expansion of agriculture in the region is converting the Cerrado and Caatinga into large farming areas, which threatens biodiversity and hastens its loss. In this study, 68 specimens of reptiles from a university collection were examined, comprising 29 species: ten lizards, one amphisbaenian, 15 snakes, two turtles and one crocodilian. They were collected from five locations in the Middle Gurguéia Basin, a region not previously evaluated for reptiles. The most abundant species is a member of Tropidurus. Comparison with eight other areas in the eastern Parnaíba Basin indicated that the diversity of reptiles in the Middle Gurguéia is similar to that in other Caatinga-Cerrado ecotone areas. The reptile assemblage in the eastern Parnaíba Basin comprises 100 species of reptiles: 39 lizards, five amphisbaenians, 50 snakes, four chelonians and two crocodilians. This study expanded the known distributions of some reptiles and recorded the first occurrence of Helicops leopardinus (Schlegel, 1837) for Piauí. A cluster analysis showed that the reptile composition concords with the habitat where species were found, i.e. Cerrado, Caatinga or ecotone. Studies that associate habitat structure with each species are essential to propose efficient strategies for reptile management and conservation for the entire Parnaíba River Basin, mostly in areas that are not yet protected

Explicit finite element implementation of a shape memory alloy constitutive model and associated analyses

Shape memory alloys (SMA) represent an important class of smart metallic materials employed in various innovative applications thanks to their unique thermomechanical behavior. Since the 1980s, several SMA constitutive models have been proposed and implemented into both commercial and academic finite element analysis software tools. Such models have demonstrated their reliability and robustness in the design and optimization of a wide variety of SMA-based components. However, most models are implemented using implicit integration schemes, thus limiting their applicability in highly nonlinear analyses. The objective of this work is to present a novel explicit integration scheme for the numerical implementation of the three-dimensional Souza-Auricchio model, a phenomenological model able to reproduce the primary SMA responses (i.e., pseudoelasticity and shape memory effect). The model constitutive equations are formulated by adopting the continuum thermodynamic theory with internal variables, following a plasticity-like approach. An elastic predictor-inelastic corrector scheme is here used to solve the time-discrete non-linear constitutive equations in the explicit framework. The proposed algorithm is investigated through several benchmark boundary-value problems of increasing complexity, considering both pseudoelastic and shape memory response in quasi-static conditions; a comparison with an implicit integration scheme is also performed. Such numerical tests demonstrate the ability of the algorithm to reproduce key material behaviors with effectiveness and robustness. Particularly, the analysis of SMA cables demonstrates the effectiveness of the explicit algorithm to solve complex problems involving widespread nonlinear contact, which prevent the convergence of the implicit scheme. Details such as mass-scaling options are also discussed