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

Finite element formulations for large strain anisotropic material with inextensible fibers

Anisotropic material with inextensible fibers introduce constraints in the mathematical formulations. This is always the case when fibers with high stiffness in a certain direction are present and a relatively weak matrix material is supporting these fibers. In numerical solution methods like the finite element method the presence of constraints - in this case associated to a possible fiber inextensibility compared to a matrix - lead to so called locking-phenomena. This can be overcome by special interpolation schemes as has been discussed extensively for volume constraints like incompressibility as well as contact constraints. For anisotropic material behaviour the most severe case is related to inextensible fibers. In this paper a mixed method is developed that can handle anisotropic materials with inextensible fibers that can be relaxed to extensible fiber behaviour. For this purpose a classical ansatz, known from the modeling of volume constraint is adopted leading stable elements that can be used in the finite strain regime.DFG/SPP/1748DFG/WR19/50-1DFG/SCHR570/23-

Response of porous SMA: a micromechanical study

Lately porous shape memory alloys (SMA) have attracted great interest as low weight materials characterized by high energy dissipation capability. In the present contribution a micromechanical study of porous SMA is proposed, introducing the simplifying hypothesis of periodic distribution of voids. The mechanical response of the heterogeneous porous medium is derived by performing nonlinear finite element micromechanical analyses considering a typical repetitive unit cell made of a circular hole in a dense SMA matrix and prescribing suitable periodicity and continuity conditions. The constitutive behavior and the dissipation energy capability of the porous Nitinol are examined for several porosity levels. Numerical applications are performed in order to test the ability of the proposed procedure to well capture the overall behavior and the key features of the special heterogeneous material

A focal plane detector design for a wide-band Laue-lens telescope

The energy range above 60 keV is important for the study of many open problems in high energy astrophysics such as the role of Inverse Compton with respect to synchrotron or thermal processes in GRBs, non thermal mechanisms in SNR, the study of the high energy cut-offs in AGN spectra, and the detection of nuclear and annihilation lines. Recently the development of high energy Laue lenses with broad energy bandpasses from 60 to 600 keV have been proposed for a Hard X ray focusing Telescope (HAXTEL) in order to study the X-ray continuum of celestial sources. The required focal plane detector should have high detection efficiency over the entire operative range, a spatial resolution of about 1 mm, an energy resolution of a few keV at 500 keV and a sensitivity to linear polarization. We describe a possible configuration of the focal plane detector based on several CdTe/CZT pixelated layers stacked together to achieve the required detection efficiency at high energy. Each layer can operate both as a separate position sensitive detector and polarimeter or work with other layers to increase the overall photopeak efficiency. Each layer has a hexagonal shape in order to minimize the detector surface required to cover the lens field of view. The pixels would have the same geometry so as to provide the best coupling with the lens point spread function and to increase the symmetry for polarimetric studies.Comment: 10 pages, 9 figure

Multi-objective optimization of nitinol stent design

Nitinol stents continuously experience loadings due to pulsatile pressure, thus a given stent design should possess an adequate fatigue strength and, at the same time, it should guarantee a sufficient vessel scaffolding. The present study proposes an optimization framework aiming at increasing the fatigue life reducing the maximum strut strain along the structure through a local modification of the strut profile.The adopted computational framework relies on nonlinear structural finite element analysis combined with a Multi Objective Genetic Algorithm, based on Kriging response surfaces. In particular, such an approach is used to investigate the design optimization of planar stent cell.The results of the strut profile optimization confirm the key role of a tapered strut design to enhance the stent fatigue strength, suggesting that it is possible to achieve a marked improvement of both the fatigue safety factor and the scaffolding capability simultaneously. The present study underlines the value of advanced engineering tools to optimize the design of medical devices

Cost-effective and accurate interlaminar stress modeling of composite Kirchhoff plates via immersed isogeometric analysis and equilibrium

The interest for composites has constantly grown in recent years, especially in the aerospace and automotive industries, as they can be moulded in complex form and geometry, as well as exhibit enhanced engineering properties. Nevertheless, despite the accelerated diffusion of laminated composites, the design of these materials is often restrained by the lack of cost-effective modeling techniques. In fact, the existing numerical strategies allowing for cheap simulations of laminated structures usually fail to directly capture out-of-plane through-the-thickness stresses, which are typically responsible for failure modes such as delamination. In this context, a stress recovery approach based on equilibrium has been recently shown to be an efficient modeling strategy in the framework of isogeometric analysis. Since immersed approaches like the finite cell method have been proven to be a viable alternative to mesh-conforming discretization for dealing with complex/dirty geometries as well as trimmed surfaces, we herein propose to extend the stress recovery approach combining the finite cell method, isogeometric analysis and equilibrium to model the out-of-plane behavior of Kirchhoff laminated plates. Extensive numerical tests showcase the effectiveness of the proposed approach

Solution of the stationary stokes and navier-stokes equations using the modified finite particle method in the framework of a least squares residual method

The present work is concerned with the solution of stationary Stokes and Navier-Stokes flows using the Modified Finite Particle Method for spatial derivative approximations and the Least Square Residual Method for the solution of the linear system deriving from the collocation procedure. The combination of such approaches permits to easily handle the numerical difficulty of the inf-sup conditions, without distinguishing between the discretizations of velocity and pressure fields. The obtained results, both in the cases of linear and non-linear flows, show the robustness of the proposed algorith

A Stability Study of some Mixed Finite Elements for Large Deformation Elasticity Problems

We consider the finite elasticity problem for incompressible materials, proposing a simple bidimensional problem for which we provide an indication on the solution stability. Furthermore, we study the stability of discrete solutions, obtained by means of some well-known mixed finite elements, and we present several numerical experiments

Hard x-ray broad band Laue lenses (80 - 600 keV): building methods and performances

We present the status of the laue project devoted to develop a technology for building a 20 meter long focal length Laue lens for hard x-/soft gamma-ray astronomy (80 - 600 keV). The Laue lens is composed of bent crystals of Gallium Arsenide (GaAs, 220) and Germanium (Ge, 111), and, for the first time, the focusing property of bent crystals has been exploited for this field of applications. We show the preliminary results concerning the adhesive employed to fix the crystal tiles over the lens support, the positioning accuracy obtained and possible further improvements. The Laue lens petal that will be completed in a few months has a pass band of 80 - 300 keV and is a fraction of an entire Laue lens capable of focusing X-rays up to 600 keV, possibly extendable down to 20 - 30 keV with suitable low absorption crystal materials and focal length. The final goal is to develop a focusing optics that can improve the sensitivity over current telescopes in this energy band by 2 orders of magnitude

A novel layered topology of auxetic materials based on the tetrachiral honeycomb microstructure

Microstructured honeycomb materials may exhibit exotic, extreme and tailorable mechanical properties, suited for innovative technological applications in a variety of modern engineering fields. The paper is focused on analysing the directional auxeticity of tetrachiral materials, through analytical, numerical and experimental methods. Theoretical predictions about the global elastic properties have been successfully validated by performing tensile laboratory tests on tetrachiral samples, realized with high precision 3D printing technologies. Inspired by the kinematic behaviour of the tetrachiral material, a newly-design bi-layered topology, referred to as bi-tetrachiral material, has been theoretically conceived and mechanically modelled. The novel topology virtuously exploits the mutual collaboration between two tetrachiral layers with opposite chiralities. The bi-tetrachiral material has been verified to outperform the tetrachiral material in terms of global Young modulus and, as major achievement, to exhibit a remarkable auxetic behaviour. Specifically, experimental results, confirmed by parametric analytical and computational analyses, have highlighted the effective possibility to attain strongly negative Poisson ratios, identified as a peculiar global elastic property of the novel bi-layered topology