Simplified modelling of chiral lattice materials with local resonators

A simplified model of periodic chiral beam-lattices containing local resonators has been formulated to obtain a better understanding of the influence of the chirality and of the dynamic characteristics of the local resonators on the acoustic behavior. The simplified beam-lattices is made up of a periodic array of rigid heavy rings, each one connected to the others through elastic slender massless ligaments and containing an internal resonator made of a rigid disk in a soft elastic annulus. The band structure and the occurrence of low frequency band-gaps are analysed through a discrete Lagrangian model. For both the hexa- and the tetrachiral lattice, two acoustic modes and four optical modes are identified and the influence of the dynamic characteristics of the resonator on those branches is analyzed together with some properties of the band structure. By approximating the generalized displacements of the rings of the discrete Lagrangian model as a continuum field and through an application of the generalized macro-homogeneity condition, a generalized micropolar equivalent continuum has been derived, together with the overall equation of motion and the constitutive equation given in closed form. The validity limits of the micropolar model with respect to the dispersion functions are assessed by comparing the dispersion curves of this model in the irreducible Brillouin domain with those obtained by the discrete model, which are exact within the assumptions of the proposed simplified model

Second-order homogenization of periodic materials based on asymptotic approximation of the strain energy: formulation and validity limits

In this paper a second-order homogenization approach for periodic material is derived from an appropriate representation of the down-scaling that correlates the microdisplacement field to the macro-displacement field and the macro-strain tensors involving unknown perturbation functions. These functions take into account of the effects of the heterogeneities and are obtained by the solution of properly defined recursive cell problems. Moreover, the perturbation functions and therefore the micro-displacement fields result to be sufficiently regular to guarantee the anti-periodicity of the traction on the periodic unit cell. A generalization of the macro-homogeneity condition is obtained through an asymptotic expansion of the mean strain energy at the micro-scale in terms of the microstructural characteristic size e; the obtained overall elastic moduli result to be not affected by the choice of periodic cell. The coupling between the macro- and microstress tensor in the periodic cell is deduced from an application of the generalised macrohomogeneity condition applied to a representative portion of the heterogeneous material (cluster of periodic cell). The correlation between the proposed asymptotic homogenization approach and the computational second-order homogenization methods is obtained through an approximation of the macrodisplacement field based on a second-order Taylor expansion. The form of the overall elastic moduli obtained through the two homogenization approaches, here proposed, is analyzed and the differences are highlighted

Wave propagation in non-centrosymmetric beam-lattices with lumped masses: discrete and micropolar modelling

The in-plane acoustic behavior of non-centrosymmetric lattices having nodes endowed with mass and rotational inertia and connected by massless ligaments with asymmetric elastic properties has been analyzed through a discrete model and a continuum micropolar model. In the first case the propagation of harmonic waves and the dispersion functions have been obtained by the discrete Floquet–Bloch approach. It is shown that the optical branch departs from a critical point with vanishing group velocity and is decreasing for increasing the norm of the wave vector. A micropolar continuum model has been derived through a continualization method based on a down-scaling law from a second-order Taylor expansion of the generalized macro-displacement field. It is worth noting that the second order elasticity tensor coupling curvatures and micro-couples turns out to be negative-definite also in the general case of non-centrosymmetric lattice. The eigenvalue problem governing the harmonic propagation in the micropolar non-centrosymmetric continuum results in general characterized by a hermitian full matrix that is exact up to the second order in the wave vector. Examples concerning square and equilateral triangular lattices have been analyzed and their acoustic properties have been derived with the discrete and continuum models. The dependence of the Floquet–Bloch spectra on the lattice non-centrosymmetry is shown together with validity limits of the micropolar model. Finally, in consideration of the negative definiteness of the second order elastic tensor of the micropolar model, the loss of strong hyperbolicity of the equation of motion has been investigated

A micropolar model for the analysis of dispersive waves in chiral mass-in-mass lattices

The possibility of obtaining band gap structures in chiral auxetic lattices is here considered and applied to the case of inertial locally resonant structures. These periodic materials are modelled as beam-lattices made up of a periodic array of rigid rings, each one connected to the others through elastic slender ligaments. To obtain low-frequency stop bands, elastic circular resonating inclusions made up of masses located inside the rings and connected to them through an elastic surrounding interface are considered and modeled. The equations of motion are obtained for an equivalent homogenized micropolar continuum and the overall elastic moduli and the inertia terms are given for both the hexachiral and the tetrachiral lattice. The constitutive equation of the beam lattice given by the Authors [15] are then applied and a system of six equations of motion is obtained. The propagation of plane waves travelling along the direction of the lines connecting the ring centres of the lattice is analysed and the secular equation is derived, from which the dispersive functions may be obtained

Multi-parametric sensitivity analysis of the band structure for tetrachiral inertial metamaterials

Tetrachiral materials are characterized by a cellular microstructure made by a periodic pattern of stiff rings and flexible ligaments. Their mechanical behaviour can be described by a planar lattice of rigid massive bodies and elastic massless beams. The periodic cell dynamics is governed by a monoatomic structural model, conveniently reduced to the only active degrees-of-freedom. The paper presents an explicit parametric description of the band structure governing the free propagation of elastic waves. By virtue of multiparametric perturbation techniques, sensitivity analyses are performed to achieve analytical asymptotic approximation of the dispersion functions. The parametric conditions for the existence of full band gaps in the low-frequency range are established. Furthermore, the band gap amplitude is analytically assessed in the admissible parameter range. In inertial tetrachiral metamaterials, stop bands can be opened by the introduction of intra-ring resonators. Perturbation methods can efficiently deal with the consequent enlargement of the mechanical parameter space. Indeed high-accuracy parametric approximations are achieved for the band structure, enriched by the new optical branches related to the resonator frequencies. In particular, target stop bands in the metamaterial spectrum are analytically designed through the asymptotic solution of inverse spectral problems. Subjects: Materials Science (cond-mat.mtrl-sci) Cite as: arXiv:1706.08754 [cond-mat.mtrl-sci] (or arXiv:1706.08754v1 [cond-mat.mtrl-sci] for this version

Damped Bloch Waves in Lattices Metamaterials with Inertial Resonators

The present paper is focused on the acoustic behaviour of periodic beam-lattices metamaterials containing inertial viscoelastic resonators connected with elastic slender ligaments. A simplified model is considered where the ligaments are considered as massless and the viscoelastic resonators are contained inside rigid rings located at the lattice nodes. Firstly, a Lagrangian model is formulated in order to assess the influence of the dynamic and viscoelastic properties of the resonators on the acoustic behaviour. An equivalent generalized micropolar model is obtained through a continualization of the discrete model and the constitutive tensors and the equation of motion are formulated. The propagation of harmonic waves is assumed and the Christoffel equation for both the discrete and the continuum model are obtained. It is shown that the hermitian matrix governing the Christoffel equation of the Lagrangian model is approximated by the corresponding one from the micropolar model with an error O (|k|3

Identifying the Best Haploidentical Donor: Are We There?

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Overall thermomechanical properties of layered materials for energy devices applications

This paper is concerned with the analysis of effective thermomechanical properties of multi- layered materials of interest for solid oxide fuel cells (SOFC) and lithium ions batteries fabrication. The recently developed asymptotic homogenization procedure is applied in order to express the overall thermoelastic constants of the first order equivalent continuum in terms of microfluctuations functions, and these functions are obtained by the solution of the corresponding recursive cell problems. The effects of thermal stresses on periodic multi-layered thermoelastic composite reproducing the characteristics of solid oxide fuel cells (SOFC-like) are studied assuming periodic body forces and heat sources, and the solution derived by means of the asymptotic homogenization approach is compared with the results obtained by finite elements analysis of the associate heterogeneous material

Early hemopoietic progenitors in the peripheral blood of patients with severe aplastic anemia (SAA) after treatment with antilymphocyte globulin (ALG), cyclosporin-A and G-CSF

ABSTRACT © F e r r a t a S t o r t i F o u n d a t i o n A. Bacigalupo et al. 134 administration of G-CSF in SAA patients leads to mobilization of hemopoietic progenitors, which are then available for analysis and can actually be harvested at weekly leukophereses and cryopreserved. 14,15 Human LTC-ICs share many of the characteristics of murine LTC-ICs, which have proven in vivo long-term repopulating ability. Materials and Methods Patients Clinical data on the patients are presented in Response Patients were classified as complete responders if they were transfusion independent with a hemoglobin level of ≥ 11 g/dL, a neutrophil count greater than 1.5ϫ10 9 /L, and a platelet count greater than 100ϫ10 9 /L; partial responders were transfusion independent with a hemoglobin level of ≥ 8 g/dL, a neutrophil count of >0.5ϫ10 9 /L, and a platelet count of >20ϫ10 9 /L. Persistence of transfusion dependence was taken as evidence of no response. Normal donors Sixteen leukaphereses from 7 normal donors treated with G-CSF (10 ug/kg/day for 5 days) were used as controls. These volunteers underwent the procedure as matched donors for their HLA-identical sibling. Informed consent was obtained from SAA patients and normal donors, and investigations were approved by our Ethical Committee. Flow cytometry PB cells recovered from each leukaphereses were processed with a work station Coulter Q-Prep (Coulter Corporated Hialeah, FL) in order to lyse erythrocytes and to fix white blood cells. Cell surface antigens were detected by direct immunofluorescence using a CD34 HPCA-2 for progenitor cells (Becton Dickinson, Mountainview, CA). Fluorescence was analyzed with an XL Coulter. Isotypically matched mouse Ig directly conjugated to fluorescein isothiocyanate (FITC) or phycoerythrin (PE) were used as negative controls in all experiments. Overall, 10 4 events were acquired on an FS (Forward Scatter) x SS (Side Scatter) diagram on all populations except platelets and debris. Immediately after staining, cells were sorted on a Coulter Epics 753 dual laser flow cytometer (Coulter Electronics, Hialeah, FL) equipped with a CICERO high-speed computer (Cytomation, Fort Collins, CO). FITC and PE were excited using the 488nm wavelength from a dedicated 5 W argon laser. In this staining protocol, it was still possible to obtain CD34 + HLA-DR + cells, even though both HLA-DR (IgG1 isotype, Becton-DickinsonImmunocytometry System) and CD15 were FITC conjugated (FITC-conjugated mouse antihuman-LeuM1, Becton-Dickinson). 18 Functional assays Light density cells from each leukapheresis were assayed for clonogenic precursors. Briefly 10 5 MNC were plated in: A. 1.1 mL consisting of Iscove's modified Dulbecco's medium (IMDM, GIBCO BRL, Life Technologies LTD, UK) + 0.9% methylcellulose (Sigma Chemical, St.Louis, MO, USA) + 30% fetal calf serum (FCS, Gibco) + 100 ng of rhGM-CSF (Sandoz, Basel, CH); B. 1.5 ml consisting of IMDM + 0.9%methylcellulose + 30% FCS + 1% bovine serum albumin (BSA, Sigma) + 10 -4 M mercaptoethanol (ME, Sigma) + rhGM-CSF (10 ng) + rhIL3 (10 ng Sandoz) + rhG-CSF (10 ng) + rhEPO (4U Cilag AG, Schaffhauser, CH) + SCF (50 ng Genzyme Corporation, Cambridge, UK). After 14 days of incubation in a humidified atmosphere at 37°C in 5% CO 2 , colonies were classified and counted using an inverted microscope (Zeiss, Germany). Sorted cells were cultured in the presence of PIXY and SCF as described. 18 MNC and freshly sorted cells were cultured in suspensions containing different cytokines and scored according to previously established criteria. 19 LTC-IC assays were performed by seeding an aliquot (usually 5ϫ10 6 MNC/flask) of light density cells over a feeder layer of irradiated (1.5 cGy) normal marrow cells. These were subcultured from adherent layers of previously established 4-week-old LTCs. LTC-ICs were maintained for 3 days at 37°C, then switched to 33°C and fed weekly by replacing half the growth medium (IMDM + 12.5% horse serum (HS, Gibco) + 12.5% FCS + 10 -4 M ME + 10 -6 M hydrocortisone, Sigma) containing half of the nonadherent cells with fresh growth medium. After 5 weeks, adherent cells were trypsinized and combined with the nonadherent fraction. These harvested cells were washed and assayed for clonogenic precursors in standard methylcellulose cultures (B). As previously reported, 14 the number of LTC-ICs present in the starting cell suspension was shown to be equal to the total CFC content of the 5-week-old LTC assay divided by 4. Statistical analysis Chi-square, Student's t-test and Mann-Whitney rank sum test were used to analyze the data. Results Patients All patients completed the designed course of IS treatment and underwent leukaphereses, which © F e r r a t a S t o r t i F o u n d a t i o n Early hemopietic progenitors in PB of treated SAA patients 135 were scheduled weekly starting on day +30 of treatment. One patient who did not become transfusion independent after a first course was treated again with a second course of ALG, CyA and G-CSF, and then a third time with CyA and G-CSF. He therefore underwent 3 courses of leukaphereses ( Flow cytometry Flow cytometry demonstrated a higher frequency of CD3 + cells Committed progenitors Samples from each apheresis were assayed for in vitro granulocytic, erythroid and multipotent progenitors (CFU-GM, BFU-E and CFU-GEMM). In our experiments we were able to grow mainly CFU-GM, with very low numbers of other colonies (in percentages: 25-100% CFU-GM, 0-30% BFU-E and 0-19% CFU-GEMM). Five patients showed significant increments in white blood cell (WBC) counts (>10ϫ10 9 /L, Early progenitors HPP-CFC were studied in 4 patients (#1, 4, 5, 6); they grew at a frequency of 0-3.4/10 5 MNC, in one case in the absence of committed progenitors. In addition, we studied LTC-ICs in 18 leukaphereses from 4 patients: in 7/18 samples LTC-ICs were present at low frequency (range: 0.4-2/10 6 MNC) when compared with collections from G-CSF-treated normal donors (range: 5.4-130/10 6 MNC); p<0.00001) Cell sorting Cells derived from 3 aphereses were sorted into CD34 + DR + and CD34+DR -CD15 -; these were then cultured in vitro with different cytokine combinations. CD34 + DR + cells showed evident increments in GM, GEMM, BFU-E and HPP colony formation Discussion It has been always difficult to design in vitro colony assays in patients with SAA, mainly because of the lack of bone marrow cells to initiate such studies. We have described the presence of hemopoietic progenitors in the peripheral blood of many SAA patients after treatment with ALG-CyA and prolonged administration of rhG-CSF. 13 By performing weekly leukaphereses in such patients, one can collect large numbers of cells which can be cryopreserved and are, at the same time, available for in vitro assays. The aim of the present study was to assess phenotypic and functional properties of such PBHP. As regards the phenotype, SAA PB cells contained large numbers of CD3 + cells, significantly more than 136 controls (p=0.006), with an inverted CD4/CD8 ratio. This is in keeping with reports of an excess of suppressor cells in SAA, When SAA cells were plated in vitro we grew prevalently CFU-GM in numbers which were significantly lower than in normal controls, with a median 28-fold reduction. BFU-E and CFU-GEMM were seen less frequently in both SAA patients and normal controls, possibly as a result of in vivo triggering with G-CSF. LTC-ICs were studied in 18 leukaphereses and scored in 7 of these, though in small numbers: they were significantly fewer than in controls (0-2 vs 5-130/10 6 MNC). In one of these patients LTC-ICs were present in the blood in the absence of peripheral blood and marrow CFU-GM, and this was also seen for HPP colonies. Therefore primitive progenitors may be present in the absence of committed progenitors, as previously suggested by hematologic reconstitution in most SAA patients in spite of no colony formation from bone marrow cells. © F e r r a t a S t o r t i F o u n d a t i o n or whether their survival is limited. When we assessed the total yield of leukaphereses from SAA patients we recovered reduced numbers of CFU-GM (p=0.05), although SAA patients underwent a median of 5 vs 2 leukaphereses performed with normal controls. It is difficult to say whether these cryopreserved cells are suitable for an autotransplant, a possibility one may wish to consider in the case of poor or absent hematologic reconstitution or in the case of evolution of the disease into overt myelodysplasia or leukemia. Highdose chemotherapy has been shown do induce complete remissions when given to SAA patients, though at a cost of prolonged periods of neutropenia; 24 the infusion of autologous cryopreserved progenitors may shorten the duration of chemotherapy-induced aplasia. The total CFU-GM content recovered from leukaphereses was in the range reported to allow hemopoietic reconstitution if infused after ablative chemo-radiotherapy, and so was the LTC-IC content in 2 out of 4 patients studied. Another important issue may be to consider blood progenitor cell mobilization as a prediction or as a measure of clinical improvement. Indeed two complete responders (#5 and #6) mobilized high numbers of CFU-GM; one patient (#2) mobilized very few CFU-GM and showed no response. In patient #3 clonogenic progenitors appeared in the blood after the second course of IS treatment and he achieved a durable response after the third course. This suggests that the presence of committed and early progenitors in the blood during IS treatment may be predictive of clinical response, in keeping with data reported by Finally, early hemopoietic progenitors mobilized with G-CSF may reseed the marrow 26 and contribute to hematologic recovery in SAA patients undergoing treatment with ALG and Cy A, as indicated by the high response rate seen with this regimen and a survival rate greater than 90%. 9 It may be possible to prove this hypothesis by using the neomycin resistance gene to mark circulating progenitors. 27 In conclusion, this study suggests that very early progenitors are found in the peripheral blood of patients with SAA after prolonged G-CSF administration and after treatment with IS therapy. The number of such early precursors is small, and the majority of cells exhibit the features of committed progenitors. It remains to be determined whether these cells contribute to hematologic recovery and whether they can be used for autografting. Early hemopietic progenitors in PB of treated SAA patients References 137 © F e r r a t a S t o r t i F o u n d a t i o

Auxetic behavior and acoustic properties of microstructured piezoelectric strain sensors

The use of multifunctional composite materials adopting piezo-electric periodic cellular lattice structures with auxetic elastic behavior is a recent and promising solution in the design of piezoelectric sensors. In the present work, periodic anti-tetrachiral auxetic lattice structures, characterized by different geometries, are taken into account and the mechanical and piezoelectrical response are investigated. The equivalent piezoelectric properties are obtained adopting a first order computational homogenization approach, generalized to the case of electro-mechanical coupling, and various polarization directions are adopted. Two examples of in-plane and out-of-plane strain sensors are proposed as design concepts. Moreover, a piezo-elasto-dynamic dispersion analysis adopting the Floquet–Bloch decomposition is performed. The acoustic behavior of the periodic piezoelectric material with auxetic topology is studied and possible band gaps are detected