Theoretical and experimental analysis of the von Mises truss subjected to a horizontal load using a new hyperelastic model with hardening

The von Mises truss has been widely studied in the literature because of its numerous applications in multistable and morphing structures. The static equilibrium of this structure was typically addresses by considering only geometric nonlinearities. However, Falope et al. (2021) presented an entirely nonlinear solution in finite elasticity and demonstrated that material nonlinearities play an important role in the prediction of both snap-through and Euler buckling. In such work, the von Mises truss was subjected to a vertical load and thus the system was symmetric and the deformations were relatively small. The present contribution extends the investigation to the case of a horizontal load, which is much more complex due to asymmetry and very large deformations. Since most rubbers employed in technological applications exhibit hardening under large stretches, we propose a new hyperelastic model capable of reproducing this behavior. The advantage of such model compared to the ones available in the literature is that the equilibrium solution maintains a straightforward mathematical form, even when considering compressibility of the material. In addition, in this work we present a new formulation in nonlinear elasticity to predict Euler buckling. The formulation takes into account shear deformation. The analytical prediction agrees well with both finite element (FE) and experimental results, thus demonstrating the accuracy of the proposed model

Analytical and experimental study of snap-through instability in truss structures

Abstrac

Buckling capacity model for timber screws loaded in compression: Experimental, analytical and FE investigations

This paper investigates the buckling of screws loaded in compression inserted into timber members. Screws are often used as a reinforcement in timber structures. However, under compression forces, they are prone to axial buckling. The current model for the screw buckling, enclosed in the EC5 proposal, is based on the general framework of EC3 for the instability of compressed steel members. The main shortcomings of the current formulation for the buckling of screws are the following. (1) The analytical expression for calculating the theoretical buckling load does not follow the observed modes. (2) Due to the need for dedicated studies, the value of the imperfection coefficient is arbitrarily chosen. This paper fills the above gaps. Firstly, a simple analytical expression for predicting the buckling of screws is proposed and validated against experimental and finite element (FE) findings. Furthermore, the formulation adopts a more accurate expression for lateral deformation based on experimental observation. Secondly, a FE model calibrated on experimental tests is used to estimate the defect coefficients of the instability curves as a function of the amplitude of the geometric defects of the screw, expressed as a fraction of its length. Finally, a Markov chain Monte Carlo analysis is carried out to simulate the capacity of screws with different sizes, assuming the uncertainty of all input parameters sampled from suitable probability distributions. The results are used to validate the proposed deterministic capacity model and estimate the uncertainty factors of the design equation

A degrading Bouc\u2013Wen model for the hysteresis of reinforced concrete structural elements

This paper presents a smooth hysteresis model for reinforced concrete (RC) structural elements based on the differential equation of the Bouc?Wen model. Stiffness degradation and strength degradation are defined by introducing a damage index that includes both dissipated energy and maximum displacement. The pinching effect acts directly on the stiffness of the system and is controlled by an activation energy. The degrading functions are connected to the actual processes with which the damage occurs, thereby giving each parameter a physical meaning. The simple formulation of the model allows a straightforward identification of the best-fitting parameters and an easy interpretation of the results. Applications to the cyclic behaviour of RC structural elements demonstrate that the model is well capable of describing complex hysteretic behaviours involving degradation and pinching effects

The Northern Cross Fast Radio Burst project -- III. The FRB-magnetar connection in a sample of nearby galaxies

Fast radio bursts (FRBs) are millisecond radio transients observed at cosmological distances. The nature of their progenitors is still a matter of debate, although magnetars are invoked by most models. The proposed FRB-magnetar connection was strengthened by the discovery of an FRB-like event from the Galactic magnetar SGR J1935+2154. In this work, we aim to investigate how prevalent magnetars such as SGR J1935+2154 are within FRB progenitors. We carried out an FRB search in a sample of seven nearby (< 12 Mpc) galaxies with the Northern Cross radio telescope for a total of 692 h. We detected one 1.8 ms burst in the direction of M101 with a fluence of $58 \pm 5$ Jy ms. Its dispersion measure of 303 pc cm$^{-3}$ places it most-likely beyond M101. Considering that no significant detection comes indisputably from the selected galaxies, we place a 38 yr$^{-1}$ upper limit on the total burst rate (i.e. including the whole sample) at the 95\% confidence level. This upper limit constrains the event rate per magnetar $\lambda_{\rm mag} < 0.42$ magnetar$^{-1}$ yr$^{-1}$ or, if combined with literature observations of a similar sample of nearby galaxies, it yields a joint constraint of $\lambda_{\rm mag} < 0.25$ magnetar$^{-1}$ yr$^{-1}$. We also provide the first constraints on the expected rate of FRBs hypothetically originating from ultraluminous X-ray (ULX) sources, since some of the galaxies observed during our observational campaign host confirmed ULXs. We obtain $< 13$ yr$^{-1}$ per ULX for the total sample of galaxies observed. Our results indicate that bursts with energies $E>10^{34}$ erg from magnetars like SGR J1935+2154 appear more rarely compared to previous observations and further disfavour them as unique progenitors for the cosmological FRB population, leaving more space open to the contribution from a population of more exotic magnetars, not born via core-collapsed supernovae.Comment: 9 pages, 4 figures, published in A&

Evolution of spin excitations from bulk to monolayer FeSe

In ultrathin films of FeSe grown on SrTiO (FeSe/STO), the superconducting transition temperature T is increased by almost an order of magnitude, raising questions on the pairing mechanism. As in other superconductors, antiferromagnetic spin fluctuations have been proposed to mediate SC making it essential to study the evolution of the spin dynamics of FeSe from the bulk to the ultrathin limit. Here, we investigate the spin excitations in bulk and monolayer FeSe/STO using resonant inelastic x-ray scattering (RIXS) and quantum Monte Carlo (QMC) calculations. Despite the absence of long-range magnetic order, bulk FeSe displays dispersive magnetic excitations reminiscent of other Fe-pnictides. Conversely, the spin excitations in FeSe/STO are gapped, dispersionless, and significantly hardened relative to its bulk counterpart. By comparing our RIXS results with simulations of a bilayer Hubbard model, we connect the evolution of the spin excitations to the Fermiology of the two systems revealing a remarkable reconfiguration of spin excitations in FeSe/STO, essential to understand the role of spin fluctuations in the pairing mechanism

Analisi di strutture reticolari in elasticità finita con applicazione a materiali nanostrutturali

Le strutture reticolari con non linearità geometriche e materiali vengono spesso analizzate mediante approcci numerici. Soluzioni dell’equilibrio in forma chiusa si trovano solamente per casi semplici di riferimento e sotto l’ipotesi di materiale elastico lineare. Tale ipotesi non è consistente con l’effettivo comportamento di solidi reali soggetti a grandi deformazioni. Pertanto, il lavoro di tesi riporta una formulazione analitica interamente non lineare per il problema dell’equilibrio e stabilità di strutture reticolari. Le aste della struttura reticolare sono riguardate come solidi iperelastici di materiale omogeneo, comprimibile e isotropo. I campi di spostamento e deformazione sono considerati grandi, senza alcuna restrizione. Il problema a valori al contorno viene risolto, ricavando così le equazioni che governano l’equilibrio. Di conseguenza, la stabilità delle configurazioni di equilibrio viene studiata attraverso un criterio energetico. La formulazione è dapprima sviluppata per il traliccio di von Mises (arco a tre cerniere), il quale rappresenta il caso più semplice di struttura reticolare. Nonostante la sua apparente semplicità, tale sistema esibisce diversi tipi di comportamento post-critico, tra cui snap-through e biforcazione. La trattazione viene poi estesa al caso della struttura reticolare a tre aste, la quale rappresenta un importante problema di riferimento, poiché mostra diversi punti critici e configurazioni di equilibrio stabili non simmetriche. Si riportano alcune applicazioni della teoria a materiali polimerici, utilizzando il modello di Mooney-Rivlin per l’energia di deformazione elastica delle aste della struttura. I risultati hanno particolare importanza per quanto concerne la validazione di simulazioni agli elementi finiti o di altre procedure numeriche. La trattazione non lineare per l’analisi di strutture reticolari in elasticità finita si applica anche allo studio del comportamento meccanico di materiali nanostrutturali. Nello specifico, in questo lavoro si analizza il grafene soggetto a grandi deformazioni piane. Gli atomi del reticolo cristallino esagonale rappresentano nodi connessi tra loro da elementi strutturali continui, le cui caratteristiche sono determinate attraverso un’equivalenza energetica con il potenziale interatomico dei legami chimici. L’equilibrio viene risolto per i casi di carico uniassiale ed equibiassiale. I risultati del lavoro dimostrano l’isotropia del grafene per piccole deformazioni, proprietà che viene persa per grandi deformazioni dando origine a un comportamento anisotropo. Si osservano inoltre soluzioni multiple e instabili dopo valori critici di deformazione. A differenza di molti altri studi in letteratura, il modello presentato in questo lavoro di tesi tiene conto delle non linearità geometriche e materiali. Ciò è necessario per una modellazione accurata del comportamento meccanico del grafene, in quanto questo materiale può raggiungere deformazioni a rottura superiori a 15-20%. I risultati dello studio permettono quindi di approfondire la comprensione dei meccanismi di deformazione del grafene e del suo complesso comportamento meccanico.The analysis of truss structures involving geometric and material nonlinearities is often performed by means of numerical approaches. Closed-form solutions of the equilibrium are provided only for simple benchmark problems, under the inconsistent hypothesis of linear constitutive behavior of the material. This hypothesis does not reflect the actual behavior of solids subjected to large deformations. Therefore, in this thesis, a fully nonlinear analytical formulation of the equilibrium and stability of truss structures is presented. The bars of the truss are regarded as hyperelastic bodies composed of a homogeneous, compressible and isotropic material. Both displacement and deformation fields are large, without any restriction. The boundary-value problem is written and the equations governing the equilibrium are derived. The stability of the equilibrium configurations is assessed through an energy criterion. The formulation is firstly obtained for the von Mises (or two-bar) truss, which is the simplest case of truss structure. Despite its apparent simplicity, it exhibits various types of post-critical behaviors, such as snap-through and bifurcation. The formulation is then extended to the three-bar truss, which is an important benchmark test because it shows a number of critical points and stable asymmetric configurations. Several applications to rubber-like materials are performed by assuming a Mooney-Rivlin law for the stored energy function of the bars. The results are of great importance for the validation of finite element simulations and other numerical procedures. The nonlinear formulation for the analysis of truss structures can be applied to the study of the mechanical behavior of nanostructured materials. In particular, this work is focused on the response of graphene subjected to large in-plane deformations. The atoms of the graphene lattice structure are viewed as nodes connected by continuum elements, whose properties are determined through an energy equivalence with the interatomic potential of the chemical bonds. The equilibrium solutions are given for the cases of uniaxial and equibiaxial tensile loads. The results show that graphene is isotropic only for small deformations, while anisotropy arises for large deformations. Multiple and unstable solutions are found after critical values of deformation. Differently from many other studies in literature, the model presented in this work accounts for both geometric and material nonlinearities. This is necessary for an accurate analysis of the mechanical behavior of graphene, because it can easily experience strains larger than 15-20% prior to failure. The results allow therefore to deepen the understanding of the mechanics of deformation of graphene and provide insights into its complex mechanical behavior

Equilibrium Paths for von Mises Trusses in Finite Elasticity

This paper deals with the equilibrium problem of von Mises trusses in nonlinear elasticity. A general loading condition is considered and the rods are regarded as hyperelastic bodies composed of a homogeneous isotropic material. Under the hypothesis of homogeneous deformations, the finite displacement fields and deformation gradients are derived. Consequently, the Piola-Kirchhoff and Cauchy stress tensors are computed by formulating the boundary-value problem. The equilibrium in the deformed configuration is then written and the stability of the equilibrium paths is assessed through the energy criterion. An application assuming a compressible Mooney-Rivlin material is performed. The equilibrium solutions for the case of vertical load present primary and secondary branches. Although, the stability analysis reveals that the only form of instability is the snap-through phenomenon. Finally, the finite theory is linearized by introducing the hypotheses of small displacement and strain fields. By doing so, the classical solution of the two-bar truss in linear elasticity is recovered.This paper deals with the equilibrium problem of von Mises trusses in nonlinear elasticity. A general loading condition is considered and the rods are regarded as hyperelastic bodies composed of a homogeneous isotropic material. Under the hypothesis of homogeneous deformations, the finite displacement fields and deformation gradients are derived. Consequently, the Piola-Kirchhoff and Cauchy stress tensors are computed by formulating the boundary-value problem. The equilibrium in the deformed configuration is then written and the stability of the equilibrium paths is assessed through the energy criterion. An application assuming a compressible Mooney-Rivlin material is performed. The equilibrium solutions for the case of vertical load present primary and secondary branches. Although, the stability analysis reveals that the only form of instability is the snap-through phenomenon. Finally, the finite theory is linearized by introducing the hypotheses of small displacement and strain fields. By doing so, the classical solution of the two-bar truss in linear elasticity is recovered

degrading Bouc-Wen model parametrers identification under cyclic load

The Bouc–Wen model of hysteresis is used in structural engineering to describe a wide range of nonlinear hysteretic systems, as consequence of its capability to produce a variety of hysteretic patterns. This research focuses on the application of the Bouc–Wen model to predict the hysteretic behaviour of reinforced concrete bridge piers. The purpose is to identify the optimal values of the parameters so that the output of the model matches as well as possible the experimental data. Two repaired and retrofitted reinforced concrete bridge pier specimens (in a 1:6 scale of a real bridge pier) tested physically in a laboratory are considered in this paper. An identification of Bouc–Wen model’s parameters is performed using the force–displacement experimental data obtained after cyclic loading tests on these two specimens. The original model involves many parameters and complex pinching and degrading functions and this makes the identification solution unmanageable and with numerical problems. Furthermore, from a computational point of view, the identification takes too much time. The novelty of this work is the proposal of a simplification of the model allowed by: simpler pinching and degrading functions; reduction of the number of parameters. The latter innovation is much effective in reducing computational efforts and is performed after a deep study of the mechanical effects of each parameter on the pier response. This simplified model is implemented in a MATLAB code and the numerical results are well fitting the experimental ones and are reliable in terms of manageability, stability, and computational time