Statistical equilibrium in simple exchange games I

Simple stochastic exchange games are based on random allocation of finite resources. These games are Markov chains that can be studied either analytically or by Monte Carlo simulations. In particular, the equilibrium distribution can be derived either by direct diagonalization of the transition matrix, or using the detailed balance equation, or by Monte Carlo estimates. In this paper, these methods are introduced and applied to the Bennati-Dragulescu-Yakovenko (BDY) game. The exact analysis shows that the statistical-mechanical analogies used in the previous literature have to be revised.Comment: 11 pages, 3 figures, submitted to EPJ

An Experimental Compliance Calibration Strategy for Mixed-mode Bending Tests

AbstractWe have developed an enhanced beam theory model of the mixed-mode bending (MMB) test, where the delaminated specimen is schematised as an assemblage of sublaminates connected by an elastic interface. We show how the interface parameters can be estimated through an experimental compliance calibration strategy. First, double cantilever beam (DCB) and end notched flexure (ENF) tests are conducted and the specimens’ compliance is measured. Then, a nonlinear least squares fitting procedure furnishes the values of the elastic interface constants. Such calibrated values can be used to interpret the results of MMB tests

A mechanical model for FRP-strengthened beams in bending

We analyse the problem of a simply supported beam, strengthened with a fibre-reinforced polymer (FRP) strip bonded to its intrados and subjected to bending couples applied to its end sections. A mechanical model is proposed, whereby the beam and FRP strip are modelled according to classical beam theory, while the adhesive and its neighbouring layers are modelled as an interface having a piecewise linear constitutive law defined over three intervals (elastic response – softening response – debonding). The model is described by a set of differential equations with appropriate boundary conditions. An analytical solution to the problem is determined, including explicit expressions for the internal forces, displacements and interfacial stresses. The model predicts an overall non-linear mechanical response for the strengthened beam, ranging over several stages: from linearly elastic behaviour to damage, until the complete detachment of the FRP reinforcement

An elastic-interface model for buckling-driven delamination growth in four-point bending tests

The paper presents a mechanical model of a four-point bending test on a delaminated specimen, considered as an assemblage of laminated beams partly connected by an elastic interface. A differential problem with suitable boundary conditions is formulated to describe the model. Then, an analytical solution is determined for both the pre- and post-critical stages. A mixed-mode fracture criterion is applied to predict the onset of delamination growth. The model is il-lustrated through comparison with some experimental results taken from the literature

An elastic-interface model for the mixed-mode bending test under cyclic loads

AbstractWe have developed a mechanical model of the mixed-mode bending (MMB) test, whereby the specimen is considered as an assemblage of two identical sublaminates, modelled as Timoshenko beams. The sublaminates are partly connected by a linearly elastic–brittle interface, transmitting stresses along both the normal and tangential directions with respect to the interface plane. The model is described by a set of suitable differential equations and boundary conditions. Based on the explicit solution of this problem and following an approach already adopted to model buckling-driven delamination growth in fatigue, we analyse the response of the MMB test specimen under cyclic loads. Exploiting the available analytical solution, we apply a fracture mode-dependent fatigue growth law. As a result, the number of cycles needed for a delamination to extend to a given length can be predicted

A cohesive-zone model for steel beams strengthened with pre-stressed laminates

We analyse the problem of a simply supported steel beam subjected to uniformly distributed load, strengthened with a pre-stressed fibre-reinforced polymer (FRP) laminate. According to the assumed application technology, the laminate is first put into tension, then bonded to the beam lower surface, and finally fixed at both its ends by suitable connections. The beam and laminate are modelled according to classical beam theory. The adhesive is modelled as a cohesive interface with a piecewise linear constitutive law defined over three intervals (elastic response, softening response, debonding). The model is described by a set of differential equations with suitable boundary conditions. An analytical solution to the problem is determined, including explicit expressions for the internal forces and interfacial stresses. For illustration, an IPE 600 steel beam strengthened with a Sika® Carbodur® FRP laminate is considered. First, the elastic limit state load of the unstrengthened beam is determined. Then, the loads corresponding to the elastic limit states in the steel beam, adhesive, and laminate for the strengthened beam are calculated. As a result, the increased elastic limit state load of the strengthened beam is obtained

Beamlike models for the analyses of curved, twisted and tapered horizontal-axis wind turbine (HAWT) blades undergoing large displacements

Abstract. Continuous ongoing efforts to better predict the mechanical behaviour of complex beamlike structures, such as wind turbine blades, are motivated by the need to improve their performance and reduce the costs. However, new design approaches and the increasing flexibility of such structures make their aeroelastic modelling ever more challenging. For the structural part of this modelling, the best compromise between computational efficiency and accuracy can be obtained via schematizations based on suitable beamlike elements. This paper addresses the modelling of the mechanical behaviour of beamlike structures which are curved, twisted and tapered in their unstressed state and undergo large displacements, in- and out-of-plane cross-sectional warping, and small strains. A suitable model for the problem at hand is proposed. Analytical and numerical results obtained by its application are presented and compared with results from 3D FEM analyses

Heterogeneous nucleation and heat flux avalanches in La(Fe, Si)13 magnetocaloric compounds near the critical point

The phase transformation kinetics of LaFe11.41Mn0.30Si1.29-H1.65 magnetocaloric compound is addressed by low rate calorimetry experiments. Scans at 1 mK/s show that its first order phase transitions are made by multiple heat flux avalanches. Getting very close to the critical point, when the transition becomes of the second order type, the step-like discontinuous behaviour associated with avalanches is smoothed out and the thermal hysteresis disappears. This result is confirmed by magneto-resistivity measurements and allows to obtain accurate values of the temperature hysteresis (DThyst = 0.37 K) at zero external magnetic field and of the critical field (Hc = 1.19 T). The number and magnitude of heat flux avalanches change as the magnetic field strength is increased, showing the interplay between the intrinsic energy barrier between phases and the microstructural disorder of the sample

Experimental characterisation of buckling-driven delamination growth in four-point bending tests

Delamination cracks in composite laminates may originate from manufacturing defects, lowenergy impacts, and many other causes. Once present, a delamination crack may propagate due to local buckling producing high interlaminar stresses at the crack front. To investigate this phenomenon, many authors have suggested carrying out four-point bending tests on composite laminated specimens with mid-span, through-the-width delamination cracks. In previous work, we developed an analytical solution for an elastic-interface model of such a test. Herein we present the results of an experimental campaign aimed at validating the abovementioned mechanical model. A 300 x 400 mm2 laminated plate was manufactured using quasi-unidirectional carbon-fibre fabric and epoxy resin by Microtex Composites for a total of 16 plies and a nominal thickness of 4.8 mm. Ten 220 x 13 mm2 specimens were cut from the plate to conduct four-point bending tests according to the ASTM standard. A 40 mm long artificial delamination was created at the mid-span of each specimen by introducing a thin layer of polytetrafluoroethylene (PTFE) between the second and third plies. The experimental tests were conducted using the facilities of the Multi-scale Analysis of Materials Laboratory (MUSAM-Lab) at IMT. A Zwick-Roell universal testing machine with 10 kN load cell was used for displacement control with a rate of 1 mm/min. The Correlated Solution kit for 2D Digital Image Correlation (DIC) was employed to measure the full-field displacement and the delamination length during the test. Snapping instability was observed, followed by crack propagation. Plots of the load vs. crack opening displacement and delamination length have been obtained and compared to the theoretical predictions of our previous model

Experimental validation of the enhanced beam-theory model of the mixed-mode bending test

We present the results of an experimental campaign on a set of specimens manufactured from a typical carbon/epoxy unidirectional laminate. Preliminary tests are performed to evaluate the elastic properties of the base laminate. Then, double cantilever beam (DCB) and end-notched flexure (ENF) tests are conducted to assess the delamination toughness in pure fracture modes I and II, respectively, and evaluate the elastic interface constants. Afterwards, mixed-mode bending (MMB) tests are carried out with three values of the lever-arm length. The outcomes of the preliminary and pure fracture mode tests are used as an input to a previously developed enhanced beam theory (EBT) model of the MMB test. Lastly, theoretical predictions and exper-imental results are compared