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A tensile test until breakage and a creep and relaxation test on a polypropylene fibre are carried out and the resulting creep and stress relaxation curves are fit by a model adopting a fraction-exponential kernel in the viscoelastic operator. The models using fraction-exponential functions are simpler than the complex ones obtained from combination of dashpots and springs and, furthermore, are suitable for fitting experimental data with good approximation allowing, at the same time, obtaining inverse Laplace transform in closed form. Therefore, the viscoelastic response of polypropylene fibres can be modelled straightforwardly through analytical methods. Addition of polypropylene fibres greatly improves the tensile strength of composite materials with concrete matrix. The proposed analytical model can be employed for simulating the mechanical behaviour of composite materials with embedded viscoelastic fibres.

The present work deals with the mechanical behavior of a large FRC slab bilaterally supported by a non-local soil. The slab is modelled as a ductile Kirchhoff plate laying on a two-parameter elastic foundation and transversally loaded by a uniform pressure applied on a circular area, thus making the problem axisymmetric. This layout covers a wide array of practical applications of fiber reinforced concrete in structural and civil engineering related to the assessment of the load carrying capacity of industrial floors, roads, airfield pavements and building foundations. The problem is governed by a fourth order linear ODE with variable coefficients, whose solution has been obtained in power series by using the Frobenius method. The analysis allows us to evaluate the influence of the size of the loaded area and the relative stiffness of the slab/subgrade system on the collapse mechanism and the corresponding load carrying capacity, as well as on the distributions of displacement, rotation, bending moments, shear force and contact pressure at the onset of collapse. Keywords Ultimate carrying capacity Á Johansen's failure criterion Á Collapse mechanics Á FRC slab Á Kirchhoff plate Á Two-parameter foundation Á Axisymmetric loading condition Á Frobenius method List of symbols a Amplitude of the loaded region b, c, d Yield loci within the plate at the onset of collapse D Flexural rigidity of the plate E Young Modulus f ctk,fl Characteristic flexural strength of plain concrete f ctk(0.05) Characteristic axial tensile strength (5 % fractile) of plain concrete f ck Characteristic compressive strength (cylinder) of plain concrete h Total slab thickness h 0 Effective depth of the cross section H 1 ð Þ 0 Hankel function of first kind of order zero I 0 Modified Bessel function of first kind of order zero J 0Bessel function of first kind of order zero k r Curvature tensor

The load carrying capacity and collapse scenarios for an infinite elastic-plastic plate resting on a twoparameter elastic foundation uniformly loaded on a small circular footprint are investigated in a general framework of stiffness and yield parameters. The present work extends the study already presented for a specific value of the Pasternak modulus and it allows the investigation of the influence of the stiffness property of the underlying soil and the amplitude of the loaded region on the load carrying capacity of the plate and the corresponding collapse mechanism. Moreover, the present analysis allows for the evaluation of the transverse deflection, slope, radial and circumferential bending moments, shearing force within the plate and the reactive pressure of the elastic subgrade at the onset of the plastic collapse together with their dependence on the foundation moduli. The effect of the ratio between negative and positive yield moments is also investigated. The amplitude and assembly of plastic regions at the onset of the plastic collapse are discussed in some detail. 459 460 LUCA LANZONI, ANDREA NOBILI, ENRICO RADI AND ANDREA SORZIA book of Timoshenko and Woinowsky-Krieger [1959]. The axisymmetric flexure of an infinite elastic plate resting on an incompressible elastic half-space is considered by Selvadurai [1977] by making use of the potential functions and Hankel transforms. The problem of an elastic plate supported by an elastic twoparameter subgrade is studied in [Wen-da and Shu 1987] in order to model the circular foundation of a cooling hyperbolic tower. Results are compared with a numerical solution obtained through a FE package. The mechanical interaction between an infinite cracked Kirchhoff plate resting on a two-parameter elastic subgrade can be found in [Nobili et al. 2014[Nobili et al. , 2015. A full-field solution is obtained therein by means of the Wiener-Hopf method and the influence of the subgrade parameters on the stress intensity factors at the crack tip are evaluated in detail.Recently, Shukla et al. [2011] have obtained the solution of a circular plate supported by a tensionless Pasternak-type subgrade by using the strain energy approach and assuming a power series expansion for the transverse deflection of the plate. Variational boundary conditions for a beam resting on a twoparameter tensionless elastic foundation have been developed in [Nobili 2012]. Shell-and plate-like elements in contact with elastic media have been adopted as a reliable model to study micro-or nanostructures in the framework of modern microelectronics based on the use of special composite materials. As an example, Ru [2001] studied the critical loading for a double-walled carbon nanotube embedded in an elastic matrix. There, the nanotube is modeled as a thin elastic cylindrical shell supported by a Winkler subgrade, which accounts for the van der Waals forces. Likewise, in order to investigate the vibrations of carbon nanotubes, Liew et al. [2006] consider a plate embedded into a Pasternak elastic medium a...

We apply Floquet theory of periodic coefficient second-order ODEs to an elastic waveguide. The waveguide is modeled as a uniform elastic string periodically supported by a discontinuous Winkler elastic foundation and, as a result, a Hill equation is found. The fundamental solutions, the stability regions, and the dispersion curves are determined and then plotted. An asymptotic approximation to the dispersion curve is also given. It is further shown that the end points of the band gap structure correspond to periodic and semiperiodic solutions of the Hill equation.