Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Fri, 03 Dec 2021 14:16:37 GMT2021-12-03T14:16:37Z101491Elastic-plastic plates on a nonlocal subgradehttp://hdl.handle.net/11380/1072226Titolo: Elastic-plastic plates on a nonlocal subgrade
Abstract: A thin elastic-plastic Kirchhoff plate resting on a nonlocal foundation subjected to an axisymmetric load distribution is investigated in the present work. The plate is assumed to obey to the Johansen yield criterion with associative flow rule, whereas the subgrade is modeled like an elastic nonlocal two-parameter foundation. The analysis of an elastic-plastic plate resting on a Winkler soil has been developed previously. Later, a generalization has been proposed by introducing a two parameter foundation, but only for a specific ratio between the soil parameters. The present study extends the previous analysis by considering an arbitrary Pasternak soil.
A method based on a contour integral is adopted here to solve in closed form the fourth-order linear ODE governing the elastic-plastic region of the plate. The boundary conditions are set by imposing proper continuity conditions for displacement, rotation, bending moment and shear force across the boundaries between the annular regions of the plate. Two different mechanisms at the onset of collapse are found, depending mainly on the amplitude of the loaded region as well as on the stiffness of the plate. The study allows to investigate the effect induced by the Pasternak soil parameters on the ultimate bearing capacity of the plate and the corresponding collapse mechanism. In particular, it is found that a circular elastic-plastic region with positive yield lines in both radial and circumferential directions occurs under the loaded area of the plate, whereas such a region degenerates into a point size plastic hinge for a Winkler foundation. Moreover, the amplitude of the loaded region is found to significantly affect the response of the system, particularly in terms of the reactive pressure distribution arising in the underlying foundation.
The study covers a wide array of practical applications in structural and civil engineering, ranging from the assessment of the ultimate bearing capacity of fiber reinforced industrial floors to the behavior of rigid road pavements near its limit state and the ultimate conditions of a building foundation.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11380/10722262015-01-01T00:00:00ZTime-harmonic analysis of antiplane crack in couple stress elastic materialshttp://hdl.handle.net/11380/1182622Titolo: Time-harmonic analysis of antiplane crack in couple stress elastic materials
Abstract: The time harmonic response of a rectilinear and semi-infinite crack in a couple stress (CS) elastic solid under Mode III loading conditions is investigated in the present work. The full-field solution of the dynamic crack problem obtained in [1] through Fourier integral transforms and the Wiener–Hopf technique is generalized here by considering more general loading conditions, consisting in arbitrary reduced stress and couple stress tractions applied at the crack faces.
The solution for quasistatic Mode III crack in indeterminate CS elastic materials was given in [2]. Later, the problem of steady-state Mode III crack propagation was investigated in [3]. In the present work, a travelling wave loading, applied in the form of generalized reduced tractions at the crack faces, is considered as the forcing term. As a result, a complex wave pattern appears, which differs significantly from the Mode III classical elastic solution. The results of the present analysis may be used as a building block to address, by means of superposition, the problem of arbitrary antiplane wave propagation in a cracked CS solid. Resonance is triggered when the applied loading is fed into the crack-tip at Rayleigh speed. Elastodynamic stress intensity factors are given, which generalize the corresponding results presented in [2] for the qusistatic framework. They incorporate the effect of the applied loading frequency and thereby account for the interplay of the diffracted waves.
A remarkable wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves moving along the crack surfaces, localized waves irradiating from the crack-tip and body waves scattered around the crack-tip. Interestingly, the localized wave solution may be greatly advantageous for defect detection through acoustic emission.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11380/11826222019-01-01T00:00:00ZSteady-state moving dislocations in quasicrystalshttp://hdl.handle.net/11380/658435Titolo: Steady-state moving dislocations in quasicrystals
Abstract: We summarize in these pages results on gliding and climbing dislocation steady-state motion in two-dimensional quasicrystals that we have presented elsewhere. The analysis is developed in infinitesimal deformation setting. Linear elastic constitutive structures are involved. We furnish closed-form solutions to the problems that we analyze. Emphasis is done on the coupling between macroscopic and microstructural events.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11380/6584352011-01-01T00:00:00ZA note on uniqueness in frictional contact rate problemhttp://hdl.handle.net/11380/1188451Titolo: A note on uniqueness in frictional contact rate problem
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/11380/11884511998-01-01T00:00:00ZOn intersonic crack propagation in poroelastic fluid-saturated solidshttp://hdl.handle.net/11380/466509Titolo: On intersonic crack propagation in poroelastic fluid-saturated solids
Abstract: A closed-form solution is provided for the stress, pore pressure and displacement fields near the tip of a dynamic crack steadily propagating in an elastic fluid-saturated porous solid at crack tip speed ranging between the faster longitudinal wave-speed and the lower between the longitudinal Biot second wave-speed and the shear wave-speed. The Biot theory of poroelasticity with inertia forces is assumed to govern the motion of the medium. At variance with the subsonic case, for intersonic crack propagation the stress and pore pressure fields display a strong discontinuity (shock wave) across symmetric rays emanating from the moving crack tip. However, for favorable velocity regimes the stress and pore pressure singularity turns out to be weaker than square-root, leading to a vanishing small energy release rate at the crack tip. The introduction of a finite length cohesive zone remedies the vanishing of fracture energy, which is due to the point size model of the process zone.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11380/4665092003-01-01T00:00:00ZSulla risposta dinamica di paratie soggette a sollecitazioni sismichehttp://hdl.handle.net/11380/466505Titolo: Sulla risposta dinamica di paratie soggette a sollecitazioni sismiche
Abstract: Nel presente lavoro vengono presentati i primi risultati di una ricerca volta a valutare la risposta dinamica di una paratia flessibile infissa a contenimento di uno strato di terreno. Nei depositi alluvionali della pianura padana si incontrano sia terreni argillosi (saturi e non) che possono essere considerati praticamente impermeabili, sia terreni granulari (sabbie, ghiaie) caratterizzati da un’elevata permeabilità. Nel primo caso è possibile valutare la risposta dinamica dello strato facendo ricorso ad un modello viscoelastico lineare, nel secondo caso un modello poroelastico lineare appare sicuramente più appropriato. Vengono, nel primo caso, analizzati gli effetti della flessibilità della parete sull’ampiezza e sulla distribuzione delle pressioni dinamiche agenti sulla paratia in seguito ad azioni sismiche orizzontali, e sulle corrispondenti sollecitazioni. A tal fine viene formulato un modello di analisi semplice ed affidabile che consente di valutare l’importanza relativa dei diversi fattori che caratterizzano il comportamento del terreno e che influiscono sulla risposta dinamica della paratia.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/11380/4665052004-01-01T00:00:00ZDuctile crack propagation at the micron scalehttp://hdl.handle.net/11380/466500Titolo: Ductile crack propagation at the micron scale
Abstract: The asymptotic fields near the tip of a crack steadily propagating in a ductile material under Mode III loading conditions are investigated by adopting an incremental version of the indeterminate theory of couple stress plasticity displaying linear and isotropic strain hardening. The adopted constitutive model is able to account for the microstructure of the material by incorporating two distinct material characteristic lengths. It can also capture the strong size effects arising at small scales, which results from the underlying microstructures. The effects of microstructure on Mode III crack tip fields mainly consist in a switch in the sign of tractions and displacement and in a substantial increase in the singularity of tractions ahead of the crack-tip, with respect to the classical solution of LEFM and EPFM. The increase in the stress singularity is essentially due to the skew-symmetric stress field, since the symmetric stress field turns out to be non-singular. Moreover, the obtained results show that the ratio between the characteristic lengths has a limited effect on the strength of the stress singularity. However, it displays a strong influence on the angular distribution of the asymptotic crack tip fields.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11380/4665002006-01-01T00:00:00ZMode III crack tip fields in couple stress elastic materials with two characteristic lengthshttp://hdl.handle.net/11380/466502Titolo: Mode III crack tip fields in couple stress elastic materials with two characteristic lengths
Abstract: In questo lavoro viene effettuata un’analisi asintotica dei campi di tensione e deformazione in prossimità dell’apice di una frattura in un materiale con microstruttura, in condizioni di modo III. Per rappresentare il comportamento del materiale è stato utilizzato il modello costitutivo elastico polare sviluppato da Koiter, che include due distinte lunghezze caratteristiche proprie della microstruttura del materiale. Pertanto, il modello considerato risulta in grado di simulare i rilevanti effetti di scala che si riscontrano in prossimità dell’apice di una frattura nei materiali con microstruttura, a distanze comparabili a quelle delle lunghezze caratteristiche. In particolare si osserva che la presenza di microstruttura comporta un notevole incremento della singolarità delle componenti antisimmetriche di tensione e, quindi, delle trazioni davanti all’apice, mentre le componenti simmetriche di tensione risultano limitate. Tali osservazioni si presentano in accordo con i risultati ottenuti considerando una sola lunghezza caratteristica del materiale. Nel presente lavoro viene inoltre evidenziata l’influenza esercitata dal rapporto tra le due lunghezze caratteristiche sugli andamenti dei campi asintotici in funzione della coordinata angolare e sul rilascio di energia in prossimità dell’apice.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11380/4665022006-01-01T00:00:00ZInstabilities and near tip crack fields in elastic, incompressible solidshttp://hdl.handle.net/11380/466506Titolo: Instabilities and near tip crack fields in elastic, incompressible solids
Abstract: A closed-form asymptotic solution is provided for velocity fields and the nominal stress rates near the tip of a stationary crack in a homogeneously pre-stressed configuration of a nonlinear elastic, incompressible material. In particular, a biaxial pre-stress is assumed with stress axes parallel and orthogonal to the crack faces. Two boundary conditions are considered on the crack faces, namely a constant pressure or a constant dead loading, both preserving an homogeneous ground state. Starting from this configuration, small superimposed Mode I or Mode II deformations are solved, in the framework of Biot’s incremental theory of elasticity. In this way a definition of an incremental stress intensity factor is introduced, slightly different for pressure or dead loading conditions on crack faces. Specific examples are finally developed for various hyperelastic materials, including the J2deformation theory of plasticity. The presence of pre-stress is shown to strongly influence the angular variation of the asymptotic crack-tip fields, even if the nominal stress rate displays a square root singularity as in the infinitesimal theory. Relationships between the solution with shear band formation at the crack tip and instability of the crack surfaces are given in evidence.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/11380/4665062002-01-01T00:00:00ZDiffraction and reflection of antiplane shear waves in a cracked couple stress elastic materialhttp://hdl.handle.net/11380/1189980Titolo: Diffraction and reflection of antiplane shear waves in a cracked couple stress elastic material
Abstract: We investigate the effect of a semi-infinite rectilinear crack on diffraction and reflection of antiplane shear waves in an elastic solid with microstructure. Waves are induced by moving shear traction vectors applied at the faces of the crack. The material behavior is described by the indeterminate theory of couple stress elasticity considering micro inertia. This elastic constitutive model accounts for the material microstructure and it is a special case of the micropolar theory; it was developed by Koiter [3] for the quasi-static regime and later extended by Eringen [1] to include dynamic effects.
The full-field solution is obtained through integral transforms and the Wiener-Hopf technique [5] and it may be used as a bulding block to solve general wave propagation problems in a cracked half-space in antiplane deformation. The solution differs significantly from the classical result given in [2] for isotropic elastic materials. Indeed, unlike classical elasticity, antiplane shear Rayleigh waves are supported in couple stress materials [4]. A complicated wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves, localized waves irradiating from and body waves scattered by the crack-tip. Wave diffraction and interference brings an important contribution to the stress intensity factors originally presented in [6] in the static framework. Resonance is triggered when the applied loading is fed into the crack-tip at Rayleigh speed and this result is confirmed by the evaluation of the energy release rate.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11380/11899802019-01-01T00:00:00Z