1,721,081 research outputs found
On toughening in Zirconia containing ceramics
No full textTransformation toughening in zirconia-containing ceramics is related to dilatational, inelastic volumetric strain. A model for steady-state, Mode I crack propagation in a pressure-sensitive, dilatational elastic-plastic material is presented, based on the Drucker-Prager yield criterion. In the framework of asymptotic analysis, results demonstrate a toughening effect related to pressure-sensitivity and volumetric inelastic strain. Asymptotic field representations may yield a deep understanding of near-crack tip stress-deformation phenomena
Green's function for incremental nonlinear elasticity: shear bands and boundary integral formulation
No full textAn elastic, incompressible, infinite body is considered subject to plane and homogeneous deformation. At a certain value of the loading, when the material is still in the elliptic range, an incremental concentrated line load is considered acting at an arbitrary location in the body and extending orthogonally to the plane of deformation. This plane strain problem is solved, so that a Green’s function for incremental, nonlinear elastic deformation is obtained. This is used in two different ways: to quantify the decay rate of self-equilibrated loads in a homogeneously stretched elastic solid; and to give a boundary element formulation for incremental deformations superimposed upon a given homogeneous strain. The former result provides a perturbative approach to shear bands, which are shown to develop in the elliptic range, induced by self-equilibrated perturbations. The latter result lays the foundations for a rigorous approach to boundary element techniques in finite strain elasticity
The quasi-static finite cavity expansion in a non-standard elasto-plastic medium
No full textA unified approach is presented for the analysis of the finite static expansion of a spherical or cylindrical cavity in an indefinite elastic-perfectly plastic medium. Mohr-Coulomb yield criterion is adopted with an arbitrary degree of non-associativity of the volumetric dilatational component of the plastic flow. This idealization makes the present analysis particularly appropriate for rock-like materials. The general solution obtained requires a numerical integration over the plastic zone. Some numerical examples, referring to both the spherical and the cylindrical cavity emphasize the determining role of the elastic deformations in the plastic region
A perturbative approach to material instabilities in anisotropic solids
No full textThe dynamic behaviour of pre-stressed, elastic orthotropic and incompressible materials is considered in the time-harmonic regime. Depending on the level of pre-stress and anisotropy, wave patterns are shown to emerge, with focussing of signals in the direction of shear bands. Varying the direction of the dynamic perturbation excites different wave patterns, which tend to degenerate to families of plane waves parallel to the shear bands, when the elliptic boundary is approached
Experimental evidence of flutter and divergence instabilities induced by dry friction
Full text linkFlutter and divergence instabilities have been advocated to be possible in elastic structures with Coulomb friction, but no direct experimental evidence has ever been provided. Moreover, the same types of instability can be induced by tangential follower forces, but these are commonly thought to be of extremely difficult, if not impossible, practical realization. Therefore, a clear experimental basis for flutter and divergence induced by friction or follower-loading is still lacking. This is provided for the first time in the present article, showing how a follower force of tangential type can be realized via Coulomb friction and how this, in full agreement with the theory, can induce a blowing-up vibrational motion of increasing amplitude (flutter) or an exponentially growing motion (divergence). In addition, our results show the limits of a treatment based on the linearized equations, so that nonlinearities yield the initial blowing-up vibration of flutter to reach eventually a steady state. The presented results give full evidence to potential problems in the design of mechanical systems subject to friction, open a new perspective in the realization of follower-loading systems and of innovative structures exhibiting 'unusual' dynamical behaviors
Perturbations and boundary integral equations for pre-stressed elastic materials
No full textThe behaviour of pre-stressed, elastic, orthotropic and incompressible materials is analysed in both the static and dynamic regimes. Perturbations caused by dipoles, either static or pulsating, are considered to investigate material instabilities arising near the boundary of ellipticity loss. The perturbation approach is capable of revealing aspects which may remain undetected using methods for material instabilities based on weak discontinuity surfaces. In the static case, for instance, the approach reveals shear band formation for a Mooney-Rivlin material, a circumstance not detected by the conventional approach. In the dynamic case, the perturbative approach provides a basis for the analysis of propagation of disturbances near the boundary of loss of ellipticity. Depending on the level of pre-stress and anisotropy, wave patterns are shown to emerge, with focussing of signals in the direction of shear bands. Varying the direction of the dynamic perturbation excites different wave patterns, which tend to degenerate to families of plane waves parallel to the shear bands, when the elliptic boundary is approached.
At the base of the perturbation approach are infinite-body Green’s functions for incremental displacements and in-plane hydrostatic stress obtained by the authors for small isochoric and plane deformation superimposed upon a nonlinear elastic and homogeneous strain. The same functions are employed to develop a boundary element technique for the solution of boundary value incremental problems. In this technique, “static” and “dynamic” contributions are uncoupled in the Green function for incremental tractions: the dynamic contributions are regular whereas the static terms are strongly singular and are solved in closed-form expressions, particularly useful for numerical calculations. The formulation is used to examine the influence of pre-stress on the vibrational response of elastic structures
On decay effects in nonlinear elasticity
No full textAn elastic, incompressible, infinite body is considered subject to biaxial, finite and homogeneous deformation. At a certain value of the loading, when the material is still in the elliptic range, a small concentrated line load is considered acting in a point of the body and extending orthogonally to the plane of deformation. This plane strain problem is solved and, using superposition of incremental solutions, two equal and opposite line loads are considered in a region of a continuum. The solution of this problem allows us to quantify the decay rate of self-equilibrated loads in finite elasticity. In particular, it is shown that the decay rate depends crucially, say, the distance of the current state from the boundary of the elliptic regime. When this boundary is approached, the solution blows up and, at the elliptic boundary, decay does not occur
Time-harmonic Green's function and boundary integral formulation for incremental nonlinear elasticity: dynamics of wave patterns and shear bands
No full textSuperimposed dynamic, time-harmonic incremental deformations are considered in an elastic, orthotropic and incompressible, infinite body, subject to plane, homogeneous - but otherwise arbitrary - deformation. The dynamic, infinite body Green's function is found and, in addition, new boundary integral equations are obtained for incremental in-plane hydrostatic stress and displacements. These findings open the way to integral methods in incremental, dynamic elasticity. Moreover, the Green's function is employed as a dynamic perturbation to analyze interaction between wave propagation and shear band formation. Depending on anisotropy and pre-stress level, peculiar wave patterns emerge with focussing and shadowing effects of signals, which may remain undetected by the usual criteria based on analysis of weak discontinuity surfaces
Asymptotic tip fields for a steadily growing crack in pressure-sensitive materials
No full textMode I steady-state, quasi-static crack propagation is analysed in elastoplastic pressure-sensitive solids obeying the Drucker-Prager yield condition. The asymptotic crack-tip fields are numerically obtained with reference to the incremental small strain theory, in the case of linear-isotropic hardening, under plane stress and plane strain conditions.
The determination of the stress and strain anear-tip fields is fundamental for the understanding of fracture in ceramics, amorphous rocks at low temperature and concrete
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