In the plastic constitutive laws the yield functions are assumed to be linear in the stresses, but generally non-linear in the internal variables which are non-decreasing measures of the contribution to plastic strains by each face of the yield surface. The structural models referred to for simplicity are aggregates of constant-strain finite elements. Influence of geometry changes on equilibrium are allowed for in a linearized way (the equilibrium equation contains a bilinear term in the displacements...
Si considera un modello discreto (per elementi finiti) di un solido o un sistema strutturale perfettamente elastoplastico, con condizioni di snervamento «linearizzate a tratti», nell’ipotesi di olonomia assunta per processi di caricamento proporzionali. Supponendo noti su base sperimentale certi spostamenti sotto assegnate azioni esterne, si formula il problema di identificare i limiti di snervamento, ossia le resistenze locali. Si dimostra che questo problema inverso di meccanica strutturale non...
Si considera un modello discreto (per elementi finiti) di un solido o un sistema strutturale perfettamente elastoplastico, con condizioni di snervamento «linearizzate a tratti», nell’ipotesi di olonomia assunta per processi di caricamento proporzionali. Supponendo noti su base sperimentale certi spostamenti sotto assegnate azioni esterne, si formula il problema di identificare i limiti di snervamento, ossia le resistenze locali. Si dimostra che questo problema inverso di meccanica strutturale non...
In the plastic constitutive laws the yield functions are assumed to be linear in the stresses, but generally non-linear in the internal variables which are non-decreasing measures of the contribution to plastic strains by each face of the yield surface. The structural models referred to for simplicity are aggregates of constant-strain finite elements. Influence of geometry changes on equilibrium are allowed for in a linearized way (the equilibrium equation contains a bilinear term in the displacements...
The constitutive model assumed in this Note is poroplastic two-phase (solid-fluid) with full saturation and stable in Drucker’s sense. A solid or structure of this material is considered, subjected to dynamic external actions, in particular periodic or intermittent, in a small deformation regime. A sufficient condition and a necessary one are established, by a «static» approach, for shakedown (or adaptation), namely for boundedness in time of the cumulative dissipated energy.
For the finite-step, backward-difference analysis of elastic-plastic solids in small strains, a kinematic (potential energy) and a static (complementary energy) extremum property of the step solution are given under the following hypotheses: each yield function is the sum of an equivalent stress and a yield limit; the former is a positively homogeneous function of order one of stresses, the latter a nonlinear function of nondecreasing internal variables; suitable conditions of "material stability"...
This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear "comparison material" is critically reviewed and compared to the criterion...
For a class of elastic-plastic constitutive laws with nonlinear kinematic and isotropic hardening, the problem of determining the response to a finite load step is formulated according to an implicit backward difference scheme (stepwise holonomic formulation), with reference to discrete structural models. This problem is shown to be amenable to a nonlinear mathematical programming problem and a criterion is derived which guarantees monotonie convergence of an iterative algorithm for the solution...
This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear "comparison material" is critically reviewed and compared to the criterion...
For the finite-step, backward-difference analysis of elastic-plastic solids in small strains, a kinematic (potential energy) and a static (complementary energy) extremum property of the step solution are given under the following hypotheses: each yield function is the sum of an equivalent stress and a yield limit; the former is a positively homogeneous function of order one of stresses, the latter a nonlinear function of nondecreasing internal variables; suitable conditions of "material stability"...
For a class of elastic-plastic constitutive laws with nonlinear kinematic and isotropic hardening, the problem of determining the response to a finite load step is formulated according to an implicit backward difference scheme (stepwise holonomic formulation), with reference to discrete structural models. This problem is shown to be amenable to a nonlinear mathematical programming problem and a criterion is derived which guarantees monotonie convergence of an iterative algorithm for the solution...
The class of elastic-plastic material models considered allows for nonassociativity, nonlinear hardening and saturation in the sense that the static internal variables are constrained by a bounding surface described through convex bounding functions. With reference to finite element, generalized variables discretization in space, two dynamic shakedown criteria are established by a kinematic approach in Koiter's sense, based on weak constitutive restrictions and centered on two suitable definitions...
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