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A theoretical link between gradient and nonlocal elasticity models, including higher order boundary conditions
Full text linkThe paper presents a recently developed rational derivation of the strain gradient elasticity model from the nonlocal (or integral) model. This kind of derivations are generally recovered just by an expansion into a Taylor series of the nonlocal strain field up to a certain order, and then
operating the integration (or averaging) over the spatial interaction domain. The latter procedure is fully consistent when the analysis is performed over an unbounded domain, but when a classical
bounded domain is analyzed it lacks in reproducing the so-called higher-order boundary conditions. In the present contributions the complete derivation is achieved employing an extended version of the Principle of Virtual Power (PVP), written in a special form in order to comply with the nonsimple
nature of the nonlocal material. Namely, extra terms are invoked in both internal and external virtual power
Thermodynamically consistent residual-based gradient plasticity theory and comparison
No full textA gradient plasticity theory for small deformations is presented within the framework of nonlocal continuum thermodynamics. The second principle (Clausius-Duhem inequality), enriched by an additional term named energy residual, is employed in conjunction with the concepts of insulation condition and locality recovery condition, in order to derive all the pertinent restrictions upon the constitutive equations. These include the expressions of the energy residual and of the plastic dissipation density, as well as the PDEs governing the gradient kinematic and isotropic hardening of the material, together with the related higher-order boundary conditions for both the fixed and the moving boundaries. Other formulations, which apparently do not make use of an energy residual, are shown to contain a latent one
A thermodynamically consistent gradient plasticity theory and comparisons with other formulations
No full textA method to transform a nonlocal model into a gradient one within elasticity and plasticity
No full textA method based on the principle of the virtual power (PVP) is presented, by which a mechanical problem of nonlocal elasticity, or plasticity, is transformed into one of gradient nature. Different Taylor series expansion techniques are applied to the driving local strain fields of the nonlocal problem, either full spatial expansion within the bulk volume, or uni-directional expansion along the normal to the thin boundary layer. This, at the limit when the boundary layer thickness tends to zero, makes the PVP of the nonlocal model transform itself into one featuring a counterpart gradient model. Also, for a class of “associated” nonlocal and gradient elasticity models (i.e. the kernel function of the former is the Green function of the latter), the mutual relationship is discussed and the existence of some related complementary formats is pointed out together with their computational relevance
Erratum to: Letter to the Editor [Engineering Fracture Mechanics 2003 (70) 1219-21]
No full textErratum and Correction
Dynamic shakedown of structures under repeated seismic loads
No full textElastic, perfectly plastic structures are considered under the action of repeated short-duration exitations of seismic type acting in an unknown time sequence, but belonging to a given polyhedral excitation domain. The basic excitations (vertices of the polyhedron) are chosen as discrete-spectrum waves each with frequencies coincident with the first natural frequencies of the structure, and amplitudes related to the ground features and earthquake intensity (according to the Kanai and Tajimi filter model) in such a way that every admissible excitation-obtained as a linear convex combination of the basic ones-has a maximum power not exceeding a given value. In the framework of unrestricted dynamic shakedown, the classic shakedown theorems are suitably cast and used for establishing alternative methods for the computation of the shakedown limit load multiplier. Considerable computational savings are obtained substituting the preceding basic excitations with single-frequency waves. Particular attention is devoted to bending frame structures. A numerical example is presented. © ASCE
Dynamic shakedown of structures with variable appended masses and subjected to repeated excitations
No full textElastic shakedown for discrete, or finite-element discretized, structures subjected to combinations of static and time-variable loads is addressed in the hypothesis of elastic-perfectly plastic material behavior. The static load is conceived as the weight of an additional mass appended to the structure, whereas the time-variable load is conceived as an unknown sequence of excitations belonging to a specified domain, with intervals between subsequent excitations during which the structure is considered as being motionless. It is shown that, in the plane of the static and time-variable load parameters, the structure's dynamic shakedown domain is nonconvex and that its boundary curve generally exhibits local minima and maxima at those static load values at which a resonant and anti-resonant structural behavior, respectively occurs. It is also shown that, for static loads close to the resonant behavior values, the shakedown limit load can be sensibly smaller than the value computed without taking the appended mass into account. The problem of evaluating the shakedown limit load is discussed and a numerical example presented
Energy-Residual-Based approach to gradient plasticity
No full textThe “energy-residual-based approach” mentioned in the title consists in a thermodynamically consistent procedure for the formulation of a phenomenological plasticity model of either strain gradient, or nonlocal (integral) type. The authors have developed this procedure on the last ten years. It seem therefore appropriate to present an update of this theory at this forum. For brevity we shell limit ourselves to strain gradient plasticity
Sviluppo storico sino al 1998 della Scienza delle Costruzioni e della Tecnica delle Costruzioni nell'Ateneo Palermitano
No full textNel contributo viene tracciata la storia della Scienza e Tecnica delle costruzioni dell'Università di Palermo a partire dalla Reale Scuola di applicazione per ingegneri e Architetti di Palermo, 1866, passando per il Gabinetto di Meccanica applicata alle Costruzioni, 1923, e per i successivi cambiamenti che portarono al Dipartimento di Ingegneria Strutturale e Geotecnica, 1985. Viene inoltre tracciata la storia dell'annesso Laboratorio di prove sui materiali da costruzione attraverso le attività svolte ed i macchinari acquisiti
A symmetric BEM approach to strain gradient elasticity for 2D static boundary-value problems
No full textThe symmetric Galerkin Boundary Element Method is used to address a class of strain gradient
elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient. With
respect to the classical elasticity, additional response variables intervene, such as the normal derivative of
the displacements on the boundary, and the work-coniugate double tractions. The fundamental solutions -
featuring a fourth order partial differential equations (PDEs) system - exhibit singularities which in 2D may
be of the order 4 1/ r .
New techniques are developed, which allow the elimination of most of the latter singularities.
The present paper has to be intended as a research communication wherein a part of the results, being
elaborated within a more general paper are reported
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