1,721,084 research outputs found
Piola’s approach to the equilibrium problem for bodies with second gradient energies. Part I: First gradient theory and differential geometry
Full text linkIn this study, some pioneering contributions, envisaged in the works of Gabrio Piola, were developed through tools of the modern differential geometry and applied to the second gradient continua. Part I introduced the variational approach for the equilibrium problem according to the first gradient theory and exploited differential geometric perspectives for the present scenario. By prescribing the stationarity of the Lagrangian energy functional, the virtual work equations for a Cauchy’s medium were recovered. The focus was on the deformation process regarded as a diffeomorphism between Riemannian embedded submanifolds, emphasizing the roles of the pullback metrics and of the covariant differentiation. Novel transport formulae were provided for normal and tangent vectors in the neighborhood of a boundary edge. The divergence theorem for curved surfaces with border was revisited, providing remarkable relationships between Lagrangian and Eulerian expressions involving projectors
Characterization of a cohesive-zone model describing damage and de-cohesion at bonded interfaces. Sensitivity analysis and mode-I parameter identification
No full textThe identification of mode-I parameters of a cohesive-zone model for the analysis of adhesive joints is
presented. It is based on an experimental–numerical methodology whereby the optimal parameters
are obtained as the solution of a nonlinear programming problem. The data set for inverse analysis is provided
either by local kinematic data, by global static data, or a combination of the two. Parameter sensitivities
are computed via direct differentiation and identification exercises are discussed that show the
effectiveness of the procedure and its stability with respect to noise and time–space sampling
Una metodologia inversa basata su misure cinematiche a scale diverse, per la calibrazione di modelli di interfaccia
No full textIn questa comunicazione si propone una metodologia inversa per la caratterizzazione
meccanica di modelli d’interfaccia, basata su misure di campo cinematiche, a scale diverse.
Si fa riferimento sia a prove in modo I in configurazione simmetrica Double Cantilever Beam
(DCB) su giunto adesivo, sia ad una prova di frattura in modo misto su un assemblato con rinforzo
a Z per applicazioni aerospaziali. Alla macroscala, le immagini digitali permettono di inquadrare
quasi l’intero provino, con una dimensione del pixel di circa 20 micron. Alla scala microscopica, sul
lato opposto del provino, viene monitorata con speciali obiettivi una regione di pochi millimetri di
lato, con al centro il giunto adesivo, con una risoluzione di circa 2 micron
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Irreducible representation of surface distributions and Piola transformation of external loads sustainable by third gradient continua
Full text linkIn this paper Piola transformations are found that relate the Eulerian and Lagrangian external loads which third gradient continua can sustain. As shown by Gabrio Piola and Paul Germain, the most effective postulation scheme in mechanics is based on the principle of virtual work and therefore continuummechanics must be mathematically founded based on the theory of distributions and on differential geometry. Using the principle of virtual work, the set of admissible external loads sustainable by third gradient continua is seen to include: i) volume force density, ii) surface density of contact force, iii) surface density of contact double force, iv) surface density of contact triple force, v) line density of edge contact forces, vi) line density of contact edge double forces and vii) contact forces concentrated on wedge points. Following the nomenclature introduced by Paul Germain, forces are dual in virtual work of virtual displacements, surface and line double forces are dual of the derivatives of virtual displacements in the normal direction(s) of the surfaces and edges constituting the boundary of the continuum, and surface triple forces are dual of the second normal derivatives of virtual displacements. Volume and surface forces transform as in first gradient Cauchy continua. Moreover we find that: a) the virtual work expended by Eulerian surface triple force, when transformed into the Lagrangian description, must be represented as the work expended by all the kinds of external Lagrangian loads listed in i)-vii); b) Eulerian surface double force transforms into Lagrangian surface double force, surface contact force and edge contact line force; c) Eulerian edge contact line double force transforms into Lagrangian edge contact line double forces, edge line forces and point concentrated wedge forces; d) Eulerian edge and wedge contact line forces transforms into their Lagrangian counterpart only. The Piola transformation formulas deduced in this paper depend on the first, second and third gradients of placement. The presented results allow for the formulation of well-posed boundary condition problems for third gradient continua in the Lagrangian description, and are relevant in computational mechanics. In view of the obtained Piola transformation formulas, the concept of dead loads needs to be modified. We believe to have given an example of how the Mechanics in the French Style, as developed on the ideas by D'Alembert and Lagrange, is still a fertile tool of invention
A Numerical Study on a Modified Arcan Test for Additive Manufacturing
No full textIn this communication reference was made to PolyLactic Acid products of 3D printing by Fused Filament Fabrication technique. To assess the fracture behavior of such manufactured parts, consistently with their transversal isotropy and brittle behavior, a modified Arcan fixture was proposed, allowing one to easily generate mixed mode loading conditions by a simple uniaxial testing machine. For a preliminary assessment of the novel equipment, a large-scale finite element model was developed. The model takes into account the presence of design tolerances and frictional contact between sample and fixture as well as interlaminar debonding within the sample, by means of explicit analyses including geometric nonlinearities. Computing costs and simulation accuracy were optimized by exploiting mass scaling, boundary conditions and diverse solutions for sample fastening
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