Vaccaro, Marzia Sara (2022) Nonlocal continuum mechanics: theoretical and finite element formulations. [Tesi di dottorato]


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Item Type: Tesi di dottorato
Resource language: English
Title: Nonlocal continuum mechanics: theoretical and finite element formulations
Vaccaro, Marzia
Date: 9 March 2022
Number of Pages: 154
Institution: Università degli Studi di Napoli Federico II
Department: Strutture per l'Ingegneria e l'Architettura
Dottorato: Ingegneria strutturale, geotecnica e rischio sismico
Ciclo di dottorato: 34
Coordinatore del Corso di dottorato:
Marotti de Sciarra, FrancescoUNSPECIFIED
Date: 9 March 2022
Number of Pages: 154
Keywords: nonlocal continuum mechanics, small-scale structures, finite element method
Settori scientifico-disciplinari del MIUR: Area 08 - Ingegneria civile e Architettura > ICAR/08 - Scienza delle costruzioni
Date Deposited: 16 Mar 2022 14:08
Last Modified: 28 Feb 2024 14:04

Collection description

The thesis aims at facing challenging topics in nonlocal continuum mechanics leading to the formulation of a nonlocal finite element methodology. Fundamental concepts of nonlocality are first illustrated and comprehensive investigations about Helmholtz's averaging kernel and its peculiar properties are provided as essential aspects to reverse integral constitutive laws and to prove inconsistencies of strain-driven nonlocal problems. A variational formulation of nonlocal elasticity is proposed to derive abstract constitutive laws from which well-posed elasticity methodologies can be obtained and exploited to provide benchmark outcomes in nonlocal mechanics. To this purpose, nonlocal continuum theories are advantageously applied to model nanocomposite small-scale structures undergoing large displacements, conceived as basic components of advanced electromechanical systems. Then, a challenging issue in nonlocal mechanics is tackled concerning reproducibility of a structural problem according to which general physical laws must be applicable to any sub-part of a continuum. Thus, a nonlocal model of elasticity based on the well-posed stress-driven formulation is conceived for assembled structural systems with concentrated and non-smooth distributed loadings, internal kinematic constraints, piecewise regular elastic and geometric properties. A constitutive differential formulation involving prescription of non-standard boundary and interface conditions is derived and exploited to develop a nonlocal finite element methodology. The proposed formulation is able to provide exact stress-driven nonlocal solutions and to reproduce the typical stiffening mechanical behaviour in agreement with the smaller-is-stiffer phenomenon affecting a wide variety of inflected micro- and nano-structures. A peculiar feature of the proposed nonlocal finite element method with respect to previous contributions, is that long range interactions involve the whole structural domain. The presented computational technique can be effectively adopted to accurately solve static, dynamic and buckling problems of nanoscopic beams and frames characterizing modern electromechanical systems.


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