NAVID SHEKARCHIZADEH

PhD Graduate

PhD program:: XXXIV


advisor: Alberto Bersani

Thesis title: Direct and Inverse Problems in Mathematics and Mechanics of Metamaterials: Numerical algorithms and their computational implementation for determining model parameters and solving generalized continuum mechanics problems

Technological advances in the past decade in additive manufacturing has provided the opportunity to fabricate metamaterials which usually have detailed and complex microstructures. This has given rise to numerous studies towards investigating the metamaterials. In this work, direct and inverse mathematical problems in mechanics of metamaterials are studied. Utilizing generalized continuum mechanics for modeling metamaterials is an efficient approach which is capable of modeling the material with higher accuracy and lower computational cost. In generalized continuum mechanics, additional constitutive parameters are present which need to be identified. Herein, an automatized optimization algorithm is presented for parameter identification of metamaterials. The parameters are validated for the dynamic regime. Moreover, the strain gradient elasticity theory is numerically implemented using a mixed formulation, and it is verified by analytical solutions. The thesis is comprised of two parts. In Part I, a summary of the fundamentals, mathematical approaches, theories of mechanics, and numerical methods and their implementation are discussed. The Part II, contains the original results of the present thesis, including two published journal articles, one accepted book chapter, and one manuscript submitted for publication.

Research products

11573/1664762 - 2022 - Studying various optimization algorithms for parameter determination of metamaterials
Shekarchizadeh, N.; Abedi, M.; Bersani, A. M. - 04d Abstract in atti di convegno
conference: International conference on nonlinear solid mechanics - ICoNSoM 2022 (Alghero (SS) - Italia)
book: International conference on nonlinear solid mechanics - ICoNSoM 2022 - Abstract book - ()

11573/1621733 - 2022 - Studying the higher-order inertia in the second-order theory of elasticity for modeling metamaterials
Shekarchizadeh, Navid; Bersani, Alberto Maria - 02a Capitolo o Articolo
book: Theoretical analyses, computations, and experiments of multiscale materials - ()

11573/1660528 - 2022 - A benchmark strain gradient elasticity solution in two-dimensions for verifying computational approaches by means of the finite element method
Shekarchizadeh, Navid; Emek Abali, Bilen; Bersani, Alberto Maria - 01a Articolo in rivista
paper: MATHEMATICS AND MECHANICS OF SOLIDS (Sage Science Press:2455 Teller Road:Thousand Oaks, CA 91320:(800)818-7243, (805)499-0721, EMAIL: sagescience@sagepub.com, INTERNET: http://www.sagepub.com/ssp/index.html, Fax: (805)499-0871) pp. 2218-2238 - issn: 1081-2865 - wos: WOS:000840935000001 (9) - scopus: 2-s2.0-85135999730 (10)

11573/1633351 - 2021 - Parameter Identification and Investigating the Effect of Higher-order Inertia in a Gradient Elasticity Model of Metamaterials in Dynamic Loading
Shekarchizadeh, N.; Bersani, A. M. - 04d Abstract in atti di convegno
conference: Workshop of the IRP Coss&Vita Advances in ELAstoDYNamics, NonLinear Mechanics and Stability of architected materials and structures (Créteil (France))
book: Workshop of the IRP Coss&Vita Advances in ELAstoDYNamics, NonLinear Mechanics and Stability of architected materials and structures - ()

11573/1633352 - 2021 - Developing an automatized optimization problem in FEniCS for parameter determination of metamaterials
Shekarchizadeh, N.; Bersani, A. M. - 04d Abstract in atti di convegno
conference: FEniCS 2021 (online)
book: Proceedings of FEniCS 2021 - ()

11573/1473340 - 2021 - Inverse analysis of metamaterials and parameter determination by means of an automatized optimization problem
Shekarchizadeh, Navid; Emek Abali, Bilen; Barchiesi, Emilio; Bersani, Alberto Maria - 01a Articolo in rivista
paper: ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND MECHANIK (Berlin: Wiley-VCH-Verl. Berlin.) pp. - - issn: 1521-4001 - wos: WOS:000605759000001 (26) - scopus: 2-s2.0-85099037048 (25)

11573/1578775 - 2021 - Parameter identification of a second-gradient model for the description of pantographic structures in dynamic regime
Shekarchizadeh, Navid; Laudato, Marco; Manzari, Luca; Abali, Bilen Emek; Giorgio, Ivan; Bersani, Alberto Maria - 01a Articolo in rivista
paper: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK (Birkhaeuser Verlag AG:Viaduktstrasse 42-44, CH 4051 Basel Switzerland:011 41 61 2050707, EMAIL: subscriptions@birkhauser.ch, INTERNET: http://www.birkhauser.ch, Fax: 011 41 61 2050792) pp. - - issn: 0044-2275 - wos: WOS:000705855500001 (14) - scopus: 2-s2.0-85116606263 (18)

11573/1341542 - 2019 - Determining the constitutive parameters of a macroscale second-gradient model for planar pantographic structures by using optimization algorithms
Shekarchizadeh, Navid; Abedi, Masoud - 04b Atto di convegno in volume
conference: 8th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry (Kassel; Germany)
book: Proceedings of the 8th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry August 28–30, 2019 in Kassel, Germany - ()

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