NAVID SHEKARCHIZADEH

PhD

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

  • 11573/1341542 - 2019 - Determining the constitutive parameters of a macroscale second-gradient model for planar pantographic structures by using optimization algorithms (04b Atto di convegno in volume)
    SHEKARCHIZADEH, NAVID
  • 11573/1473340 - 2021 - Inverse analysis of metamaterials and parameter determination by means of an automatized optimization problem (01a Articolo in rivista)
    SHEKARCHIZADEH, NAVID; BERSANI, ALBERTO MARIA
  • 11573/1578775 - 2021 - Parameter identification of a second-gradient model for the description of pantographic structures in dynamic regime (01a Articolo in rivista)
    SHEKARCHIZADEH, NAVID; GIORGIO, IVAN; BERSANI, ALBERTO MARIA
  • 11573/1633351 - 2021 - Parameter Identification and Investigating the Effect of Higher-order Inertia in a Gradient Elasticity Model of Metamaterials in Dynamic Loading (04d Abstract in atti di convegno)
    SHEKARCHIZADEH, NAVID; BERSANI, ALBERTO MARIA
  • 11573/1633352 - 2021 - Developing an automatized optimization problem in FEniCS for parameter determination of metamaterials (04d Abstract in atti di convegno)
    SHEKARCHIZADEH, NAVID; BERSANI, ALBERTO MARIA
  • 11573/1621733 - 2022 - Studying the higher-order inertia in the second-order theory of elasticity for modeling metamaterials (02a Capitolo o Articolo)
    SHEKARCHIZADEH, NAVID; BERSANI, ALBERTO MARIA
  • 11573/1660528 - 2022 - A benchmark strain gradient elasticity solution in two-dimensions for verifying computational approaches by means of the finite element method (01a Articolo in rivista)
    SHEKARCHIZADEH, NAVID; BERSANI, ALBERTO MARIA

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