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Determining the volume fraction in 2-phase composites and bodies using time varying applied fields

Lookup NU author(s): Professor Mihai Putinar



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


© 2023 The AuthorsA body Θ containing two phases, which may form a periodic composite with microstructure much smaller that the body, or which may have structure on a length scale comparable to the body, is subjected to slowly time varying boundary conditions that would produce an approximate uniform field in Θ were it filled with homogeneous material. Here slowly time varying means that the wavelengths and attenuation lengths of waves at the frequencies associated with the time variation are much larger than the size of Θ, so that we can make a quasistatic approximation. At least one of the two phase does not have an instantaneous response but rather depends on fields at prior times. The fields may be those associated with electricity, magnetism, fluid flow in porous media, or antiplane elasticity. We find, subject to these approximations, that the time variation of the boundary conditions can be designed so boundary measurements at a specific time t=t0 exactly yield the volume fractions of the phases, independent of the detailed geometric configuration of the phases. Moreover, for specially tailored time variations, the volume fraction can be exactly determined from measurements at any time t, not just at the specific time t=t0. We also show how time varying boundary conditions, not oscillating at the single frequency ω0, can be designed to exactly retrieve the response at ω0.

Publication metadata

Author(s): Mattei O, Milton GW, Putinar M

Publication type: Article

Publication status: Published

Journal: Journal of the Mechanics and Physics of Solids

Year: 2023

Volume: 175

Print publication date: 01/06/2023

Online publication date: 31/03/2023

Acceptance date: 27/03/2023

Date deposited: 03/05/2023

ISSN (print): 0022-5096

ISSN (electronic): 1873-4782

Publisher: Elsevier Ltd


DOI: 10.1016/j.jmps.2023.105292


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