arXiv subjects

Michael J. A. Smith

Publications and source records attributed to Michael J. A. Smith.

5 recordsLinked to original sources

arXiv2021

Modelling hollow thermoplastic syntactic foams under high-strain compressive loading

The mechanical response of syntactic foams comprising hollow thermoplastic microspheres (HTMs) embedded in a polyurethane matrix were experimentally examined under uniaxial compressive strain. Phenomenological strain energy models were subsequently developed to capture both the axial stress-strain and transverse strain response of the foams. HTM syntactic foams were found to exhibit increased small-strain stiffness with reduced density, revealing a highly tuneable and extremely lightweight syntactic foam blend for applications. The foams were also found to become strongly compressible at large strains and possess a high threshold for plastic deformation, making them a robust alternative to hollow glass microsphere syntactic foams. The non-standard transverse strain relationship exhibited by HTM syntactic foams at high filling fractions was captured by Ogden-type strain energy models. The thermal characteristics of these syntactic foams were also explored with Differential Scanning Calorimetry testing which showed that HTMs have a negligible impact on the thermal characteristics of the matrix.

cond-mat.soft↗

arXiv2021

Geometrical and Mechanical Characterisation of Hollow Thermoplastic Microspheres for Syntactic Foam Applications

Recently, hollow thermoplastic microspheres, such as Expancel made by Nouryon, have emerged as an innovative filler material for use in polymer-matrix composites. The resulting all-polymer syntactic foam takes on excellent damage tolerance properties, strong recoverability under large strains, and favourable energy dissipation characteristics. Despite finding increasing usage in various industries and applications, including in coatings, films, sealants, packaging, composites for microfluidics, medical ultrasonics and cementious composites, there is a near-complete absence of statistical geometrical information for Expancel microspheres. Further, their mechanical properties have not yet been reported. In this work we characterise the geometrical quantities of two classes of Expancel thermoplastic microspheres using X-ray computed tomography, focused ion beam and electron microscopy. We also observe the spatial distribution of microspheres within a polyurethane-matrix syntactic foam. We show that the volume-weighted polydisperse shell diameter in both classes of microsphere follows a normal distribution. Interestingly, polydispersity of the shell wall thickness is not observed and in particular the shell thickness is not correlated to the shell diameter. We employ the measured geometrical information in analytical micromechanical techniques in the small strain regime to determine, for the first time, estimates of the Young's modulus and Poisson's ratio of the microsphere shell material. Our results contribute to potential future improvements in the design and fabrication of syntactic foams that employ thermoplastic microspheres. Given the breadth of fields which utilise thermoplastic microspheres, we anticipate that our results, together with the methods used, will be of use in a much broader context in future materials research.

physics.app-ph↗

arXiv2018

NumBAT: The integrated, open source Numerical Brillouin Analysis Tool

We describe NumBAT, an open-source software tool for modelling stimulated Brillouin scattering in waveguides of arbitrary cross-section. It provides rapid calculation of optical and elastic dispersion relations, field profiles and gain with an easy-to-use Python front end. Additionally, we provide an open and extensible set of standard problems and reference materials to facilitate the bench-marking of NumBAT against subsequent tools. Such a resource is needed to help settle discrepancies between existing formulations and implementations, and to facilitate comparison between results in the literature. The resulting standardised testing framework will allow the community to gain confidence in new algorithms and will provide a common tool for the comparison of experimental designs of opto-acoustic waveguides.

physics.optics↗

arXiv2018

Reflection from a multi-species material and its transmitted effective wavenumber

We formally deduce closed-form expressions for the transmitted effective wavenumber of a material comprising multiple types of inclusions or particles (multi-species), dispersed in a uniform background medium. The expressions, derived here for the first time, are valid for moderate volume fractions and without restriction on the frequency. We show that the multi-species effective wavenumber is not a straightforward extension of expressions for a single species. Comparisons are drawn with state-of-the-art models in acoustics by presenting numerical results for a concrete and a water-oil emulsion in two dimensions. The limit of when one species is much smaller than the other is also discussed and we determine the background medium felt by the larger species in this limit. Surprisingly, we show that the answer is not the intuitive result predicted by self-consistent multiple scattering theories. The derivation presented here applies to the scalar wave equation with cylindrical or spherical inclusions, with any distribution of sizes, densities, and wave speeds. The reflection coefficient associated with a half-space of multi-species cylindrical inclusions is also formally derived.

physics.class-ph↗

arXiv2016

Evaluation and regularization of generalized Eisenstein series and application to 2D cylindrical harmonic sums

In the study of periodic media, conditionally convergent series are frequently encountered and their regularization is crucial for applications. We derive an identity that regularizes two-dimensional generalized Eisenstein series for all Bravais lattices, yielding physically meaningful values. We also obtain explicit forms for the generalized series in terms of conventional Eisenstein series, enabling their closed-form evaluation for important high symmetry lattices. Results are then used to obtain representations for the related cylindrical harmonic sums, which are also given for all Bravais lattices. Finally, we treat displaced lattices of high symmetry, expressing them in terms of origin-centered lattices via geometric multi-set identities. These identities apply to all classes of two-dimensional sums, allowing sums to be evaluated over each constituent of a unit cell that possesses multiple inclusions.

math-ph↗