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Assessment of Reuss, Tamura, and LRVE models for vibration analysis of functionally graded nanoplates

Shahsavari Davood, Karami Behrouz

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 2

art. no. e92, 1--13

EN

Majority of structural analysis on functionally graded materials utilized Voigt and Mori-Tanaka micromechanical modelling. The current article is focused on free vibration response of inhomogeneous nano-size plate resting on elastic foundations against different micromechanical models (i.e., Reuss, Tamura, and LRVE). For the elastic foundation type, Winkler, Pasternak, and Kerr mediums are modelled one by one. The nanoplate is modelled based on a quasi-3D shear deformation plate theory which is in relation with general strain gradient theory by employing Hamilton principle, then the model is solved analytically via Navier solution procedure. This exact model determines fourfold coupled (stretching-axial-bending-shear) response with estimating softening-stiffness and hardening-stiffness mechanisms of nano-sized systems. Finally, numerical results are provided to represent the influence of size-dependent effects on vibrations of embedded nanoplate obtained through different micromechanical models.

2

Ocena wpływu wyboru modelu mikromechanicznego na prognozowanie orientacji włókien oraz właściwości mechaniczne kompozytu WPC

Frącz Wiesław, Janowski Grzegorz

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

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2019

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z. 91 [299], nr 1-2

5--16

PL

W pracy oceniono efektywność zastosowania modeli mikromechanicznych Folgara-Tuckera oraz RSC w prognozowaniu powtryskowej orientacji włókien w matrycy polimerowej dla specyficznego kompozytu WPC złożonego z matrycy polimerowej PP oraz napełniacza, tj. włókien drzewnych w ilości 15% mas. Obliczone wartości składowych tensora orientacji włókien w matrycy polimerowej pozwoliły również na ocenę wpływu zastosowanych modeli mikromechanicznych na możliwości prognozowania właściwości mechanicznych kompozytu WPC z zastosowaniem modelu homogenizacji Mori-Tanaka. Należy zauważyć, że domyślnym modelem mikromechanicznym stosowanym w wielu programach CAE specjalizowanych w zakresie procesu formowania wtryskowego jest model Folgara-Tuckera. Istotna staje się więc ocena przydatności modelu RSC, który nie jest modelem domyślnym i próba odpowiedzi, czy można go stosować w prognozowaniu właściwości przetwórczych i mechanicznych kompozytów WPC.

EN

This article evaluates the effectiveness of selected micromechanical models, such as Folgar-Tucker and RSC, in numerical calculations concerning fiber orientation prediction in a polymer matrix for the WPC composite containing 15% by mass of wood fibers. In addition, the obtained values of fiber orientation tensor in the polymer matrix allowed to assess the influence of the applied micromechanical models on the possibilities of predicting the mechanical properties of the WPC composite using the Mori-Tanaka homogenization model. It should be noted that the default micromechanical model suggested in CAE software including the injection moulding process modules is the Folgar-Tucker model. Hence, it is important to investigate whether the second optional model, i.e. RSC, should be the main model used in predicting the processing and mechanical properties of WPC composites.

3

Viscoelastic properties of asphalt concrete using micromechanical self-consistent model

Alam S. Y., Hammoum F.

Archives of Civil and Mechanical Engineering

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2015

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Vol. 15, no. 1

272--285

EN

The mechanical properties of Hot Mix Asphalt (HMA) mixes are often characterized by its viscoelastic behavior. Viscoelasticity coupled with the thermo-mechanical nature of asphalt offers time-temperature dependence to the mechanical properties of HMA mixes. Also, the wide range of distribution of particles, and several orders of magnitude of differences in the mechanical properties between constituents cause a wide range of stress and strain distribution within the microstructure. In this paper, micromechanical modeling has been performed to study the relationship between individual material properties, their interaction within the microstructure, and the macroscopic properties of HMA mix. The analytical model based on N phase self-consistent scheme allows calculating the complex modulus and phase angle of HMA mixes from the mechanical properties of its constituents and designed mix data. In the mix microstructure, aggregates and sand are classified using simple sieve analysis test. Asphalt and sand mastic film thicknesses around the aggregates are calculated for each class and introduced into the model.