A 2D micromechanical modelling of anisotropy in granular media

We propose a two-dimensional modelling of the anisotropy of granular media based on the use of a second order or a fourth order fabric tensor describing the distribution of the contact probability. This fabric tensor-based approach is then combined with a new kinematic localization rule and yields an efficient homogenization scheme for anisotropic granular media

A 4th order fabric tensor approach applied to granular media

International audienceIn this paper, we propose a micromechanical approach of the behavior of granular media, which takes into account the anisotropy by means of a fourth order fabric tensor. The proposed approach is implemented in an homogenization scheme based on Voigt and Reuss localization assumption. The fabric tensor-based approach is then combined with a new kinematic localization rule and yields a general homogenization scheme for anisotropic granular media

Size-dependent parametrisation of active vibration control for periodic piezoelectric microplate coupled systems: A couple stress-based isogeometric approach

We propose a couple stress based isogeometric analysis (IGA) model for the study of active vibration control in periodic piezoelectric microplate coupled systems. The model integrates the modified couple stress elasticity, which accounts for microstructure effects but necessitates the implementation of at least C1 continuous finite elements, and the IGA finite element, which fulfils the element continuity criterion. This complementary combination enables size-dependent parametrisation of the feedback vibration controller for piezoelectric microplate coupled systems. Therefore, we examined a two-parameter control relationship that modulates the voltage gain within the sensor-to-actuator circuit in relation to mass and stiffness with the account for varying problem sizes. To assess the vibration properties of the microplate system, we performed bandgap analysis and compared the results to transient responses. Additionally, we investigated the impact of couple stress on bandgaps and devised a computational methodology for determining optimal control parameters concerning the desired vibration bandgaps. Our computational procedure serves as valuable tool for assisting in the parametrisation of feedback vibration controllers in microplates with tunable vibration bandgaps

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

In this paper, a new defective phononic crystal (PC) microbeam model in a thermal environment is developed with the application of modified couple stress theory (MCST). By using Hamilton’s principle, the wave equation and complete boundary conditions of a heated Bernoulli–Euler microbeam are obtained. The band structures of the perfect and defective heated PC microbeams are solved by employing the transfer matrix method and supercell technology. The accuracy of the new model is validated using the finite element model, and the parametric analysis is conducted to examine the influences of size and temperature effects, as well as defect segment length, on the band structures of current microbeams. The results indicate that the size effect induces microstructure hardening, while the increase in temperature has a softening impact, decreasing the band gap frequencies. The inclusion of defect cells leads to the localization of elastic waves. These findings have significant implications for the design of microdevices, including applications in micro-energy harvesters, energy absorbers, and micro-electro-mechanical systems (MEMS)

A non-classical couple stress based Mindlin plate finite element framework for tuning band gaps of periodic composite micro plates

International audienceComposite micro plates with periodic microstructure at very small length scale have been a focus of intensive research. When length scale of the microstructure descends below millimetre level, size effects may emerge. To account for microstructure effect on the elastic wave band gap of microscopic composite plates, we propose a numerical framework based on the modified couple stress theory of elasto-dynamics associated with a non-classical 3-node triangular (T3) Mindlin plate finite element. Since couple stress elasto-dynamics incorporates dependence on the material scale length, the proposed approach is sensitive to size effects with microscopic problems while remaining compatible with macroscopic problems. In terms of the finite element implementation, we implemented a T3 plate finite element with 9 nodal degrees of freedom under the Mindlin kinematics assumptions. The approach presents enhanced flexibility to discretize complex microstructures owing to the triangular element topology, and offers sensitivity to account for size effects of microscopic problems. Therefore, it represents a good option for the design of band gap periodic composite micro plates. Validation of the framework is performed through comparison with both analytical and numerical models

Numerical simulation of the interaction between waves and pile breakwater with horizontal slotted plates

Pile breakwaters are a coastal structure designed to protect harbors and coastlines from wave attacks while allowing water circulation and fish passage. Conventional pile breakwaters reduce wave transmission by decreasing porosity, but this increases wave reflection and impact on the breakwater. This study proposes a novel structure called pile breakwaters with horizontal slotted plates (PHSP) to enhance wave dissipation by inducing turbulence and jet phenomena. A comprehensive analysis using a numerical wave tank based on OpenFOAM and OlaFlow is conducted to simulate the interaction between waves and PHSP under various wave conditions. The numerical results are validated using experimental data and theoretical formulas and are compared with conventional pile breakwaters. The study investigates the effects of different parameters on wave transmission, reflection, and energy dissipation. The findings demonstrate that PHSP can effectively double wave energy dissipation, considerably reduce wave transmission, and adapt to diverse wave environments through parameter adjustments

Size effects on a one-dimensional defective phononic crystal sensor

The influence of size effects on one-dimensional defective phononic crystal (PnC) sensors based on simplified strain gradient elasticity theory (SSGET) is studied in this paper. PnCs have been widely used in high-sensitivity gas and liquid sensors by introducing defects to disrupt the perfect PnC modes. In comparison with classical elasticity theory, the SSGET includes two microstructure-related material parameters that can accurately reflect the size effects of the structure. In this paper, the stiffness matrix method was used to calculate the transmission coefficients of the proposed model, avoiding the numerical instability of the transfer matrix method. The results show that the size effects at the microscale affect the perfect PnC bandgap’s frequency range, and the microstructure constants impress the resonant frequency while detecting liquids. Consequently, the accuracy of the sensor is reduced. These findings provide a theoretical basis for designing microscale PnC sensors

Multiaxial Fatigue Analysis of Jacket-Type Offshore Wind Turbine Based on Multi-Scale Finite Element Model

The fatigue damage of a local joint is the key factor accounting for the structural failure of a jacket-type offshore wind turbine. Meanwhile, the structure experiences a complex multiaxial stress state under wind and wave random loading. This paper aims to develop a multi-scale modeling method for a jacket-type offshore wind turbine, in which local joints of the jacket are modeled in a detail by using solid elements, and other components are modeled via the common beam element. Considering the multiaxial stress state of the local joint, multi-axial fatigue damage analysis based on the multiaxial S–N curve is performed using equivalent Mises and Lemaitre methods. The uniaxial fatigue damage data of the jacket model calculated using the multi-scale finite element model are compared with those of the conventional beam model. The results show that the tubular joint of jacket leg and brace connections can be modeled using the multi-scale method, since the uniaxial fatigue damage degree can reach a 15% difference. The comparison of uniaxial and multiaxial fatigue results obtained using the multi-scale finite element model shows that the difference can be about 15% larger. It is suggested that the multi-scale finite element model should be used for better accuracy in the multiaxial fatigue analysis of the jacket-type offshore wind turbine under wind and wave random loading

A Transversely Isotropic Magneto-electro-elastic Circular Kirchhoff Plate Model Incorporating Microstructure Effect

International audienceA non-classical model for transversely isotropic magneto-electro-elastic circular Kirchhoff plates is established based on the extended modified couple stress theory. The Gibbs-type variational principle is used to obtain the governing equations and boundary conditions. To illustrate the newly derived model, the static bending problem of a clamped circular plate subjected to a uniformly distributed constant load is solved numerically by Fourier-Bessel series. The numerical results show that the values of transverse displacement, electric and magnetic potentials predicted by the current model are always smaller than those of the classical model, and the differences are diminishing as the plate thickness increases. In addition, it is shown that the magneto-electro-elastic coupling effect plays an important role in the transverse displacement, electric potential and magnetic potential of the magneto-electro-elastic circular Kirchhoff plates. Furthermore, several reduced specific models are provided for simpler cases

Active tuning of vibration for periodic piezoelectric micro systems: a non-local Mindlin plate finite element approach

International audienceThe present paper is aimed to propose a multi-parameter feedback control method combined with couple stress elasticity to model piezoelectric micro plate coupled systems. The proposed methodology can be used to design controllers for tuning vibration and wave propagation properties of micro scale plates based on coupled piezoelectric sensors and actuators. Specifically, we use a three-parameter relationship that describes the voltage gain within the sensor-to-actuator circuit involving multiple dependence based on mass, damping and stiffness. Consequently, effect of these parameters can be simulated either independently or collectively so as to obtain the optimal control strategy with respect to the required vibroacoustic properties. Meanwhile, since micro plates are involved, the inherent microstructure effects must be accounted for. Hence, the modified couple stress elasto-dynamics is applied and the micro plate model is discretised with a four-node quadrilateral non-conforming element that offers nodal compatibility with high-order theories of elasticity. Based on the proposed numerical methodology, we investigated the feedback control parametrisation for a reference micro plate coupled system which presents significant microstructure effects. Our analysis allowed characterisation of the three control parameters based on their individual effects, and revealed that their combined effect cannot be predicted by considering direct superposition of their individual behaviours. Therefore, the proposed computational methodology provides a convenient solution for the choice and parametrisation of the feedback controller leading to tunable band gap properties of micro scale plate structures