On Some Thermoelastic Problem of a Nonhomogeneous Long Pipe

The paper deals with the thermoelastic problem of a multilayered pipe subjected to normal loadings on its inner surface and temperature differences on its internal and external surfaces. Two types of nonhomogeneous pipe materials of pipe are considered: (1) a ring-layered composite composed of two repeated thermoelastic solids with varying thickness and (2) a functionally graded ring layer. The ring-layered pipe with periodic structure is investigated by using the homogenized model with microlocal parameters. A homogenization approach is proposed for the modelling of the FGM pipe. The analysis of obtained circumferential, radial and axial stress is presented in the form of figures and discussed in detail. It was shown that the proposed approach to the homogenization allows us to correctly calculate the averaged characteristics in the representative cell (the macro-characteristics) and also the characteristics dependent on the choice of the component in the representative cell (the micro-characteristics) for both microperiodic composites and functionally graded materials.

Extending a Homogenized Model for Characterizing Multidirectional Jellyroll Failure in Prismatic Lithium-Ion Batteries

Lithium-ion batteries have been widely used in electric vehicles but may cause severe internal short circuit during extreme intrusion-type accidents. A well-defined homogenized model of battery or jellyroll is necessary for safety assessment and design on large-scale structure level. In our previous study, the jellyroll of prismatic lithium-ion battery cell shows anisotropic mechanical behavior and failure tolerance. For homogenized characterization of jellyroll, in the present paper, the user subroutine of a constitutive model taking anisotropy into account is implanted into Abaqus finite element analysis software, which is capable of capturing the force versus displacement responses along different loading directions before jellyroll failure. To extend the capability of the homogenized model, five single-parameter failure criteria and two combined failure criteria are examined in predicting the failure onsets in jellyroll along different directions. The result proves the combined failure criteria is competent to correctly predict the multidirectional failure onsets compared with the single-parameter ones.

Homogenization of piezoelectric planar Willis materials

Homogenization theories provide models that simplify the constitutive relations of heterogeneous media while retaining their macroscopic features. These theories have shown how the governing fields can be macroscopically coupled, even if they are microscopically independent. A prominent example is the Willis theory which predicted the strain-momentum coupling in elastodynamic metamaterials. Recently, a theory that is based on the Green’s function method predicted analogous electro-momentum coupling in piezoelectric metamaterials. Here, we develop a simpler scheme for fibrous piezoelectric composites undergoing antiplane shear waves. We employ a source- driven approach that delivers a unique set of effective properties for arbitrary frequency-wavevector pairs. We numerically show how the resultant homogenized model recovers exactly the dispersion of free waves in the composite. We also compute the effective properties in the long-wavelength limit and off the dispersion curves, and show that the resultant model satisfy causality, reciprocity and energy conservation. By contrast, we show how equivalent models that neglect the electromomentum coupling violate these physical laws.

Homogenization effects on simulated pultruded glass fibre reinforced laminate under compression – from static to dynamic models

This study presents a numerical analysis of failure in pultruded glass fibre reinforced polymer (GFRP) with three reinforcement layers, subjected to out-of-plane compressive loadings at low and high strain rates (10-3 s-1 and 103 s-1). The simulations targets to a computationally efficient homogenization with different element types and sizes. A single-element model was created to demonstrate the highest level of homogenization. The material properties in the homogenized model were calculated using the ESAComp (Altair) software. The 3D Hashin failure criterion was implemented as a user-defined subroutine into the finite element method using Abaqus (Simulia/Dassault Systemes) to predict the failure. The comparison between different meshes and elements shows the sufficient accuracy of the homogenized model to predict the material response at the damage onset, but the location of the crack was not accurately predicted as expected. High-rate impact simulations of the Split Hopkinson Pressure Bar tests showed that the mesh does not significantly affect the failure (strain) predicted by the homogenized model.

An Interface Anticrack in a Periodic Two–Layer Piezoelectric Space under Vertically Uniform Heat Flow

This paper aims to investigate 3D static thermoelectroelastic problem of a uniform heat flow in a bi-material periodically layered space disturbed by a thermally and electrically-insulated rigid sheet-like inclusion (so-called anticrack) situated at one of the interfaces. An approximate analysis of the considered laminated composite is given in the framework of the homogenized model with microlocal parameters. Accurate results are obtained by constructing suitable potential solutions and reducing to the corresponding homogeneous thermoelectromechanical (or thermomechanical) anticrack problems. The governing boundary integral equation for a planar interface anticrack of arbitrary shape is derived in terms of a normal stress discontinuity. As an illustration, a complete solution for a rigid circular inclusion is obtained in terms of elementary functions and interpreted from the failure perspective. Unlike existing solutions for defects at the interface of materials, the solution obtained displays no oscillatory behavior.

Lattice structure optimization and homogenization through finite element analyses

Lattice topology optimization can stimulate the design of new materials with spatially dependent properties with composite parts or three-dimensional printed components. The present work considers a mounting bracket for an industrial robotic arm as a case study, having as the main objective the increase of the fundamental frequency and secondly its mass reduction. Two design approaches were considered by using the ANSYS software: the first stage optimized the orthotropic lattice material by establishing an optimal variable cubic cell lattice density distribution in the geometric model; the second stage used a homogenized model based on the lattice optimization resulted from the previous stage and considered different volume fractions and variable density for four different types of cells. Homogenization increased the stiffness of the bracket by using the same cubic lattice cell and the fundamental frequency increased from 1227 Hz obtained with lattice optimization to 1366 Hz after homogenization. For the unoptimized bracket the fundamental frequency was only 839 Hz. The mass was reduced to more than half. The most effective proved to be the midpoint lattice cell as by homogenization the mass was reduced from 45.5 kg to 18.22 kg.

Fast and spectrally accurate numerical methods for perforated screens (with applications to Robin boundary conditions)

This paper considers the use of compliant boundary conditions to provide a homogenized model of a finite array of collinear plates, modelling a perforated screen or grating. While the perforated screen formally has a mix of Dirichlet and Neumann boundary conditions, the homogenized model has Robin boundary conditions. Perforated screens form a canonical model in scattering theory, with applications ranging from electromagnetism to aeroacoustics. Interest in perforated media incorporated within larger structures motivates interrogating the appropriateness of homogenized boundary conditions in this case, especially as the homogenized model changes the junction behaviour considered at the extreme edges of the screen. To facilitate effective investigation we consider three numerical methods solving the Helmholtz equation: the unified transform and an iterative Wiener–Hopf approach for the exact problem of a set of collinear rigid plates (the difficult geometry of the problem means that such methods, which converge exponentially, are crucial) and a novel Mathieu function collocation approach to consider a variable compliance applied along the length of a single plate. We detail the relative performance and practical considerations for each method. By comparing solutions obtained using homogenized boundary conditions to the problem of collinear plates, we verify that the constant compliance given in previous theoretical research is appropriate to gain a good estimate of the solution even for a modest number of plates, provided we are sufficiently far into the asymptotic regime. We further investigate tapering the compliance near the extreme endpoints of the screen and find that tapering with $\tanh $ functions reduces the error in the approximation of the far field (if we are sufficiently far into the asymptotic regime). We also find that the number of plates and wavenumber has significant effects, even far into the asymptotic regime. These last two points indicate the importance of modelling end effects to achieve highly accurate results.