Dynamic Finite Element Modelling and Vibration Analysis of Prestressed Layered Bending–Torsion Coupled Beams

Free vibration analysis of prestressed, homogenous, Fiber-Metal Laminated (FML) and composite beams subjected to axial force and end moment is revisited. Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) models are developed and presented. The frequency results are compared with those obtained from the conventional FEM (ANSYS, Canonsburg, PA, USA) as well as the Homogenization Method (HM). Unlike the FEM, the application of the DFE formulation leads to a nonlinear eigenvalue problem, which is solved to determine the system’s natural frequencies and modes. The governing differential equations of coupled flexural–torsional vibrations, resulting from the end moment, are developed using Euler–Bernoulli bending and St. Venant torsion beam theories and assuming linear harmonic motion and linearly elastic materials. Illustrative examples of prestressed layered, FML, and unidirectional composite beam configurations, exhibiting geometric bending-torsion coupling, are studied. The presented DFE and FEM results show excellent agreement with the homogenization method and ANSYS modeling results, with the DFE’s rates of convergence surpassing all. An investigation is also carried out to examine the effects of various combined axial loads and end moments on the stiffness and fundamental frequencies of the structure. An illustrative example, demonstrating the application of the presented methods to the buckling analysis of layered beams is also presented.

Study on Mechanical Problems of Complex Rock Mass by Composite Material Micromechanics Methods: A Literature Review

The mechanical analysis of complex rock mass is a difficult problem, which often occurs in scientific research and practical engineering. Many achievements have been made in the study of rock mass composite problems by composite material micromechanics method, but it has not been well summarized so far. This paper summarizes in detail the research status of complex rock mass problems by composite material micromechanics method at home and abroad, including the application of the Eshelby equivalent inclusion theory and self-consistent model in rock mass composite problems, and the application of the homogenization method in jointed rock mass and other rock mass composite problems such as anchored rock mass, layered rock mass, and salt rock mass with impurities. It is proposed that the structural similarity and mechanical analysis similarity should be satisfied when the composite material micromechanics method is used to study the complex rock mass. Finally, the problems that need to be further studied are put forward. The research results provide a valuable reference for the study of complex rock mass by the composite material micromechanics method.

Effect of Carbon Nanofiber Clustering on the Micromechanical Properties of a Cement Paste

The use of carbon nanofibers (CNFs) in cement systems has received significant interest over the last decade due to their nanoscale reinforcing potential. However, despite many reports on the formation of localized CNF clusters, their effect on the cement paste micromechanical properties and relation to the mechanical response at the macroscopic scale are still not fully understood. In this study, grid nanoindentation coupled with scanning electron microscopy and energy dispersive spectroscopy was used to determine the local elastic indentation modulus and hardness of a portland cement paste containing 0.2% CNFs with sub-micro and microscale CNF clusters. The presence of low stiffness and porous assemblage of phases (modulus of 15–25 GPa) was identified in the cement paste with CNFs and was attributed primarily to the interfacial zone surrounding the CNF clusters. The CNFs favored the formation of higher modulus C–S–H phases (>30 GPa) in the bulk paste at the expense of the lower stiffness C–S–H. Nanoindentation results combined with a microscale–macroscale upscaling homogenization method further revealed an elastic modulus of the CNF clusters in the range from 18 to 21 GPa, indicating that the CNF clusters acted as compliant inclusions relative to the cement paste.

Design of a Lightweight Multilayered Composite for DC to 20 GHz Electromagnetic Shielding

The work aims to design a trilayer composite dedicated to electromagnetic shielding over a large frequency range, from 1 Hz to 20 GHz. Analytical and numerical models are used to determine the shielding effectiveness (SE) of this composite in the case of a planar shield. The shield is constituted of a support layer, a magnetic layer, and a conductive layer. Two possible designs are considered. To simplify the numerical calculation, a homogenization method and the Artificial Material Single Layer (AMSL) method are used. The proposed composite shows a good shielding capacity over the whole studied frequency range, with shielding effectiveness higher than 17 dB and 75 dB, respectively, in the near-field (1 Hz–1 MHz) and far-field (1 MHz–20 GHz). Both homogenization and AMSL methods show good suitability in near-field and allow one to greatly reduce the calculation time.

Analysis of unbalanced laminate composites with imperfect interphase: Effective properties via asymptotic homogenization method

This work addresses the Asymptotic Homogenization Method (AHM) to find all the non-zero independent constants of the fourth-order elasticity tensor of a theoretically infinite periodically laminated composite. The concept of Unit Cell describes the domain, comprised of two orthotropic composite plies separated by an isotropic interphase. A general case with an unbalanced composite is considered. Thus, the coupled components of the tensor are expected. Both analytical and numerical solutions are derived. In addition, an interphase degradation model is proposed to evaluate its effect on the effective properties of the media. Two different stacking sequences are considered with five degrees of interphase imperfection each. The results show good agreement between the analytical and numerical solutions. In addition, it is clear that the more imperfect the interphase is, the more affected the effective properties of the media are, especially those dependent on the stacking direction.

Homogenization of fully nonlinear rod lattice structures: on the size of the RVE and micro structural instabilities

This work investigates the possibility of applying two-scale computational homogenization to rod lattice structures emerging, for instance, from additive manufacturing. The influence of the number of unit cells within the representative volume element (RVE), thus, the RVE’s size on the homogenized mechanical response is studied for occurring microscopic structural instabilities. Therein, the macro-scale, described in terms of three-dimensional continuum mechanics, is coupled to the micro-scale described by geometrically exact rods, enabling arbitrary large deformations and rotations. A special feature of the presented framework is that the rods building the lattice structures are not restricted to deform purely elastically but may deform inelastically. The mechanical response of lattice structures is investigated by applying the developed homogenization method to an exemplary lattice. Under special loads the structure reaches an instable state and may buckle. The appearance of instabilities depends on the geometric properties of the lattice’s underlying rods and the RVE’s size.

Geometrical model of lobular structure and its importance for the liver perfusion analysis

A convenient geometrical description of the microvascular network is necessary for computationally efficient mathematical modelling of liver perfusion, metabolic and other physiological processes. The tissue models currently used are based on the generally accepted schematic structure of the parenchyma at the lobular level, assuming its perfect regular structure and geometrical symmetries. Hepatic lobule, portal lobule, or liver acinus are considered usually as autonomous functional units on which particular physiological problems are studied. We propose a new periodic unit—the liver representative periodic cell (LRPC) and establish its geometrical parametrization. The LRPC is constituted by two portal lobulae, such that it contains the liver acinus as a substructure. As a remarkable advantage over the classical phenomenological modelling approaches, the LRPC enables for multiscale modelling based on the periodic homogenization method. Derived macroscopic equations involve so called effective medium parameters, such as the tissue permeability, which reflect the LRPC geometry. In this way, mutual influences between the macroscopic phenomena, such as inhomogeneous perfusion, and the local processes relevant to the lobular (mesoscopic) level are respected. The LRPC based model is intended for its use within a complete hierarchical model of the whole liver. Using the Double-permeability Darcy model obtained by the homogenization, we illustrate the usefulness of the LRPC based modelling to describe the blood perfusion in the parenchyma.

Numerical Modelling of the Powder Metallurgical Manufacturing Chain of High Strength Sintered Gears

This paper presents a digital model for the powder metallurgical (PM) production chain of high-performance sintered gears based on an integrated computational materials engineering (ICME) platform. Discrete and finite element methods (DEM and FEM) were combined to describe the macroscopic material response to the thermomechanical loads and process conditions during the entire production process. The microstructural evolution during the sintering process was predicted on the meso-scale using a Monte-Carlo Model. The effective elastic properties were determined by a homogenization method based on modelling a representative volume element (RVE). The results were subsequently used for the FE modelling of the heat treatment process. Through the development of multi-scale models, it was possible obtain characteristics of the microstructural features. The predicted hardness and residual stress distributions allowed the calculation of the tooth root load bearing capacity of the heat-treated sintered gears.