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The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly  symmetric trans-Sasakian manifolds. Finally, they give a nontrivial example of three-dimensional proper trans-Sasakian manifold.

The authors have used the tensorial approach to achieve the goal.

A second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g.

The authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication.

This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks.

The work presents a detailed comparison with reference solutions published in the literature –when available– and numerical results computed using a commercial cell-centred finite volume software.

The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%.

The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.

In this paper, three research topics are presented referring to different aspects of multifield problems in civil engineering. The first example deals with long term behaviour of wood under multiaxial states of stress and the effect of moisture changes on the deformation behaviour of wood. The second example refers to the application of a three‐phase model for soils to the numerical simulation of dewatering of soils by means of compressed air. The soil is modelled as a three phase‐material, consisting of the deformable soil skeleton and the fluid phases – water and compressed air. The third example is concerned with computational durability mechanics of concrete structures. As a particular example of chemically corrosive mechanisms, the material degradation due to the dissolution of calcium and external loading is addressed.

A series of all-atom molecular-level computational analyses is carried out in order to investigate mechanical transverse (and longitudinal) elastic stiffness and strength of p-phenylene terephthalamide (PPTA) fibrils/fibers and the effect various microstructural/topological defects have on this behavior. The paper aims to discuss these issues.

To construct various defects within the molecular-level model, the relevant open-literature experimental and computational results were utilized, while the concentration of defects was set to the values generally encountered under “prototypical” polymer synthesis and fiber fabrication conditions.

The results obtained revealed: a stochastic character of the PPTA fibril/fiber strength properties; a high level of sensitivity of the PPTA fibril/fiber mechanical properties to the presence, number density, clustering and potency of defects; and a reasonably good agreement between the predicted and the measured mechanical properties.

When quantifying the effect of crystallographic/morphological defects on the mechanical transverse behavior of PPTA fibrils, the stochastic nature of the size/potency of these defects was taken into account.

The purpose of this paper is to study the effect of particle shapes (spherical particle and nonspherical fiber) on their orientation distributions in indoor environment.

This paper adopted a particle model to predict the fibrous particle flow and distribution, and analyzed the orientation distributions of nonspherical fiber particles and spherical particles in airflows like indoor places. Fokker-Planck model was employed to solve the orientation behavior of nonspherical fiber particles.

The simulation results discover that the nonspherical airborne fiber particles have very different characteristics and behaviors and their orientation distributions are totally different from the uniform distribution of spherical particles. The investigation of the particle orientation tensor and orientation strength indicates that the airflow field becomes more anisotropic due to the suspended fibers. The airborne fiber particles increase the viscosity of the room airflow due to the fiber induced additional viscosity.

Orientation tensor, strength and additional viscosity in fibrous flow are seldom investigated indoor. This research reveals that the particle shape has to be considered in the analysis of particle transport and distribution in indoor places as most suspended indoor particles are nonspherical.

Derives a formulation for spatial stress tensors and spatial material tensors of hyperelastic material. Looks at a class of materials with the strain energy function decomposed into a volumetric and a deviatoric part. Separate terms formulate the strain energy with respect to the invariants of the left Cauchy‐Green tensor. Stress and material tensors, which play a crucial role in the solution process of the finite element formulation, are derived solely in the current configuration. Applies the described framework to several different constitutive models based on phenomenologically and physically motivated material descriptions. Proposes a formulation for the finite element implementation of van der Waals material. Compares numerical results with experimental investigations given in the literature. For three‐dimensional finite element computations standard elements and mixed elements, based on a three‐field variational principle where displacements, the hydrostatic pressure and the dilatations are independent variables, are used.

An anisotropic modelling of hollow porous cylinders under harmonic axial loading is proposed to simulate the in vivo behavior of structural elements of cortical bone called osteons. The peripheral surface of the medium is supposed to be impermeable, except on possible existing cracks. Numerical tests are performed by analytical and finite element methods based on the Biot poroelastic theory. The influence of microcracks on the fluid flow is numerically investigated. The findings show that the existence of peripheral cracks directly modifies the stimulation of the mechano‐sensitive network of the bone. Thus, this study attempts to propose a likely mechanism by which bone can sense changes of the surrounding mechanical environment.

The purpose of this study is to quantify the impact of the variation of microstructural features on macroscopic and microscopic fields. The application of multi-scale methods in the context of constitutive modeling of microheterogeneous materials requires the choice of a representative volume element (RVE) of the considered microstructure, which may be based on some idealized assumptions and/or on experimental observations. In any case, a realistic microstructure within the RVE is either computationally too expensive or not fully accessible by experimental measurement techniques, which introduces some uncertainty regarding the microstructural features.

In this paper, a systematical variation of microstructural parameters controlling the morphology of an RVE with an idealized microstructure is conducted and the impact on macroscopic quantities of interest as well as microstructural fields and their statistics is investigated. The study is carried out under macroscopically homogeneous deformation states using the direct micro-macro scale transition approach.

The variation of microstructural parameters, such as inclusion volume fraction, aspect ratio and orientation of the inclusion with respect to the overall loading, influences the macroscopic behavior, especially the micromechanical fields significantly.

The systematic assessment of the impact of microstructural parameters on both macroscopic quantities and statistics of the micromechanical fields allows for a quantitative comparison of different microstructure morphologies and a reliable identification of microstructural parameters that promote failure initialization in microheterogeneous materials.

The numerical simulation of two‐dimensional incompressible complex flows of viscoelastic fluids is presented. The context is one, relevant to the food industry (dough kneading), of stirring within a cylindrical vessel, where stirrers are attached to the lid of the vessel. The motion is driven by the rotation of the outer vessel wall, with various stirrer locations. With a single stirrer, both a concentric and an eccentric configuration are considered. A double‐stirrer eccentric case, with two symmetrically arranged stirrers, is also contrasted against the above. A parallel numerical method is adopted, based on a finite element semi‐implicit time‐stepping Taylor‐Galerkin/pressure‐correction scheme. For viscoelastic fluids, constant viscosity Oldroyd‐B and two shear‐thinning Phan‐Thien/Tanner constitutive models are employed. Both linear and exponential models at two different material parameters are considered. This permits a comparison of various stress, shear and extensional properties and their respective influences upon the flow fields generated. Variation with increasing speed of vessel and change in mixer geometry are analysed with respect to the flow kinematics and stress fields produced. Optimal kneading scenarios are commended with asymmetrical stirrer positioning, one‐stirrer proving better than two. Then, models with enhanced strain‐hardening, amplify levels of localised maxima in rate‐of‐work done per unit power consumed. Simulations are conducted via distributed parallel processing, performed on work‐station clusters, employing a conventional message passing protocol (PVM). Parallel results are compared against those obtained on a single processor (sequential computation). Ideal linear speed‐up with the number of processors has been observed.

The purpose of this paper is to examine the macroscopic and microscopic fields of fiber suspensions in the non‐isothermal situations, also to examine the effect of fiber on this non‐isothermal system.

Control equations are coupled and simultaneously solved by collocated finite volume method on fully triangular meshes.

Temperature dependence and wall temperature have significant effect on both macroscopic and microscopic fields of fiber suspensions. Moreover, the influence of fiber on the non‐isothermal system is similar to that of the isothermal system.

This is the first time that the microstructures of both molecules and fibers are presented in the non‐isothermal condition and it is hoped that the results will provide more insight into the microscopics of complex flows.