Relations Of Continuum Mechanics Research Articles

Two-way fluid-structure interaction study of twisted tape insert in a circular tube having integral fins with nanofluid

This work deals with fluid-structure interaction (FSI), one of the emerging areas of numerical simulation and calculation. This research shows a numerical study investigating heat transfer enhancement and fluid-structure interaction in a circular finned tube by using alumina nanofluid as a working fluid with a typical twisted tape that has a twisting ratio of 1.85. The studied nanofluid volumes of fraction are φ=0, 3, 5 % under conditions of laminar and turbulent flow. The solution for such problems is based on the relations of continuum mechanics and is mostly done with numerical methods. FSI occurs when the flow of fluid influences the properties of a structure or vice versa. It is a computational challenge to deal with such problems due to complexity in defining the geometries, nature of the interaction between a fluid and solid, intricate physics of fluids and requirements of computational resources. CFD investigations were made based on the numerical finite volume techniques to solve the governing three-dimensional partial differential equations to get the influence of inserted twisted tape and concentration of nanofluid on heat transfer enhancement, friction loss, average Nusselt number, velocity profile, thermal performance factor characteristics, and two-way interaction in a circular tube at laminar and turbulent flow. The governing continuity, momentum and energy transfer equations are solved using Ansys Fluent and Transient Structural. The simulation results show that the deformations of two-way coupling fluctuate from side to side, with 0.004 mm, as maximum amplitude, located at the typical twisted tape center. Heat transfer dissipation improved by adding fins and as Reynolds numbers increase the heat transfer behavior increases.

On universal relations in continuum mechanics: A discussion centred on shearing motions

A local universal relation is an equation between the stress components and the position vector components which holds for any material in an assigned constitutive family. Although universal relations may be of great help to modellers in characterizing the material behaviour, they are often ignored. In this paper we briefly discuss the valuable insights that universal relations may offer in solid mechanics and determine novel universal relations associated with shearing motions in nonlinearly elastic and nonlinearly viscoelastic materials of differential type.

A Personal Appreciation of Walter Noll

Walter Noll is personally acknowledged to have been an inspirational teacher and an exemplar in his analysis of fundamental concepts and relations in Continuum Mechanics. Attention is drawn to unfounded criticisms of two aspects of his work and how considerations of local spatial and temporal averaging of microscopic behaviour can complement and inform the continuum viewpoint. Remarks on such considerations briefly summarise the results of published works which both utilised Noll’s direct notation and attempted to emulate his precision and clarity.

Establishing experiments in tensor nonlinear theories of continuum mechanics

A basic scheme of establishing experiments to find three material functions of tensor nonlinear constitutive relations in continuum mechanics is described. These material functions depend on the three invariants of a stress state. It is proposed to use long hollow cylindrical specimens suitable to implement any combination of the following realizable stress states: uniaxial tension, torsion, longitudinal shear, and uniform compression.

Analysis of volume-average relations in continuum mechanics

In this paper, volume-average relations related to the multilevel modelling process in continuum mechanics are analysed and the concept of average consistency is investigated both analytically and numerically. These volume averages are used in the computational homogenization technique, where a transition of the mechanical properties from the local, microscopic, to the global, macroscopic, length scale is obtained. The representative volume element (RVE) is used as a reference placement and the solution, in terms of volume-averaged stress, will depend on which boundary conditions are chosen for the RVE. Three types of boundary conditions – periodic, affine and anti-periodic – are analysed with respect to the average consistence for the kinematical and stress relations used in continuum mechanics. The inconsistence is quantified by introducing the inconsistence ratio. It is shown analytically that some average stress relations are fulfilled, assuming the periodic boundary condition and anti-periodic traction vector, whereas the average relations connected to the deformation are in general not average consistent. The inconsistence is investigated in a plane model using the finite element technique. The numerical investigation has shown that the inconsistence ratios related to the deformation are also average consistent in the examples considered.

A Comparison of One‐Way and Two‐Way Coupling Methods for Numerical Analysis of Fluid‐Structure Interactions

The interaction between fluid and structure occurs in a wide range of engineering problems. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid‐structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. One possibility for reducing the computational effort of fluid‐structure simulations is the use of one‐way coupled simulations. In this paper, different problems are investigated with one‐way and two‐way coupled methods. After an explanation of the solution strategy for both models, a closer look at the differences between these methods will be provided, and it will be shown under what conditions a one‐way coupling solution gives plausible results.

Molecular-dynamic modeling of mechanical properties of free defect metal nanocrystals

Nowadays, nanotechnologies are rapidly progressing, and the necessity has arisen in obtaining predictable properties of nanostructures by processes using various thermomechanical actions exerted on starting systems. In the present article, results of a molecular-dynamic study of the mechanical failure of a three-dimensional copper nanocrystal under uniaxial tension are reported. Two types of uniaxial tension were considered: • extension of the crystal with one boundary rigidly fixed and the other boundary starting moving at the initial time with a constant velocity v 0; • extension of the crystal with a Heaviside-function force F 0. Based on the mesoanalysis performed, relations of continuum mechanics were checked for nanosize objects, and mechanical characteristics of copper nanoclusters, such as the stress versus strain relation and the Young’s modulus, were obtained in the whole range of external actions examined ( v 0 = 10–1000 m/s, F 0 = 1–20 GPa). Local criteria of dynamic fracture of defect-free copper nanocrystals are established. The limiting static stress–strain diagram is shown to coincide with the results obtained for the dynamic case. The results are checked on the nanocrystals, the size of which is greater than initial one. The critical nanocrystal size is revealed, beginning with that the crystal size has not effect on calculated mechanical characteristics.

Analysis of Nonlinear Effects of Penetration of a Cylindrical Striker into Sandy Ground

To determine the forces of resistance to penetration of a striker into grounds, we analyze the applicability of various models of the behavior of ground media and study the influence of the strength of interacting media on the value of the contact force. We substantiate the validity of the method of “inverted” experiment used for the evaluation of the force of resistance to penetration of a striker into ground by recording strains formed in a measuring rod. The mathematical model used for the description of deformation of media is formulated on the basis of the relations of continuum mechanics and the theory of plastic yield. The statement of the problem corresponds to the inverted experiment in which a container filled with ground hits the immobile measuring rod (striker). The obtained numerical value of the force of resistance to penetration of the striker into ground qualitatively and quantitatively agrees with the parameters recorded in the measuring rod.

On universal relations in continuum mechanics

This paper is devoted to a systematic study of local universal relations in continuum mechanics. We show that it is possible to determine the complete set of independent universal relations whose characterization is obtained by linear universal rules. A historical review of the literature on the topic and various significant examples are given.

Modeling of penetrant diffusion in glassy polymers with an integral sorption deborah number

AbstractA mathematical model was developed to explain the anomalous penetrant diffusion behavior in glassy polymers. The model equations were derived by using the linear irreversible thermodynamics theory and the kinematic relations in continuum mechanics, showing the coupling between the polymer mechanical behavior and penetrant transport. The Maxwell model was used as the stress–strain constitutive equation, from which the polymer relaxation time was defined. An integral sorption Deborah number was proposed as the ratio of the characteristic relaxation time in the glassy region to the characteristic diffusion time in the swollen region. With this definition, an integral sorption process was characterized by a single Deborah number and the controlling mechanism was identified in terms of the value of the Deborah number. The model equations were two coupled nonlinear differential equations. A finite difference method was developed for solving the model equations. Numerical simulation of integral sorption of penetrants in glassy polymers was performed. The simulation results show that (1) the present model can predict Case II transport behavior as well as the transition from Case II to Fickian diffusion and (2) the integral sorption Deborah number is a major parameter affecting the transition. © 1993 John Wiley & Sons, Inc.

Some generalizations of the thermodynamic relations of continuum mechanics for irreversible processes

Some generalizations of the thermodynamic relations of continuum mechanics for irreversible processes