Elastic-plastic states of a rotating inhomogeneously heated strain hardening hollow shaft

Based on Tresca's yield criterion and the flow rule associated with it, the behaviour of a linearly strain-hardening elastic-plastic hollow shaft subject to a positive radial temperature gradient and monotonously increasing angular speed is studied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constitutive modelling of thermo-viscoelastic-plastic behaviour of adhesively bonded joints

For ductile structural adhesives under thermal and mechanical loading, a thermo-viscoelastic-plastic interfacial constitutive model is introduced using a generalised MAXWELL solid in series with a thermal strain element and a ST.-VENANT body with isotropic hardening for plasticity. The temperature dependency of the viscosity is taken into account on assuming thermorheologically simple material behaviour, while the yield threshold and the hardening parameters depend on empirical functions of temperature. Numerical examples for the model verification and validation are discussed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time and temperature dependent deformation of poly(ether ether ketone) (PEEK)

The stress-strain behavior in tension and the effect of temperature on the creep of poly(ether ether ketone) (PEEK) have been studied. At room temperature, 130° below the glass-transition temperature, the material does not become brittle, and the specimens show necking in tension over a wide range of elongation rates. The stress and strain at yield and the strain at break are almost linear functions of the logarithmic elongation rate. The values of stress and strain at yield increase slightly with increasing elongation rate, while the strain at break decreases markedly. The short-term creep tests were conducted at temperatures extending from 20 to 200°C. The glass-transition temperature was found to be about 155°C. The creep of PEEK is greatest at temperatures above 130°C. In the glass region the time dependence of the deformation is much weaker. It has been found that the time-temperature relation for PEEK corresponds well with its thermorheological simplicity in the temperature range investigated. The data on the temperature shift factor below and above the glass-transition temperature may be fitted separately to the Arrhenius and Williams-Landel-Ferry (WLF) equations, respectively. The long-term creep tests show that PEEK has excellent creep resistance at room temperature. After 14-month tests at a stress level of 30 MPa the total strain exceeds the instantaneous elastic strain only by a factor of 1.15.Institute of Polymer Mechanics. Latvian Academy of Sciences, 23 Aizkraukles St., LV-1006 Riga. Latvia. Department of Polymeric Materials, Chalmers University of Technology. S-412 96 Gothenburg, Sweden. Published in Mekhanika Kompozitnykh Materialov, No. 6, pp. 734–746, November–December, 1997.     

A unified thermal-hardening and thermal-softening constitutive model of soils

Based on the modified Cam-clay model and the concept of subloading yield surface, a thermo-elastoplastic model of normally consolidated and overconsolidated soils is presented in detail. The model is able to describe the thermal-hardening and thermal-softening mechanical behavior of soils with a unified set of parameters. A thermo-induced equivalent stress is proposed to consider the effect of temperature on yield surface and evolution of overconsolidation during shearing process. At the same time, the effect of temperature on the shear stress ratio at the critical state is also implemented in the model. Through comparing the simulated results with test results under different loading and temperature conditions, the availability and the accuracy of the proposed model are carefully verified. Finally, the generating mechanism of the thermal-hardening and thermal-softening mechanical behavior of soil under non-isothermal condition is discussed based on the proposed model.     

Synthesis scheme for hybrid methods of solving boundary problems

A scheme is proposed for the development of a numericoanalytic boundary problem technique that can synthesize the mesh-projective method with the integral transform method to yield an effective hybrid method for the determination of the temperature field in a body from a moving heat source with given dependences of the thermophysical parameters on temperature.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 19–22, 1987.     

Direct evaluation of limit states of heterogeneous materials under cyclic thermo-mechanical loadings

Classical shakedown theorems and their extensions to various material models rest on the temperature-independent coefficients. In this paper, the lower-bound of direct methods is extended to the application on the heterogeneous materials with temperature dependent yield strength and elastic modulus. Moreover, a numerical platform is developed, which makes the practical application more convenient and efficient. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A one-dimensional approach to the chemical and thermo-mechanical coupled modeling of curing adhesives including plasticity

The modeling and simulation of curing adhesives is of great importance for industrial applications, mainly for the automotive industry. The one-dimensional model proposed here combines known viscoelastic models for curing material with effects of plasticity. To describe these plasticity effects, a yield stress with isotropic hardening is formulated as an equation of temperature and degree of cure. The proposed model therefore includes viscoelastic properties, thermo-chemical shrinkage and the aforementioned plasticity characteristics, all as functions of temperature and degree of cure. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal stresses in a cylindrical panel with free ends

Elastic stress state of a thick-walled cylindrical panel, which is subjected to a positive temperature gradient in the radial direction, is investigated under generalized plane strain conditions. In particular, the stress distributions in the panel at the elastic limit according to von Mises' yield criterion are studied. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chaotic Behavior in Slowly Varying Systems of Nonlinear Differential Equations

A technique is developed to find parameter regions of chaotic behavior in certain systems of nonlinear differential equations with slowly varying periodic coefficients. The technique combines previous results on how to find branches of periodic solutions which terminate with a homoclinic orbit and results on how to find chaotic trajectories in the neighborhood of homoclinic trajectories of the autonomous system. The technique is applied to the continuous stirred tank reaction A → B, for which it is shown that a slowly varying periodic flow rate can yield aperiodic temperature fluctuations.     

Galerkin method for a nonlinear parabolic–elliptic system with nonlinear mixed boundary conditions

Materials which are heated by the passage of electricity are usually modeled by a nonlinear coupled system of two partial differential equations. The current equation is elliptic, while the temperature equation is parabolic. These equations are coupled one to another through the conductivities and the Joule effect. A computationally attractive discretization method is analyzed and shown to yield optimal error estimates in H¹. © 1993 John Wiley & Sons, Inc.     

Optimization of two-layered steel/aluminum hollow cylinders under combined load

Subject of the investigation is a two-layered tube under generalized plane strain subject to a combination of internal pressure and an elevated temperature at the inner surface. Criterion for the permissible stress is the yield criterion by von Mises, and the elastic limits are given as well as a way for a straightforward optimization procedure in respect of the weight of the device is shown. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A modified Artificial Bee Colony algorithm for structural damage identification under varying temperature based on a novel objective function

This paper presents a modified Artificial Bee Colony algorithm for structural damage identification. Meanwhile, the effect of temperature variation is considered and the change of temperature will lead to the alteration of Young's modulus of material. A novel objective function is proposed as the combinations of the partial mode shape curvature data, alterations of natural frequencies, and a sparse penalty term. Such an objective is found to be sensitive to structural damage while not sensitive to environmental effects. On the other hand, To render the standard Artificial Bee Colony algorithm more powerful and robustness, two local search strategies are introduced into the employed and onlooker bee phase of the Artificial Bee Colony algorithm, respectively. Two numerical examples and a laboratory verification are employed to verify the efficiency and advantage of the proposed algorithm. The final results show that the present algorithm could yield more satisfactory identification results compared with other state-of-the-art evolutionary algorithms, even high-level noise and temperature variation are considered; and the proposed novel objective function is more sensitive to structural damages, compared with the traditional mode-shape-based objective function.     

Buoyancy-assisted flow of yield stress fluids past a cylinder: Effect of shape and channel confinement

The aiding-buoyancy mixed convection heat transfer in Bingham plastic fluids from an isothermal cylinder of elliptical and circular shape in a vertical adiabatic channel is numerically investigated. For a fixed shape of the elliptical cylinder E = 2 (ratio of major to minor axes), the effect of confinement is studied for three values of blockage ratio, B, defined as the ratio of the channel width to the circumference of the cylinder/π, as 6.5, 2.17 and 1.3. In order to delineate the role of cross-section of the cylinder, results are also presented here for a circular cylinder of the same heat transfer area as the elliptical cylinder. The results presented herein span the range of conditions as: Bingham number, 0 ≤ Bn ≤ 100, Reynolds number, 1 ≤ Re ≤ 40, and Prandtl number, 1 ≤ Pr ≤ 100 over the range of Richardson number Ri = 0 (pure forced convection) to Ri = 10. Extensive results on drag coefficient, local and surface averaged values of the Nusselt number and yield surfaces are presented herein to elucidate the combined effects of buoyancy, blockage ratio and fluid yield stress. The morphology of the yield surfaces shows that the unyielded plug regions formed upstream and downstream of the cylinder grow faster at low Reynolds numbers with the increasing yield stress effects under the weak buoyancy forces, i.e., small values of Grashof or Richardson number. The heat transfer enhancement is observed with the increasing channel-confinement due to the sharpening of the temperature gradients near the surface of the cylinder. The average Nusselt number shows a positive dependence on the Reynolds number, Prandtl number and Richardson number irrespective of the shape of the cylinder or the type of fluid. By employing the modified definitions of the dimensionless parameters (based on the two choices of the overall effective fluid velocity), predictive correlations have been established for estimating the value of the average Nusselt number in a new application.     

Plastic flow in very low temperature regime within annular micropores

The rate of deformation for glassy (amorphous) matter confined in microscopic domain at very low temperature regime was investigated using a rate-state-dependent model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be the enhanced rate of deformation and (shear) yield stress due to the almost vanishing viscosity in micropores subjected to some surface conditions: The relatively larger roughness (compared to the macroscopic domain) inside micropores and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the (plastic) flow in micropores. By using the boundary perturbation method, we obtained a class of microscopic fields for the rate of deformation and yield stress at low temperature regime with the presumed small wavy roughness distributed along the walls of an annular micropore.     

Plastic flow in very low temperature regime within annular micropores

The rate of deformation for glassy (amorphous) matter confined in microscopic domain at very low temperature regime was investigated using a rate-state-dependent model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be the enhanced rate of deformation and (shear) yield stress due to the almost vanishing viscosity in micropores subjected to some surface conditions: The relatively larger roughness (compared to the macroscopic domain) inside micropores and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the (plastic) flow in micropores. By using the boundary perturbation method, we obtained a class of microscopic fields for the rate of deformation and yield stress at low temperature regime with the presumed small wavy roughness distributed along the walls of an annular micropore.     

Numeric modeling of thermal pollution in Plomin bay area

In order to analyze the thermal pollution of the Plomin bay induced by the used cooling water released from Plomin 1 and Plomin 2 thermal power plants, flow simulations and temperature field analysis were conducted. The measurements of the bay surface temperature field were carried out as well as the corresponding 3D water flow simulations on the realistically modeled bay. The accuracy of the simulation results was evaluated by the comparison of computed and measured surface temperatures. Furthermore, numerical meshes of different density were used in order to determine model sensitivity where the results showed a significant effect of the mesh density on the simulation results. Although the simulations obtained with a denser mesh yield more accurate results and allow for the reconstruction of heated water surface flow with better reliability, the sparser mesh provided sufficiently accurate results as well. The overall temperature field obtained with the numerical model agrees well with the measured temperature values, which demonstrates the successful application of the 3D flow numerical model on the Plomin bay thermal pollution problem.      

Nonsimilar boundary layer analysis of double-diffusive convection from a vertical truncated cone in a porous medium with variable viscosity

This work presents a boundary layer analysis about variable viscosity effects on the double-diffusive convection near a vertical truncated cone in a fluid-saturated porous medium with constant wall temperature and concentration. The viscosity of the fluid is assumed to be an inverse linear function of the temperature. A boundary layer analysis is employed to derive the nondimensional nonsimilar governing equations, and the transformed boundary layer governing equations are solved by the cubic spline collocation method to yield computationally efficient numerical solutions. The obtained results are found to be in good agreement with previous papers on special cases of the problem. Results for local Nusselt and Sherwood numbers are presented as functions of viscosity-variation parameter, buoyancy ratio, and Lewis number. For a porous medium saturated with a Newtonian fluid with viscosity proportional to an inverse linear function of temperature, higher value of viscosity-variation parameter leads to the decrease of the viscosity in fluid flow, thus increasing the fluid velocity as well as the local Nusselt number and the local Sherwood number.     

Numerical analysis of processes of thermoplastic deformation of axisymmetric bodies with regard for unloading

We investigate the thermoelastoplastic state of an isotropic homogeneous medium under the action of temperature loads. A mathematical model of plastic flow is considered. We propose a method for constructing an unconditionally stable numerical scheme of the finite-element method for the solution of such problems. The process of propagation of the primary and secondary unloading zones in a body is shown. The time distribution of the intensity of plastic strain at a corner point of the body is presented. Results obtained without regard for the dependence of the yield strength on temperature and with regard for it are investigated.     

Analysis of stress and strain in tension cylindrical sample

One of the basic engineering problem occurring during the numerical analysis is to define the function of yield stress of material in the real conditions of a technological process. These properties are necessary to calculate the deformation and the state of stress and strain in the surface layer of an object. An inappropriate selection of the mechanical properties of the material is the reason of the occurrence of errors in numerical calculations of a continuous object, considered as a boundary and initial problem. Scientific investigations are being conducted with the aim to develop a database concerning yield stresses for different metals, depends on complex conditions of thermo-dynamical loads, e.g. temperature, the equivalent of the strain and the strain rate. The article presents a method of the determination of this dependence while using an experimental and numerical analysis. During the model investigations on the INSTRON testing machine, the force of elongation of the sample is measured and then calculations are made of the displacement of nodes of finite elements, plotted on outside surface of sample. The process is considered as a multi nonlinear problem. For this reason, an incremental method of motion and deformation of solid in an updated Lagrange formulation is used. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Buoyant Poiseuille–Couette flow with viscous dissipation in a vertical channel

Steady combined forced and free convection is investigated in a vertical channel having a wall at rest and a moving wall subjected to a prescribed shear stress. The moving wall is thermally insulated, while the wall at rest is kept at a uniform temperature. The analysis deals with the fully–developed parallel flow regime. The governing equations yield a boundary value problem, that is solved analytically by employing a power series expansion of the velocity field with respect to the transverse coordinate. It is shown that the nonlinear interplay between buoyancy and viscous dissipation may determine the existence of dual solutions of the boundary value problem corresponding to fixed values of the applied shear stress on the moving wall and of the hydrodynamic pressure gradient. It is shown that a nontrivial fully separated flow may occur such that the hydrodynamic pressure gradient is zero and the shear stress vanishes on both walls. E. Magyari: On leave from Institute of Building Technology, ETH – Zürich