scholarly journals Visco-elastic-plastic movement of wood material

2020 ◽  
Author(s):  
С.М. Базаров ◽  
И.К. Говядин ◽  
А.В. Елкин
Keyword(s):  
Equations Of Motion ◽  
Strain Tensor ◽  
Temperature Fields ◽  
Wood Material ◽  
Elastic Plastic ◽  
Relaxation Parameters ◽  
Liquid States ◽  
Biopolymer Mechanics ◽  
Scalar Relaxation ◽  
Polymer State

Материал древесины как природный полимер в зависимости от характера теплового движения может находиться в трех релаксационных состояниях: стеклообразном, в котором возможны только колебательные движения атомов в макромолекулах, высокоэластичном, в котором возможны колебательные движения звеньев и сегментов и их взаимная подвижность, вязкотекучем, в котором имеет место подвижность макромолекул и элементов надмолекулярной структуры в целом. Этим состояниям соответствуют агрегатные структуры: первому твердая, второму твердая и третьему жидкая. В тепловом поле при повышении температуры происходят переходы полимера из одного релаксационного состояния в другое. При охлаждении происходят переходы в обратном направлении. В пространственно градиентных температурных полях полимер может находиться одновременно в твердом и жидком состояниях. Представленным трем релаксационным состояниям полимера ставится в соответствие обобщенная модель вязко-упруго-пластического тела. Уравнения движения материала древесины построены на основании феноменологических представлений механики сплошной среды, замыкание уравнений выполнено на основе связи тензора напряжений с тензором деформаций в соответствии с выбранной реологической моделью для материала древесины как полимера. Уравнения построены для однородной сплошной среды, при переходе к неоднородной скалярные релаксационные параметры состояния полимера необходимо представлять в тензорной форме. Данное исследование может рассматриваться как элемент основ механики биополимеров. Wood material, as a natural polymer, depending on the nature of thermal motion can be in three relaxation States: glassy, in which only vibrational movements of atoms in macromolecules are possible highly elastic, in which vibrational movements of links and segments are possible, and their mutual mobility viscous, in which there is mobility of macromolecules and elements of supramolecular structure as a whole. These States correspond to aggregate structures: the first solid, the second solid and the third liquid. In the thermal field, when the temperature rises, the polymer transitions from one relaxation state to another. When cooled, transitions occur in the opposite direction. In spatially gradient temperature fields the polymer can be simultaneously in solid and liquid States. The generalized model of visco-elastic-plastic body is put in accordance with the presented three relaxation States of the polymer. The equations of motion of the material of wood is built on the basis of phenomenological concepts of continuum mechanics, the circuit equations is made on the basis of when the stress tensor with the strain tensor in accordance with the selected rheological model for wood material, like a polymer. The equations are constructed for a homogeneous continuous medium, in the transition to inhomogeneous scalar relaxation parameters of the polymer state must be represented in tensor form. This study can be considered as an element of the foundations of biopolymer mechanics.

Numerical analysis of high-speed wheel/rail adhesion under interfacial liquid contamination using an elastic-plastic asperity contact model

2016 ◽  
Vol 231 (1) ◽  
pp. 63-74
Author(s):  
Bing Wu ◽  
Tao Wu ◽  
Zefeng Wen ◽  
Xuesong Jin
Keyword(s):  
Surface Roughness ◽  
High Speed ◽  
Present Model ◽  
Temperature Fields ◽  
Elastic Model ◽  
Asperity Contact ◽  
Roughness Parameters ◽  
Slip Ratio ◽  
Elastic Plastic ◽  
Train Speed

The objective of this paper is to investigate the high-speed wheel/rail adhesion under interfacial liquids contamination using a numerical model. This model considers the rheological property of interfacial liquids, elastic-plastic deformation of microasperities contact and the temperature across the film thickness. The pressure and the temperature fields can be obtained. The effects of train speed, surface roughness parameters, characteristic shear stress, and the slip ratio are investigated. Furthermore, the present model is compared with the elastic model and the elastic-plastic model without considering the thermal effect. The numerical results show that the train speed and temperature affects the wheel/rail adhesion significantly.

scholarly journals Additive Manufacturing of Complex Components through 3D Plasma Metal Deposition—A Simulative Approach

Metals ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 574 ◽  
Author(s):  
Khaled Alaluss ◽  
Peter Mayr
Keyword(s):  
Temperature Field ◽  
Additive Manufacturing ◽  
Residual Stresses ◽  
Field Distribution ◽  
Base Material ◽  
Metal Deposition ◽  
Temperature Fields ◽  
Experimental Investigations ◽  
Temperature Field Distribution ◽  
Elastic Plastic

This study examines simulative experimental investigations on the additive manufacturing of complex component geometries using 3D plasma metal deposition (3DPMD). Here, complex contour surfaces for a cross-rolling tool were produced from weld metals in multilayer technology through 3DPMD. As a consequence of the special features of 3DPMD with large-weld metal volumes, greatly differing properties between base material/deposited material and asymmetrical heat input, the resulting shrinkage, deformation and residual stresses are particularly critical. These lead to dimensional and form deviations as well as the formation of cracks, which has a negative influence on the quality of the plasma deposition-welded component structures. By means of the thermo-elastic-plastic simulation model, the temperature field distribution, deformation, and residual stresses occurring during additive 3DPMD of tool contours were predicted and analyzed. The temperature field distribution and its gradients were determined using the ellipsoid heat-source model for the 3DPMD process. On this basis, a coupled thermo-elastic-plastic structural–mechanical analysis was performed. Accordingly, the results achieved were used for the production of almost-net-shaped tool contour surfaces with predefined layer properties. The acquired simulation results of the temperature fields, deformation, and residual stress condition show good alignment with the experimental results.

scholarly journals Velocity and temperature derivatives in high- Reynolds-number turbulent flows in the atmospheric surface layer. Part 3. Temperature and joint statistics of temperature and velocity derivatives

2007 ◽  
Vol 589 ◽  
pp. 103-123 ◽  
Author(s):  
G. GULITSKI ◽  
M. KHOLMYANSKY ◽  
W. KINZELBACH ◽  
B. LÜTHI ◽  
A. TSINOBER ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Temperature Gradient ◽  
Turbulent Flows ◽  
Strain Tensor ◽  
Turbulent Energy ◽  
Temperature Gradients ◽  
Temperature Fields ◽  
Essential Difference ◽  
High Reynolds ◽  
Technical Achievement

This is part 3 of our work describing experiments in which explicit information was obtained on all the derivatives, i.e. spatial derivatives, ∂/∂xj, and temporal derivatives, ∂/∂t, of velocity and temperature fields (and all the components of velocity fluctuations and temperature) at the Reynolds numberReλ~104.This part is devoted to the issues concerning temperature with the emphasis on joint statistics of temperature and velocity derivatives, based on preliminary results from a jet facility and the main results from a field experiment. Apart from a number of conventional results, these contain a variety of results concerning production of temperature gradients, such as role of vorticity and strain, eigen-contributions, geometrical statistics such as alignments of the temperature gradient and the eigenframe of the rate-of-strain tensor, tilting of the temperature gradient, comparison of the true production of the temperature gradient with its surrogate. Among the specific results of importance is the essential difference in the behaviour of the production of temperature gradients in regions dominated by vorticity and strain. Namely, the production of temperature gradients is much more intensive in regions dominated by strain, whereas production of temperature gradients is practically independent of the magnitude of vorticity. In contrast, vorticity and strain are contributing equally to the tilting of the vector of temperature gradients.The production of temperature gradients is mainly due to the fluctuative strain, the terms associated with mean fields are unimportant. It was checked directly (by looking at corresponding eigen-contributions and alignments), that the production of the temperature gradients is due to predominant compressing of fluid elements rather than stretching, which is true of other processes in turbulent flows, e.g. turbulent energy production in shear flows. Though the production of the temperature gradient and its surrogate possess similar univariate PDFs (which indicates the tendency to isotropy in small scales by this particular criterion), their joint PDF is not close to a bisector. This means that the true production of the temperature gradient is far from being fully represented by its surrogate. The main technical achievement is demonstrating the possibility of obtaining experimentally joint statistics of velocity and temperature gradients.

Elastic-Plastic Modeling of Kinematic Hardening Materials Based on F=FeFp Decomposition and the Logarithmic Strain Tensor

Volume 1 ◽  
2004 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Flow Rule ◽  
Deformation Gradient Tensor ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Corotational Rate ◽  
Stress Components ◽  
Shear Problem

In this paper, based on the multiplicative decomposition of the deformation gradient tensor an elastic-plastic modeling of kinematic hardening materials is introduced. In this model, the elastic constitutive equation as well as the flow rule and hardening equation are expressed in terms of the corotational rate of the elastic and plastic logarithmic strains. As an application, the simple shear problem is solved and the stress components are plotted versus shear displacement for a kinematic hardening material.

Elastic-Plastic Modeling of the Hardening Materials Based on an Eulerian Strain Tensor and a Proper Corotational Rate

2005 ◽  
Author(s):  
Reza Naghdabadi ◽  
Kamyar Ghavam
Keyword(s):  
Kinematic Hardening ◽  
Strain Tensor ◽  
Back Stress ◽  
Flow Rule ◽  
Governing Equations ◽  
Plastic Part ◽  
Elastic Plastic ◽  
Eulerian Strain ◽  
Corotational Rate ◽  
Conjugate Stress

In this paper a model for analyzing elastic-plastic kinematic hardening materials is introduced, based on the additive decomposition of the corotational rate of an Eulerian strain tensor In this model, the elastic constitutive equation as well as the flow rule and the hardening equation is expressed in terms of the elastic and plastic parts of the corotational rate of the mentioned Eulerian stain tensor and its conjugate stress tensor. In the flow rule, the plastic part of the corotational rate of the Eulerian strain tensor is related to the difference of the deviatoric part of the conjugate stress and the back stress tensors. A proportionality factor is used in this flow rule which must be obtained from a consistency condition based on the von Mises yield criterion. A Prager type kinematic hardening model is used which relates the corotational rate of the back stress tensor to the plastic part of the corotational rate of the Eulerian strain tensor. Also in this paper a proper corotational rate corresponding to the Eulerian strain tensor is introduced. Finally the governing equations for the analysis of elastic-plastic kinematic hardening materials are obtained. As an application, these governing equations are solved numerically for the simple shear problem and the stress and back stress components are plotted versus the shear displacement. The results are compared with those, which are available in the literature.

Effects of Partial Slip on the Analytic Heat and Mass Transfer for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Viscous Fluid ◽  
Exact Solutions ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Incompressible Viscous Fluid ◽  
Temperature Fields ◽  
Partial Slip ◽  
Shear Stresses ◽  
Rotating Disk Flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed about its axis. The recent study (Turkyilmazoglu, 2009, “Exact Solutions for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow,” Int. J. Non-Linear Mech., 44, pp. 352–357) is extended to account for the effects of partial flow slip and temperature jump imposed on the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions for the flow and temperature fields. Explicit expressions representing the flow properties influenced by the slip as well as a uniform suction and injection are extracted, including the velocity, vorticity and temperature fields, shear stresses, flow and thermal layer thicknesses, and Nusselt number. The effects of variation in the slip parameters are better visualized from the formulae obtained.

scholarly journals Imitating Simulation of Thermomechanical Processing of Metals

2021 ◽  
Vol 12 (4) ◽  
pp. 31-36
Author(s):  
Akhmedov Akrom Burkhanovich Et al.
Keyword(s):  
Metal Cutting ◽  
Thermomechanical Processing ◽  
Strain Tensor ◽  
Cutting Tools ◽  
Distribution Patterns ◽  
Temperature Fields ◽  
Technological Problem ◽  
Plastic Deformations ◽  
Mesh Free ◽  
Mesh Free Method

Thermomechanical processing of metals by cutting is a complicated technological problem that is difficult for mathematical simulation. The various phenomena observed in this process are so closely intertwined with each other and their interaction is so complex that eleven relatively independent theories not coming yet to a holistic unity are focused on the cutter edge. These are a theory of chip formation, metal cutting mechanics, a friction theory in metalworking, thermodynamics of cutting, a theory of wear and resistance of cutting tools. A mesh-free method of Smoothed Particle Hydrodynamics (SPH) has been used for simulation in this paper. The SPH-based simulation in LS-DYNA is performed to predict cutting forces and plastic deformations for machining processing of metals by cutting. The results characterizing the distribution patterns of the strain tensor components and the temperature field at different points in time and space have been presented. The performed studies have demonstrated that it is possible to use changes in the temperature fields as a criterion for estimating the elastic-plastic deformations.

Exact formulations of non-linear planar and spatial Euler–Bernoulli beams with finite strains

2011 ◽  
Vol 226 (5) ◽  
pp. 1225-1236 ◽  
Author(s):  
M H Abedinnasab ◽  
H Zohoor ◽  
Y-J Yoon
Keyword(s):  
Strain Field ◽  
Dynamic Models ◽  
Equations Of Motion ◽  
Strain Tensor ◽  
Bernoulli Beam ◽  
Cross Sectional ◽  
Elastic Deformations ◽  
Non Linear ◽  
Lagrange Strain ◽  
Euler Bernoulli Beam

Using Hamilton’s principle, exact equations of motion for non-linear planar and spatial Euler–Bernoulli beams are derived. In the existing non-linear Euler–Bernoulli beam formulations, some elastic terms are dropped by differentiation from the incomplete Green–Lagrange strain tensor followed by negligible elastic deformations of cross-sectional frame. On the other hand, in this article, the exact strain field concerning considerable elastic deformations of cross-sectional frame is used as a source in differentiations. As a result, the achieved closed-form equations are exact and more accurate than formerly reported equations in the literature. Moreover, the applicable dynamic model of inextensional beams which is fully accurate, yet simple has been shown. The planar and inextensional dynamic models have been compared with the existing dynamic models in the literature, and the proposed dynamic models demonstrate significant improvements in the numerical results. Finally, experiments on the carbon fibre rods verify the model presented for inextensional beams.

A High-Order Theory for Dynamic Buckling and Postbuckling Analysis of Laminated Cylindrical Shells

1999 ◽  
Vol 121 (1) ◽  
pp. 94-102 ◽  
Author(s):  
M. R. Eslami ◽  
M. Shariyat
Keyword(s):  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Strain Tensor ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Order Theory ◽  
High Order ◽  
Nonlinear Equations Of Motion ◽  
Laminated Composite Shells ◽  
Made In

Using a high-order Reisner-Mindlin-type shear deformation theory in a power series form, the general large deformation form of the Green strain tensor for imperfect cylindrical shells is introduced. Then, based on Hamilton’s principle, the equations of motion are derived for laminated composite shells. Related constitutive equations are also proposed. In this formulation, temperature dependency of material properties is considered, too. No simplifications are made in solving the coupled nonlinear equations of motion. Finally, few examples of the well-known references are reconsidered for comparison purposes.

The Simplest 3- and 4-Noded Fully-Parameterized ANCF Plate Elements

2012 ◽  
Author(s):  
Oleg Dmitrochenko ◽  
Marko Matikainen ◽  
Aki Mikkola
Keyword(s):  
Inertial Frame ◽  
Absolute Nodal Coordinate Formulation ◽  
Equations Of Motion ◽  
Strain Tensor ◽  
Large Rotation ◽  
Plate Elements ◽  
Highly Nonlinear ◽  
Elastic Forces ◽  
Rotation Parameters ◽  
Lagrange Strain

In this research, the simplest kinematical models of triangular and rectangular plate finite elements using the absolute nodal coordinate formulation (ANCF) are presented. The ANCF is the finite-element large-displacement-and-rotation approach, which uses the inertial-frame nodal position vectors and their derivatives (slopes) only, without employing any rotation parameters or their equivalent. As a consequence, the kinematics of the elements becomes linear, simplifying the inertia part of the equations of motion, which is also linear. In contrary, due to the need for employing the Green-Lagrange strain tensor, the elastic forces normally appear in a more complicated highly-nonlinear manner than in other large-rotation formulations. In this research, to reduce the computational burden, two new plate elements are proposed that are the simplest possible triangular and rectangular elements in the fully-parameterized ANCF: they employ transverse slopes only, without using longitudinal slopes.

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