scholarly journals Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

Crystals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1392
Author(s):  
Peter Trusov ◽  
Alexey Shveykin ◽  
Nikita Kondratev
Keyword(s):  
Coordinate System ◽  
Crystal Plasticity ◽  
A Priori ◽  
Deformation Gradient ◽  
Rigid Motion ◽  
Constitutive Law ◽  
Current Configuration ◽  
Treatment Processes ◽  
Rate Form ◽  
Moving Coordinate

In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes.

scholarly journals A Note on the Barotropic Forecast Using a Moving Coordinate System

1956 ◽  
Vol 34 (3) ◽  
pp. 164-168 ◽  
Author(s):  
S. Syono ◽  
K. Gambo ◽  
K. Miyakoda ◽  
M. Aihara ◽  
S. Manabe
Keyword(s):  
Coordinate System ◽  
Moving Coordinate

scholarly journals Operating on Tensors within Dynamic Coordinate Frames

2018 ◽  
Author(s):  
Keith C. Afas
Keyword(s):  
Coordinate System ◽  
Continuum Mechanics ◽  
Theoretical Models ◽  
Tensor Calculus ◽  
Dynamic Distortion ◽  
Coordinate Frames ◽  
Moving Coordinate ◽  
Calculus Of Moving Surfaces

This paper puts forward an alteration for Tensor Calculus utliized in a coordinate system which is under a dynamic distortion drawing inspiration from similar fields such as the Calculus of Moving Surfaces (CMS). The paper establishes transformation laws for Tensors within these regions and establishes Operators such as the Tensorial Field Derivative which enforce a Tensorial Transformation on Tensors defined within a Dynamically Moving coordinate system. This variation of Tensor Calculus can be utilized to observe how disciplines such as QFT and Continuum Mechanics would change to accomodate for a distorting coordinate system and can be utliized to develop new theoretical models which account for this temporal distortion particularly within Biological Settings.

A Class of Singularly Perturbed Convection-Diffusion Problems with a Moving Interior Layer. An a Posteriori Adaptive Mesh Technique

2004 ◽  
Vol 4 (1) ◽  
pp. 105-127 ◽  
Author(s):  
Grigory I. Shishkin ◽  
Lidia P. Shishkina ◽  
Pieter W. Hemker
Keyword(s):  
Coordinate System ◽  
Transition Layer ◽  
A Priori ◽  
Adaptive Mesh ◽  
Singularly Perturbed ◽  
Finite Difference Schemes ◽  
A Posteriori ◽  
Interior Layer ◽  
Convection Diffusion ◽  
Mesh Technique

AbstractWe study numerical approximations for a class of singularly perturbed convection-diffusion type problems with a moving interior layer. In a domain (segment) with a moving interface between two subdomains, we consider an initial boundary value problem for a singularly perturbed parabolic convection-diffusion equation. Convection fluxes on the subdomains are directed towards the interface. The solution of this problem has a moving transition layer in the neighbourhood of the interface. Unlike problems with a stationary layer, the solution exhibits singular behaviour also with respect to the time variable. Well-known upwind finite difference schemes for such problems do not converge ε-uniformly in the uniform norm. In the case of rectangular meshes which are (a priori or a posteriori ) locally condensed in the transition layer. However, the condition for convergence can be considerably weakened if we take the geometry of the layer into account, i.e., if we introduce a new coordinate system which captures the interface. For the problem in such a coordinate system, one can use either an a priori, or an a posteriori adaptive mesh technique. Here we construct a scheme on a posteriori adaptive meshes (based on the solution gradient), whose solution converges ‘almost ε-uniformly’.

The Motion Planning for Spherical Robot with Two Motors

2015 ◽  
Vol 789-790 ◽  
pp. 688-692
Author(s):  
Xin Wang
Keyword(s):  
Particle Swarm Optimization ◽  
Angular Velocity ◽  
Motion Planning ◽  
Coordinate System ◽  
Optimization Problem ◽  
Kinematic Model ◽  
Pso Algorithm ◽  
Spherical Robot ◽  
Swarm Optimization ◽  
Moving Coordinate

In this paper, we proposed a spherical robot with two motors in the horizontal and vertical directions which derive the robot to do omni-directionally roll. Based on the structure of the robot, we derived the kinematic model using inertial and moving coordinate system. In order to minimize the energy of the system, an optimization problem with two optimization variables which are the parameters to control the angular velocity of the motors is given. After that, a particle swarm optimization (PSO) algorithm is used to solve the optimization problem. The simulation shows that the motion planning with the algorithm has high precision.

Spray-Quenching for Process-Integrated Heat Treatment of Construction Components

2014 ◽  
Author(s):  
Thibaud Bucquet ◽  
Udo Fritsching
Keyword(s):  
Heat Treatment ◽  
Process Integration ◽  
A Priori ◽  
Parameter Study ◽  
Flat Plates ◽  
Temperature Dependent ◽  
Automated Production ◽  
Treatment Processes ◽  
Cylindrical Parts ◽  
Metallic Parts

Spray quenching processes in heat treatment processes of specimen and components demonstrated its efficiency and potential of direct in-process integration in applications as forging or sheet metal forming. Ensuring local quenching homogeneity and offering a range of quenching intensities, spray-quenching provides optimal solutions to carry out energy-efficient, homogeneous and intensive heat treatment processes. In this contribution, spray quenching of specimen using twin-fluid, flat-spray nozzles is evaluated in order to integrate the heat treatment process within an automated production line of forging or forming components. The quenching strategies firstly aim at providing appropriate microstructures (homogeneous and bainitic) to forged metallic parts of various geometries. Experiments and simulations are carried out to derive optimal cooling strategies. Temperature-dependent heat transfer coefficient (HTC) distributions based on a parameter study of the spray nozzle involving thermography have been evaluated. Transient heat transport simulations where the components are quenched according to local and dynamic HTC distribution using various arrangements of the nozzle field were performed. It is shown that the a priori simulated process parameters provided homogeneous microstructures in the components. The characteristic specimen geometries under investigation range from flat plates to cylindrical parts as e.g. stepped shafts. The possibility to extend spray quenching to more complex-shaped specimen geometries is outlined.

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