Power-Formula Viscoplasticity, Its Modification and Some Applications

1984 ◽  
Vol 106 (4) ◽  
pp. 383-387 ◽  
Author(s):  
Yu Chen
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Boundary Value Problems ◽  
Physical Phenomenon ◽  
Boundary Value ◽  
The Body ◽  
Dislocation Dynamics ◽  
Basic Relation ◽  
Mathematical Form ◽  
Rate Dependent

A power viscoplastic constitutive equation was first proposed by Bodner and Partom in 1972. This specific formula has its origin in the physical phenomenon of dislocation dynamics and due to the simplicity of its mathematical form, it is a useful constitutive equation in solving boundary value problems. In this paper a brief review of the basic relation is given, followed by discussion of some relatively less known features of this formula. The body of the paper deals with the modification of the equation to explore its potential in several directions. The first modification consists of making the “threshold stress” strain rate dependent. The second modification aims of modeling strain rate history dependency. Due to space the formulation of the boundary value problems of uniaxial testing and its implementation through finite element programs will not be reported here. Results demonstrating the effect of strain rate and strain-rate history are presented. They are in good qualitative agreement with available experimental data.

scholarly journals Solution of inverse non-stationary boundary value problems of diffraction of plane pressure wave on convex surfaces based on analytical solution

2020 ◽  
Vol 18 (4) ◽  
pp. 676-680
Author(s):  
Olga Egorova ◽  
Ko Ye
Keyword(s):  
Analytical Solution ◽  
Boundary Value Problems ◽  
Pressure Wave ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
The Body ◽  
Parabolic Cylinder ◽  
Pressure Jump ◽  
Stationary Boundary ◽  
Special Cases

Research in the field of unsteady interaction of shock waves propagating in continuous media with various deformable barriers are of considerable scientific interest, since so far there are only a few scientific works dealing with solving problems of this class only for the simplest special cases. In this work, on the basis of analytical solution, we study the inverse non-stationary boundary-value problem of diffraction of plain pressure wave on convex surface in form of parabolic cylinder immersed in liquid and exposed to plane acoustic pressure wave. The purpose of the work is to construct approximate models for the interaction of an acoustic wave in an ideal fluid with an undeformable obstacle, which may allow obtaining fundamental solutions in a closed form, formulating initial-boundary value problems of the motion of elastic shells taking into account the influence of external environment in form of integral relationships based on the constructed fundamental solutions, and developing methods for their solutions. The inverse boundary problem for determining the pressure jump (amplitude pressure) was also solved. In the inverse problem, the amplitude pressure is determined from the measured pressure in reflected and incident waves on the surface of the body using the least squares method. The experimental technique described in this work can be used to study diffraction by complex obstacles. Such measurements can be beneficial, for example, for monitoring the results of numerical simulations.

Non-Linear Wave Loads Acting on Obliquely Slowly Advancing Platform

2009 ◽  
Author(s):  
Yasunori Nihei ◽  
Sota Sugimoto ◽  
Takashi Tsubogo ◽  
Weiguang Bao ◽  
Takeshi Kinoshita
Keyword(s):  
Boundary Value Problems ◽  
Potential Theory ◽  
Boundary Value ◽  
The Body ◽  
Linear Wave ◽  
Wave Loads ◽  
Forward Speed ◽  
Wave Drift ◽  
Non Linear ◽  
Drift Force

It is necessary to evaluate wave drift force for ships advancing obliquely. There are some approaches, for instance the strip method, solving the Navier-Stokes equation directly in the fluid domain (CFD), potential theory and so on. In the present study, the non-linear wave loads acting on the ship with constant oblique forward speed is considered based on the potential theory. Consistent perturbation expansion based on two parameters, i.e. the incident wave slope and the ratio of the forward speed compared to the phase velocity of the waves, is performed on a moving frame (body-fixed) coordinate system to simplify the problem. So obtained boundary value problems for each order of potentials is solved by means of the hybrid method. The fluid domain is divided into two regions by an artificial circular cylinder surrounding the body. The potential in the inner region is expressed by an integral over the boundary surface with a Rankin source as its Green function while it is expressed in the eigen function expansion for the outer region. Consequently, the boundary value problems can be solved efficiently. In the present paper, the authors will discuss the effects of the obliquely advancing on the wave drift force in a diffraction wave field up to the order proportional to the advancing speed. An ellipsoid model is used in the calculation and the wave drift force is evaluated for various Froude number.

scholarly journals On the Uniqueness Classes of Solutions of Boundary Value Problems for Third-Order Equations of the Pseudo-Elliptic Type

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 80
Author(s):  
Abdukomil Risbekovich Khashimov ◽  
Dana Smetanová
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
The Body ◽  
Energy Estimates ◽  
Uniqueness Theorems ◽  
Elliptic Type ◽  
Third Order ◽  
Body Form ◽  
The Third

The paper is devoted to solutions of the third order pseudo-elliptic type equations. An energy estimates for solutions of the equations considering transformation’s character of the body form were established by using of an analog of the Saint-Venant principle. In consequence of this estimate, the uniqueness theorems were obtained for solutions of the first boundary value problem for third order equations in unlimited domains. The energy estimates are illustrated on two examples.

scholarly journals On a new class of electro-elastic bodies. II. Boundary value problems

2013 ◽  
Vol 469 (2155) ◽  
pp. 20130106 ◽  
Author(s):  
R. Bustamante ◽  
K. R. Rajagopal
Keyword(s):  
Electric Field ◽  
Boundary Value Problems ◽  
Constitutive Relations ◽  
Boundary Value ◽  
Electric Displacement ◽  
Cylindrical Tube ◽  
The Body ◽  
Elastic Bodies ◽  
Nonlinear Relation ◽  
Elastic Slab

In part I of this two-part paper, a new theoretical framework was presented to describe the response of electro-elastic bodies. The constitutive theory that was developed consists of two implicit constitutive relations: one that relates the stress, stretch and the electric field, and the other that relates the stress, the electric field and the electric displacement field. In part II, several boundary value problems are studied within the context of such a construct. The governing equations allow for nonlinear coupling between the electric and stress fields. We consider boundary value problems wherein both homogeneous and inhomogeneous deformations are considered, with the body subject to an electric field. First, the extension and the shear of an electro-elastic slab subject to an electric field are studied. This is followed by a study of the problem of a thin circular plate and a long cylindrical tube, both subject to an inhomogeneous deformation and an electric field. In all the boundary value problems considered, the relationships between the stress and the linearized strain are nonlinear, in addition to the nonlinear relation to the electric field. It is emphasized that the theories that are currently available are incapable of modelling such nonlinear relations.

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