On the Uniqueness and Stability of Endochronic Theories of Material Behavior

1978 ◽  
Vol 45 (2) ◽  
pp. 263-266 ◽  
Author(s):  
I. S. Sandler
Keyword(s):  
Numerical Solution ◽  
Yield Condition ◽  
Material Behavior ◽  
Dynamic Problems ◽  
Classical Plasticity ◽  
Internal Barriers

A stability and uniqueness analysis of endochronic models without internal barriers has been performed by means of the construction of certain simple dynamic problems. It has been shown that serious difficulties can arise when such models are used and that they are unsuitable for the numerical solution of mechanical problems. The deficiencies in the endochronic models may be circumvented by the introduction of internal barriers, but these have much the same features as the yield condition of classical plasticity.

Analytical Solution of a Borehole Problem Using Strain Gradient Plasticity

2002 ◽  
Vol 124 (3) ◽  
pp. 365-370 ◽  
Author(s):  
X.-L. Gao
Keyword(s):  
Analytical Solution ◽  
Strain Gradient ◽  
Plastic Region ◽  
Yield Condition ◽  
Plasticity Theory ◽  
Strain Gradient Plasticity ◽  
Spatial Gradient ◽  
Gradient Plasticity ◽  
Present Solution ◽  
Classical Plasticity

An analytical solution is presented for the borehole problem of an elasto-plastic plane strain body containing a traction-free circular hole and subjected to uniform far field stress. A strain gradient plasticity theory is used to describe the constitutive behavior of the material undergoing plastic deformations, whereas the generalized Hooke’s law is invoked to represent the material response in the elastic region. This gradient plasticity theory introduces a higher-order spatial gradient of the effective plastic strain into the yield condition to account for the nonlocal interactions among material points, while leaving other relations in classical plasticity unaltered. The solution gives explicit expressions for the stress, strain, and displacement components. The hole radius enters these expressions not only in nondimensional forms but also with its own dimensional identity, unlike classical plasticity-based solutions. As a result, the current solution can capture the size effect in a quantitative manner. The classical plasticity-based solution of the borehole problem is obtained as a special case of the present solution. Numerical results for the plastic region radius and the stress concentration factor are provided to illustrate the application and significance of the newly derived solution.

On numerical solution of dynamic problems in the nonlinear theory of reinforced shells

1996 ◽  
Vol 32 (7) ◽  
pp. 532-536 ◽  
Author(s):  
S. Yu. Bogdanov ◽  
P. Z. Lugovoi ◽  
V. F. Meish ◽  
N. A. Shul'ga
Keyword(s):  
Numerical Solution ◽  
Nonlinear Theory ◽  
Dynamic Problems

On Uniqueness in Ideally Elastoplastic Problems in Case of Nonassociated Flow Rules

1972 ◽  
Vol 39 (4) ◽  
pp. 983-987 ◽  
Author(s):  
H. H. Bleich
Keyword(s):  
Yield Condition ◽  
Dynamic Problems ◽  
General Proof ◽  
Inertia Forces ◽  
Arbitrary Selection ◽  
Selection Of

It is known that in the quasi-static treatment of ideally elastoplastic solids, lack of uniqueness may occur unless associated flow rules are used. This has been illustrated by a simple example in reference [3]. The present study shows that the uniqueness difficulties in the foregoing and in similar situations disappear, if inertia forces are included in the analysis. As inertia forces in nature are unavoidable there may therefore be nothing improper in the use of nonassociated flow rules. One is simply not permitted to replace the actual dynamic situation in the limit by a quasi-static one. It is shown, however, that an entirely arbitrary selection of yield condition and flow rules is not permissible, but that the combination must satisfy a requirement which is derived. No general proof of uniqueness of dynamic problems for material prescriptions satisfying this requirement is as yet available. It is the purpose of the paper to induce interested investigators to search for such a general proof.

Boundary Element Methods in Dynamic Analysis

1987 ◽  
Vol 40 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Dimitri E. Beskos
Keyword(s):  
Dynamic Analysis ◽  
Numerical Solution ◽  
Boundary Element ◽  
Vibration Isolation ◽  
Plane Motion ◽  
Boundary Element Methods ◽  
Material Behavior ◽  
Brief Assessment ◽  
Time Domains ◽  
Plates And Shells

A review of boundary element methods for the numerical solution of dynamic problems of linear elasticity is presented. The integral formulation and the corresponding numerical solution of three- and two-dimensional elastodynamics from the direct boundary element method viewpoint and in both the frequency and time domains are described. The special case of the anti-plane motion governed by the scalar wave equation is also considered. In all the cases both harmonic and transient dynamic disturbances are taken into account. Special features of material behavior such as viscoelasticity, inhomogeneity, anisotropy, and poroelasticity are briefly discussed. Some other nonconventional boundary element methods as well as the hybrid scheme that results from the combination of boundary and finite elements are also reviewed. All these boundary element methodologies are applied to: soil-structure interaction problems that include the dynamic analysis of underground and above-ground structures, foundations, piles, and vibration isolation devices; problems of crack propagation and wave diffraction by cracks; and problems dealing with the dynamics of beams, plates, and shells. Finally, a brief assessment of the progress achieved so far in dynamic analysis is made and areas where further research is needed are identified.

Plastic Internal Variables Formalism of Cyclic Plasticity

1976 ◽  
Vol 43 (4) ◽  
pp. 645-651 ◽  
Author(s):  
Y. F. Dafalias ◽  
E. P. Popov
Keyword(s):  
The State ◽  
Material Behavior ◽  
Cyclic Plasticity ◽  
Internal Variables ◽  
State Variables ◽  
Stress Space ◽  
General Development ◽  
Loading Function ◽  
Plastic Modulus ◽  
Classical Plasticity

The notion of Plastic Internal Variables (PIV) is used in reformulating, in a general form, the equations of rate-independent plasticity. The stress, temperature, and the PIV are the state variables for the present development. Loading-unloading is defined in terms of the usual loading function of classical plasticity. The concept of discrete memory parameters entering the constitutive equations for the PIV is introduced, in order to describe realistically the material behavior under cyclic loading. Within the framework of the general development, a simple model is constructed. By generalizing uniaxial experimental observations the concept of the “bounding surface” in stress space is introduced, defined in terms of appropriate PIV. This surface always encloses the yield surface, and their proximity in the course of their coupled translation and deformation in stress space during plastic loading determines an appropriate quantity function of the state variables and a corresponding discrete memory parameter on which the value of the plastic modulus depends. The model is compared with experimental results in a uniaxial case.

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