A unified approach to quasi-static shakedown problems for elastic-plastic solids with piecewise linear yield surface

Meccanica ◽  
1978 ◽  
Vol 13 (2) ◽  
pp. 109-120 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Yield Surface ◽  
Piecewise Linear ◽  
Unified Approach ◽  
Elastic Plastic

scholarly journals Surface construction for orthrotropic perfectly elastic-plastic Murnaghan material

2021 ◽  
Vol 66 (3) ◽  
pp. 298-306
Author(s):  
O. L. Shved
Keyword(s):  
Singular Point ◽  
Yield Surface ◽  
Biaxial Tension ◽  
Piecewise Linear ◽  
Repeated Loading ◽  
Elastic Plastic ◽  
Work Area ◽  
Plastic Process ◽  
Basic Generator

The problem of constructing a yield surface is described. The magnitude of the stress velocity potential is explained graphically. The parameters of an elastic-plastic process are introduced: a modified R. Schmidt parameter and an analogue of the Lode parameter, the sign of which changes only when the singular point of the plasticity curve passes. The formal work area of the Murnaghan law is calculated, the real area will be much smaller. An effect similar to the Bauschinger effect for the deviator of the stress tensor is assumed to be fair. In the basic experiments of uniaxial and biaxial tension, compression and shear, a piecewise-linear generator with vertices at the corresponding singular points of the plasticity curves is determined. The magnitude of the effect is approximated by a quadratic dependence in the place parameter and piecewise-linear one in the hardening parameter. According to the magnitude of the effect, at the point of the active process there is a singular point of the curve, into which the basic generator moves. The yield surface is constructed by ductility curves drawn through the generator. Determination of the magnitude of the effect under repeated loading after unloading is considered.

The Role of Epistemic Uncertainty of Contact Models in the Design of Mechanical Systems

2013 ◽  
Author(s):  
M. R. Brake
Keyword(s):  
Constant Coefficient ◽  
Epistemic Uncertainty ◽  
Piecewise Linear ◽  
Mechanical Systems ◽  
Coefficient Of Restitution ◽  
Rigid Body Dynamics ◽  
Contact Model ◽  
Elastic Plastic ◽  
Contact Models ◽  
The Impact

Impact is a wide-spread phenomenon in mechanical systems that can have a significant effect on the systems dynamics, stability, wear, and damage. The simulation of impact in complex, mechanical systems, however, is often too computationally intensive for high fidelity finite element analyses to be useful as design tools. As a result, rigid body dynamics and reduced order model simulations are often used, with the impact events modeled by ad hoc methods such as a constant coefficient of restitution or penalty stiffness. The effect of epistemic uncertainty in the choice of contact model is investigated in this paper for a representative multiple-degree of freedom mechanical system. Five contact models are considered in the analysis: a constant coefficient of restitution model, a piecewise-linear stiffness and damping (i.e. Kelvin-Voight) model, two similar elastic-plastic constitutive models, and one dissimilar elastic-plastic constitutive model. The predictions of wear and mechanical failure are assessed for each of the contact models. The ramifications of the choice of the contact model for an optimization study of the system’s geometric design are also presented. These results emphasize the importance of choosing an accurate contact model when simulations are being used to drive the design of a system.

Limit analysis of plates with piecewise linear yield surface

Meccanica ◽  
1972 ◽  
Vol 7 (2) ◽  
pp. 105-110 ◽  
Author(s):  
Ferdinando Laudiero
Keyword(s):  
Yield Surface ◽  
Limit Analysis ◽  
Piecewise Linear

Unified Approach for Notch Stress Strain Conversion (NSSC) Rules

2012 ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Interpolation Method ◽  
Notch Root ◽  
Three Dimensional ◽  
Linear Interpolation ◽  
Unified Approach ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Strain Behavior ◽  
Notch Stress ◽  
Non Linear

There are several simplified methods, known as notch stress-strain conversion (NSSC) rules that provide an approximate formula to relate local elastic-plastic stresses and strains at the notch root to those estimated elastically. This paper investigates a unified approach that estimates non-linear and history dependent stress-strain behavior of the notches using the conventional NSSC rules. A non-linear interpolation method is adapted to estimate the elastic-plastic stress and strain at notches. A comparison is made between the finite element results for several notch configurations (with and without three dimensional effects) and those obtained from NSSC rules and the proposed formulation.

Assessment of the Twice-Yield Method for Elastic-Plastic Fatigue Analysis

2006 ◽  
Author(s):  
W. Reinhardt
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Yield Surface ◽  
Fatigue Analysis ◽  
Half Cycle ◽  
Proportional Loading ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Effective Yield ◽  
Von Mises

The twice-yield (2 Sy) method was proposed by Kalnins as a convenient method to perform an elastic-plastic fatigue analysis using Finite Element analysis. With this method, only a single loading half cycle needs to be run. However, since the shape of the effective yield surface used in this method deviates from the actual von Mises yield surface, the method may conceivably deviate from the solution obtained by elastic-plastic cycle-by-cycle analysis. This paper aims to evaluate the twice-yield method for elastic-plastic fatigue analysis, which is conventionally done cycle-by-cycle. It compares the predictions of plastic strain from the twice-yield method and cycle-by-cycle analysis using some generic examples with non-proportional loading histories as they are frequently encountered in practice.

The Incremental Strain Growth of Elastic-Plastic Bodies Subjected to High Levels of Cyclic Thermal Loading

1984 ◽  
Vol 51 (3) ◽  
pp. 470-474 ◽  
Author(s):  
A. R. S. Ponter ◽  
A. C. F. Cocks
Keyword(s):  
Mechanical Loading ◽  
Yield Surface ◽  
Thermal Loading ◽  
Local Curvature ◽  
Cyclic Thermal Loading ◽  
Elastic Plastic ◽  
Plastic Shakedown ◽  
Incremental Strain

A linearized method of analysis proposed in an accompanying paper [1] is used to obtain the ratchet rate for two types of thermal loading problems where parts of the structure experience reversed plastic straining. For structures that can shakedown plasticially it is found that for a given increment of load beyond the plastic shakedown boundary, the rate of ratchet increases with increasing level of thermal loading. When a structure is unable to shakedown plastically it ratchets at low mechanical loading as the result of a localized mechanism that involves some reversed plasticity. It is shown that the ratchet rate in such situations can be substantial but its value is very dependent on the local curvature of the yield and not the accuracy of the yield surface itself.

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