A variational-based homogenization model for plastic shakedown analysis of porous materials with a large range of porosity

In classical plasticity the shakedown analysis is among the most important basic problems. The principles of shakedown analysis are counterparts to those of limit analysis in the sense that they provide static and kinematic approaches to the question of whether or not shakedown will occur for a body under multiple variable loading conditions. The principles of limit analysis provide static and kinematic approaches to the question of whether or not the plastic limit state will be reached by a body under proportional loading. The principles of shakedown analysis are, however, considerably more difficult to apply than those of limit analysis. In spite of these difficulties, shakedown analysis is a vital and developing topic in plasticity and a great number of applications have been made. At the application of the plastic analysis and design methods the control of the plastic behaviour of the structures is an important requirement. Since the shakedown analysis provide no information about the magnitude of the plastic deformations and residual displacements accumulated before the adaptation of the structure, therefore for their determination bounding theorems and approximate methods have been proposed.

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Rigid Plastic Shakedown Analysis and its Application for a Bearing Capacity Problem of a Multi-footing System

Journal of Applied Mechanics ◽

10.2208/journalam.3.379 ◽

2000 ◽

Vol 3 ◽

pp. 379-386

Author(s):

Shunichi KOBAYASHI ◽

Nozomu GENJO ◽

Takeshi TAMURA

Keyword(s):

Bearing Capacity ◽

Rigid Plastic ◽

Shakedown Analysis ◽

Plastic Shakedown

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Shakedown Fatigue Limits for Materials With Minute Porosity

Journal of Applied Mechanics ◽

10.1115/1.3005961 ◽

2009 ◽

Vol 76 (3) ◽

Author(s):

Jehuda Tirosh ◽

Sharon Peles

Keyword(s):

Porous Materials ◽

Endurance Limit ◽

Stress Amplitude ◽

Material Behavior ◽

Space Industry ◽

Pressure Dependency ◽

Elastic Shakedown ◽

Plastic Shakedown ◽

Gurson's Model ◽

Dual Bounds

The intention of this study is to predict the fatigue-safe long life behavior of elastoplastic porous materials subjected to zero-tension fluctuating load. It is assumed that the materials contain a dilute amount of voids (less than 5%) and obey Gurson’s model of plastic yielding. The question to be answered is what would be the highest allowable stress amplitude that a porous material can endure (the “endurance limit”) when undergoing an infinite number of loading/unloading cycles. To reach the answer we employ the two shakedown theorems: (a) Melan’s static shakedown theorem (“elastic shakedown”) for establishing the lower bound to fatigue limit and (b) Koiter’s kinematic shakedown theorem (“plastic shakedown”) for establishing its upper bound. The two bounds are formulated rigorously but solved with some numerical assistance, mainly due to the nonlinear pressure dependency of the material behavior and the complex description of the plastic flow near stress-free voids. Both bounds (“dual bounds”) are adjusted to capture Gurson-like porous materials with noninteractive voids. General residual stresses (either real or virtual) are presented in the analysis. They are assumed to be time-independent as generated, say, by permanent temperature gradient between void surfaces and remote material boundaries. Such a situation is common, for instance, in ordinary porous sleeves (used in space industry and alike). A few experiments agree satisfactorily with the shakedown bounding concept.

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Lower Bound Methods in Elastic-Plastic Shakedown Analysis

ASME 2010 Pressure Vessels and Piping Conference: Volume 1 ◽

10.1115/pvp2010-26088 ◽

2010 ◽

Author(s):

Wolf Reinhardt ◽

Reza Adibi-Asl

Keyword(s):

Lower Bound ◽

Plastic Material ◽

Shakedown Analysis ◽

Elastic Plastic ◽

Perfectly Plastic ◽

Efficient Calculation ◽

Asme Code ◽

Elastic Shakedown ◽

Plastic Shakedown

Several methods were proposed in recent years that allow the efficient calculation of elastic and elastic-plastic shakedown limits. This paper establishes a uniform framework for such methods that are based on perfectly-plastic material behavour, and demonstrates the connection to Melan’s theorem of elastic shakedown. The paper discusses implications for simplified methods of establishing shakedown, such as those used in the ASME Code. The framework allows a clearer assessment of the limitations of such simplified approaches. Application examples are given.

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