A General Solution to the Two-Surface Plasticity Theory

1997 ◽  
Vol 119 (1) ◽  
pp. 20-25 ◽  
Author(s):  
Wei Jiang
Keyword(s):  
General Solution ◽  
Constitutive Modeling ◽  
Maximum Size ◽  
Stress Path ◽  
Plasticity Theory ◽  
Material Behavior ◽  
Surface Model ◽  
Surface Plasticity ◽  
Line Parallel ◽  
Linear Loading

This paper obtains a closed-form general solution to the two-surface plasticity theory for linear stress paths. The simple two-surface model is discussed first. It is shown that according to this model, the response of the material stabilizes immediately during the first loading cycle. That is, the memory surface reaches its maximum size with a radius equal to the maximum effective stress and then remains unchanged thereafter, while the yield center translates along a line parallel to the stress path, thus always leading to a constant plastic strain growth rate. As a result, the model predicts that under any cyclic linear loading conditions, the material response can always be ratchetting, with no possibility of shakedown of any kinds, which violates those aspects of material behavior that are generally deemed essential in constitutive modeling. The general two-surface theory is also discussed in this paper, and some comments are made.

Constitutive modeling for the mechanical behavior of rubber with filler particles

2021 ◽  
Author(s):  
Sankalp Gour ◽  
Deepu Kumar Singh ◽  
Deepak Kumar ◽  
Vinod Yadav
Keyword(s):  
Mechanical Properties ◽  
Carbon Black ◽  
Mechanical Behavior ◽  
Experimental Observation ◽  
Continuum Mechanics ◽  
Constitutive Modeling ◽  
Carbon Nanoparticles ◽  
Material Behavior ◽  
Experimental Results ◽  
Filler Particles

Abstract The present study deals with the constitutive modeling for the mechanical behavior of rubber with filler particles. An analytical model is developed to predict the mechanical properties of rubber with added filler particles based on experimental observation. To develop the same, a continuum mechanics-based hyperelasticity theory is utilized. The model is validated with the experimental results of the chloroprene and nitrile butadiene rubbers filled with different volume fractions of carbon black and carbon nanoparticles, respectively. The findings of the model agree well with the experimental results. In general, the developed model will be helpful to the materialist community working in characterizing the material behavior of tires and other rubber-like materials.

A Modified Gradient Plasticity Theory for Micro-Bending and Micro-Torsion Size Effects

2004 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Rashid K. Abu Al-Rub
Keyword(s):  
Size Effects ◽  
Scale Parameter ◽  
Plasticity Theory ◽  
Material Behavior ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Non Local ◽  
Material Length Scale ◽  
Material Length

The definition and magnitude of the intrinsic length scale are keys to the development of the theory of plasticity that incorporates size effects. Gradient plasticity theory with a material length scale parameter is successfully in capturing the size dependence of material behavior at the micron scale. However, a fixed value of the material length-scale is not always realistic and that different problems could require different values. Moreover, a linear coupling between the local and non-local terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings. A generalized gradient plasticity model with a non-fixed length scale parameter is proposed. This model assesses the sensitivity of predictions in the way in which the local and non-local parts are coupled. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.

A General Solution for the Pressurized Elastoplastic Tube

1992 ◽  
Vol 59 (1) ◽  
pp. 20-26 ◽  
Author(s):  
David Durban ◽  
Michael Kubi
Keyword(s):  
General Solution ◽  
Finite Strain ◽  
Cylindrical Tube ◽  
Yield Function ◽  
Material Behavior ◽  
Deformation Pattern ◽  
Perfectly Plastic ◽  
Plastic Phase ◽  
Thin Walled ◽  
Elastic Perfectly Plastic

The problem of a thick-walled cylindrical tube subjected to internal pressure is investigated within the framework of continuum plasticity. Material behavior is modeled by a finite strain elastoplastic flow theory based on the Tresca yield function. The deformation pattern is restricted by the plane-strain condition but arbitrary hardening and elastic compressibility are accounted for. A general solution is given in terms of quadratures. The analysis also includes treatment of a second plastic phase, characterized by corner relations, that may develop at the inner boundary. It is shown that the interface between the two plastic regions moves initially outwards and then, beyond a certain strain level, it moves back inwards. Some useful and simple results are given for thin-walled tubes of hardening materials and for thick-walled elastic/perfectly plastic tubes.

Semi-analytical and semi-numerical method for the single soil layer consolidation problem

2017 ◽  
Vol 34 (3) ◽  
pp. 960-987 ◽  
Author(s):  
Tao Cheng ◽  
Keqin Yan ◽  
Jun-Jie Zheng ◽  
Xian-Feng Luo ◽  
Ding-Bang Zhang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Numerical Method ◽  
Pore Water ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Stress Path ◽  
Surface Model ◽  
Model Framework ◽  
Content Type ◽  
Simplified Solution

Purpose This paper aims to present a simplified solution method for the elasto-plastic consolidation problem under different stress paths. Design/methodology/approach First, a double-yield-surface model is introduced as the constitutive model framework, and a partial derivative coefficient sequence is obtained by using numerical approximation using Gauss nuclear function to construct a discretization constitutive model which can reflect the influence of different stress paths. Then, the model is introduced to Biot’s consolidation theory. Volumetric strain of each step as the right-hand term, the continuity equation is simplified as a Poisson equation and the fundamental solution is derived by the variable separation method. Based on it, a semi-analytical and semi-numerical method is presented and implemented in a finite element program. Findings The method is a simplified solution that is more convenient than traditional coupling stiffness matrix method. Moreover, the consolidation of the semi-infinite foundation model is analyzed. It is shown that the numerical method is sufficiently stable and can reflect the influence of stress path, loading distribution width and some other factors on the deformation of soil skeleton and pore water pressure. Originality/value Original features of this research include semi-numerical semi-analytical consolidation method; pore water pressure and settlements of different stress paths are different; maximum surface uplift at 3.5a; and stress path is the main influence factor for settlement when loading width a > 10 m.

Isotropic–kinematic hardening model for coarse granular soils capturing particle breakage and cyclic loading under triaxial stress space

2016 ◽  
Vol 53 (4) ◽  
pp. 646-658 ◽  
Author(s):  
Qingsheng Chen ◽  
Buddhima Indraratna ◽  
John P. Carter ◽  
Sanjay Nimbalkar
Keyword(s):  
Cyclic Loading ◽  
Critical State ◽  
Kinematic Hardening ◽  
Plasticity Theory ◽  
Particle Breakage ◽  
Granular Soils ◽  
Stress Space ◽  
Bounding Surface ◽  
Bounding Surface Plasticity ◽  
Surface Plasticity

In this paper, a simple but comprehensive cyclic stress–strain model that incorporates particle breakage for granular soils including ballast and rockfill has been proposed on the basis of bounding surface plasticity theory within a critical state framework. Particle breakage and its effects are captured by a critical state line that is translated in voids ratio–stress space according to the dissipated energy (plastic work), through a hyperbolic function. A comprehensive equation related to particle breakage is proposed for the stress–dilatancy relationship to capture the complex dilatancy of granular soils. By extending Masing’s rule to bounding surface plasticity theory and introducing a generalized homological centre, a combined isotropic–kinematic hardening rule and a mapping rule have been established to simulate more realistically the response of gravelly soils under cyclic loading. The applicability and accuracy of this model are demonstrated by comparing its predictions with experimental results for different types of granular soils, including rockfill, under both monotonic and cyclic loading conditions. This study shows that the model can capture the characteristic features of coarse granular soils under complex loading paths.

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