Omar Khalid
Perfect plasticity in Abaqus is a highly sought-after topic, with many users seeking to define plastic properties and model real-world material behaviour. Abaqus provides a range of plasticity models, including incremental plasticity theory, which forms the basis of most elastic-plastic response models. Users must specify the appropriate plasticity model for their chosen material, with the option to calibrate model parameters using experimental data or empirical relationships. Abaqus then employs advanced numerical methods to predict plastic deformation under varying loading conditions. To define perfect plasticity, true stress and true strain values are essential for Abaqus to correctly interpret data in the input file. The Johnson-Cook plasticity model is a notable example, suited for modelling high-strain-rate deformation of metals. This model is a type of Mises plasticity, including hardening law and rate dependence. Abaqus also offers kinematic hardening for materials subjected to cyclic loading and isotropic hardening in both Abaqus/Standard and Abaqus/Explicit. Users can define an elastic-perfectly plastic material with no hardening or specify work hardening rules.
| Characteristics | Values |
|---|---|
| Plasticity models | Rate-independent or rate-dependent |
| Rate-independent model | Constitutive response does not depend on the rate of deformation |
| Rate-dependent model | Response depends on the rate at which the material is strained |
| Plasticity models provided for | Metals, soils, polymers, crushable foams, concrete |
| Stress output | Given as "true" (Cauchy) stress |
| Plasticity data | Requires true stress and true strain values |
| Clay plasticity | Models mechanical behaviour of clay soils |
| Clay plasticity characteristics | High compressibility, time-dependent behaviour, sensitivity to moisture content |
| Clay plasticity model | Requires performing a description of elastic deformation using linear elastic or porous elastic material models |
| Johnson-Cook model | Used for isotropic hardening in ABAQUS/Explicit |
| Cast iron plasticity constitutive model | Simulates elastoplastic characteristics of grey cast iron |
| Defining plastic properties | Common in Abaqus |
| Model parameters | Calibrated using experimental data or empirical relationships |
| Modelling material plasticity | Requires specific steps in Abaqus |
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What You'll Learn
True stress and strain
True stress is defined as the applied load divided by the actual cross-sectional area of the specimen at that load. In other words, it is the load divided by the instantaneous cross-sectional area, which changes with time as the specimen deforms. On the other hand, engineering stress assumes that the cross-sectional area of the material remains constant throughout the test.
True strain is logarithmic, while engineering strain is linear. True strain is calculated as the change in instantaneous length over time and is expressed as an integral. Engineering strain, on the other hand, is the change in length over the original length.
The difference between true and engineering stress and strain becomes significant as the deformation increases. At low strains, the differences between the two are negligible. However, as the load increases and the specimen changes shape more drastically, the true values become more relevant, especially when the strain exceeds a few percent. Therefore, true stress and strain are recommended for use in FEA models, providing a more accurate representation of the stress-strain relationship.
In the context of defining perfect plasticity in Abaqus, true stress and strain play a crucial role in accurately defining the plastic behaviour of ductile materials. Abaqus provides various plasticity models, such as the Johnson-Cook model, that can be used to simulate real-world material behaviour and predict plastic deformation under different loading conditions. By specifying the appropriate plasticity model and inputting relevant data, such as strain rate dependence and temperature dependence, users can effectively define and analyse the perfect plasticity behaviour of materials in Abaqus.
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Plastic Poisson's ratio
To define perfect plasticity in Abaqus, users must specify the appropriate plasticity model for the material. Abaqus provides a perfectly plastic material option with no hardening, or work hardening can be specified. Isotropic hardening is available in both Abaqus/Standard and Abaqus/Explicit, and Johnson-Cook hardening is available only in Abaqus/Explicit. In addition, Abaqus offers kinematic hardening for materials subjected to cyclic loading.
For most common materials, the Poisson's ratio falls within the range of 0 to 0.5. The Poisson's ratio varies for different materials and is dependent on factors such as the type of material, its structure, and its mechanical properties.
In Abaqus, plasticity models are written as rate-independent or rate-dependent. A rate-independent model is one in which the constitutive response does not depend on the rate of deformation, while in a rate-dependent model, the response does depend on the rate at which the material is strained. The plasticity models in Abaqus are based on incremental plasticity theory, which assumes that the variation of elastic strain is the same as the variation in the rate of deformation. This assumption leads to defining the stress measure as the "true" (Cauchy) stress, which is the form in which all stress output in Abaqus is given.
To avoid convergence issues when defining a perfect plastic region in Abaqus, it is recommended to add a slight slope to the model. This is because, in a perfect plastic model, the plastic strain increases while the stress remains constant, which can lead to convergence problems. By adding a slight slope, this issue can be mitigated.
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Clay plasticity
Techniques for evaluating clay plasticity focus on determining the optimal water content required for plastic deformation. However, a consolidated method for measuring clay plasticity has not yet been established. Potters often compare the plasticity of two clay samples by throwing them on a potter's wheel, providing a practical way to assess their relative plasticity. In industry, plasticity is often gauged by observing how clay behaves in forming machines, its drying characteristics, and its stickiness.
When defining perfect plasticity in Abaqus, users must specify the appropriate plasticity model for the material. Abaqus provides the option to define a perfectly plastic material with no hardening or to specify work hardening. Work hardening can be isotropic hardening or Johnson-Cook hardening, which is available in Abaqus/Explicit. To avoid convergence issues when working with perfect plasticity in Abaqus, it is recommended to add a slight slope in the perfect plastic region.
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Plasticity modelling
Abaqus provides models for incremental plasticity theory, which is based on a few fundamental postulates. The basic equations of the models are defined in their general form, and plasticity models are written as rate-independent or rate-dependent models. In rate-independent models, the constitutive response does not depend on the rate of deformation, while in rate-dependent models, the response depends on the rate at which the material is strained. Abaqus also provides models for concrete and jointed material plasticity, where the yield behaviour is modelled with several independent inelastic flow systems.
To define plasticity data in Abaqus, true stress and true strain values must be used. Abaqus requires these values to interpret the data in the input file correctly. If material test data are supplied using nominal stress and strain values, they must be converted to true stress and true strain. The relationship between true strain and nominal strain can be established by expressing the nominal strain and solving for the true strain. The relationship between true stress and nominal stress is formed by considering the incompressible nature of plastic deformation and assuming the elastic volumetric deformation is negligible.
Abaqus offers specialized plasticity models specifically designed to capture the intricate behaviour of engineering materials. For example, the cast iron plasticity constitutive model simulates the elastoplastic characteristics of grey cast iron, which exhibits greater brittleness when subjected to tension compared to most metals. Abaqus also provides a clay plasticity model that captures the non-elastic behaviour of clay materials. This model utilizes a yield function based on three stress invariants and incorporates a strain hardening theory that alters the size of the yield surface based on the inelastic volumetric strain.
When modelling plasticity in Abaqus, users can define an elastic-perfectly plastic material or specify work hardening. Isotropic hardening is available in both Abaqus/Standard and Abaqus/Explicit, while Johnson-Cook hardening is only available in Abaqus/Explicit. Johnson-Cook hardening is particularly suited for modelling high-strain-rate deformation of metals and is used in adiabatic transient dynamic analysis. To avoid convergence problems when adding a perfect plastic region, a slight slope should be added to the model.
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Hardening plasticity
When defining plasticity in Abaqus, users must specify the appropriate plasticity model for the material. Abaqus offers different hardening plasticity types, including perfectly plastic material (with no hardening) and work hardening. Isotropic hardening is available in both Abaqus/Standard and Abaqus/Explicit, while Johnson-Cook hardening is exclusive to Abaqus/Explicit. Abaqus also provides kinematic hardening for materials subjected to cyclic loading.
Isotropic hardening dictates that the yield surface remains at the centre, retaining its shape but expanding with an increase in plastic deformation. If a solid is plastically deformed, unloaded, and then reloaded in compression, its yield stress will have increased compared to the first cycle. This is because isotropic hardening causes the yield surface to expand uniformly, resulting in increased yield strength.
Kinematic hardening rules, on the other hand, can accurately assess the elastic-plastic response of materials under loading cycles. They account for the Bauschinger effect and the material's memory over the plastic deformation process. The yield surface does not expand but translates in the direction of stress rise, maintaining its area and shape. Prager introduced a primary kinematic hardening rule, a linear hardening rule that successfully translates the yield surface in deviatoric stress space.
The Johnson-Cook plasticity model in Abaqus/Explicit is well-suited for modelling high-strain-rate deformation of metals. It is a particular type of Mises plasticity that includes analytical forms of the hardening law and rate dependence. This model is generally employed in adiabatic transient dynamic analysis.
In summary, Abaqus offers various hardening plasticity options, including isotropic hardening, kinematic hardening, and the Johnson-Cook model. These options enable users to accurately define and model the hardening behaviour of materials under different loading conditions.
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Frequently asked questions
The first step is to use the equations relating the true stress to the nominal stress and strain and the true strain to the nominal strain to convert the nominal stress and nominal strain to true stress and true strain.
Once these values are known, use the equation relating the plastic strain to the total and elastic strains to determine the plastic strains associated with each yield stress value.
The *PLASTIC option in Abaqus defines the post-yield behaviour for most metals. The data pairs on the *PLASTIC option define the true stress as a function of true plastic strain.
To avoid convergence problems, add a slight slope in the perfect plastic region.
