# BKIN Or BISO–Understanding the Enhanced Models in ANSYS Constitutive Models

When dealing with elastoplastic nonlinear analysis of materials such as reinforced steel, steel, and concrete, it is crucial to select the appropriate constitutive model. Taking reinforced steel as an example, the most common constitutive models are BKIN and BISO. BKIN represents the Linear Kinematic Hardening Model, while BISO represents the Isotropic Hardening Model. Many students find it confusing when it comes to choosing the constitutive model, often relying on others’ reference codes for modification. Today, I will briefly introduce the commonly used enhanced models.

But before diving into the details, let’s first provide a brief explanation of elastoplastic analysis.

In the field of statics analysis, there are two types: elastic analysis and elastoplastic analysis. In the elastic analysis phase, stress and strain are proportional, meaning stress equals strain multiplied by the elastic modulus. Once the load is removed, the material returns to its original state. In contrast, the elastoplastic analysis phase occurs when the material exceeds its elastic limit and continues to be loaded, causing the material to enter the plastic stage. Unloading at this point will not restore the material to its original state.

During the analysis process, total strain can be divided into elastic strain and plastic strain. Elastic strain is proportional to stress. To describe the overall deformation process of a structure, the key lies in establishing the relationship between plastic strain and stress, which is referred to as elastoplastic constitutive modeling.

There are various factors that influence plastic strain, such as loading history (which is why elastoplastic analysis involves load steps), temperature, stress, strain rate, and internal factors like yield strength and damage.

For ANSYS, when simulating elastoplastic analysis, the plastic development is mainly described based on the following three criteria:

1. Yield criterion: During the loading process, once the material’s equivalent stress exceeds the yield stress, the program determines that it has entered a plastic state. This solves the transition from elasticity to plasticity.
2. Flow criterion: When plastic strain occurs in a component, the flow criterion defines the direction of strain. In other words, the flow criterion can describe how the plastic strain components develop at each load increment after reaching yield.
3. Hardening criterion: It describes how the initial yield criterion evolves with increasing plastic strain.

In the third criterion, hardening refers to the fact that after the material undergoes plastic deformation in the yield stage, unloads, and then loads to yield again, the new yield point is higher than the original yield point.

The first yield point corresponds to the “initial yield criterion,” and each subsequent yield point is slightly higher than the previous one. This developmental process is known as hardening.

The hardening process can be categorized into two types: equivalent hardening and kinematic hardening.

Equivalent hardening: If the hardening effect is the same in all directions after loading and unloading in one direction, it is referred to as equivalent hardening.

Taking BKIN as an example, its constitutive model is as follows:

Kinematic hardening: If the hardening effect differs in different directions after loading and unloading, it is referred to as kinematic hardening.

Taking BISO as an example, its constitutive model is as follows (note the difference in yield stress for tension and compression):

Based on the definitions, the main difference between the two lies in the direction of hardening. This provides us with guidance for selecting a specific constitutive model.

For general unidirectional loading, the difference between the two models is not significant since it does not involve the loading-unloading process. However, for cyclic loading, it is advisable to choose the kinematic hardening model (BISO) instead of the equivalent hardening model (BKIN). For example, in elastoplastic seismic time history analysis of reinforced concrete, especially in hysteresis simulation, this point should be particularly noted.

The above explanation was for bilinear models. If we consider multilinear models, then students might be more familiar with MKIN and MISO. If we consider nonlinear models, they correspond to CHABOCHE and NLISO, respectively. The principles are similar, and students can refer to ANSYS’ help documentation for more details.

Good Luck!

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