Introduction
This project features a comprehensive set of Abaqus models for 3D continuum elements, using a custom VUMAT subroutine. The model is based on the Modified Johnson Cook (MJC) thermo-viscoplastic model combined with the Hershey yield surface. If you work with high-strain-rate applications such as impact analysis, metal forming, or crash simulations, this modeling package will enhance your workflow.
What is the Modified Johnson Cook (MJC) Viscoplastic Model?
The Modified Johnson Cook (MJC) model is a material behavior framework designed to simulate how materials respond to different strain rates and temperatures. It’s an enhanced version of the classic Johnson Cook model, which was developed to predict the behavior of metals under extreme conditions like impacts or explosions.
The MJC model can take into account:
- Work hardening (how a material becomes stronger as it’s deformed)
- Thermal softening (how a material weakens at elevated temperatures.)
- Strain rate sensitivity (how material behavior changes with different speeds of loading)
In this implementation, the thermal softening is assumed to be due to adiabatic heating due to the plastic work being converted into heat. This is appropriate for short duration, high strain-rate scenarios, where heat conduction can be considered negligible.
By using the MJC model, simulations can more accurately reflect real-world conditions, making it ideal for industries like automotive and aerospace, where materials often experience both high temperatures and high strain rates.
What is the Hershey Yield Surface?
The Hershey yield surface is an advanced model for predicting when a material will begin to deform plastically under stress.
The Hershey yield surface can be viewed as a hybrid between the von Mises and the Tresca yield surfaces. The figure shows the form of the yield surface for different values of the exponent m. For the value m = 1, the criterion becomes Tresca and for a value of 2, the von Mises criterion is obtained. Other values of m gives a hybrid of the two.
Typically, real metals will have a yield surface that is somewhere in between the Tresca and von Mises yield surfaces. This behaviour can be described by the Hershey yield surface by setting an appropriate value of the exponent m.
This implementation assumes isotropic work hardening, meaning that the yield surface will be able to grow as it deforms plastically, but it will grow independent of the direction of the applied load.
Why Use the MJC Model and Hershey Yield Surface Together?
Using both the Modified Johnson Cook (MJC) model and the Hershey yield surface gives you a more precise simulation of material behavior under extreme conditions. The MJC model accounts for changes in temperature due to plastic dissipation as well as plastic strain rate, while the Hershey yield surface realistically describes the yielding behavior of metals. Together, they enable simulations that closely replicate the performance of real-world materials, even under extreme conditions.
This combination becomes especially important in applications where high-speed impacts, high temperatures, or both affect materials—such as in crash tests, ballistic impact studies, and advanced manufacturing processes like hot metal forming.
How are the Equations Solved?
Every time step, the VUMAT subroutine is responsible for updating the stress and internal variables describing effects such as work hardening, temperature, etc. For every integration point in every element of the mesh, a set of nonlinear equations governing the material model have to be solved. To solve these equations, a return mapping algorithm is used. First an elastic predictor step is performed which gives a predicted stress state. If this stress is outside the yield surface, a plastic corrector step is performed. This corrector step is solved by an iterative scheme. The selected scheme in this implementation is a robust algorithm called the cutting plane method, suitable for explicit codes.
Why Use Abaqus for These Simulations?
Abaqus is a widely-used, powerful finite element analysis (FEA) software that is known for its robustness in simulating complex behaviors. It is highly adaptable for modeling a range of materials, including metals, composites, and plastics.
Abaqus allows you to use predefined material models, but in cases where more customization is required—like with the MJC model and Hershey yield surface—a user-defined material subroutine becomes essential. This is where the VUMAT subroutine comes into play.
What is a VUMAT Subroutine in Abaqus?
The VUMAT subroutine in Abaqus allows users to define their own material behavior, beyond what is available in the standard software package. VUMAT subroutines can be used together with Abaqus Explicit which is a good choice when dealing with short duration, dynamic, highly non-linear problems. When predefined material models fall short, VUMAT integrates more sophisticated models. The files provided in this package gives examples of such a subroutine that implements the MJC thermo-viscoplastic model and the Hershey yield surface.
In this project, the VUMAT subroutine enables Abaqus to simulate complex material behavior by implementing the MJC model and Hershey yield surface. This level of customization is critical for accurately predicting how materials will perform under extreme conditions. This can significantly impact design decisions in engineering applications.
Who Can Benefit from This Project?
This modeling package is ideal for engineers and researchers working in fields where accurate material behavior prediction is essential, such as:
- Automotive: For crash simulations and safety analysis
- Aerospace: For high-temperature and high-stress component design
- Defense: For ballistic impact analysis and protective gear design
- Manufacturing: For metal forming, welding, and other high-temperature processes
- Material Science: For research into new materials that require advanced simulation techniques
Whether you’re developing new materials or optimizing designs for extreme conditions, this package gives you the tools to simulate real-world scenarios with unparalleled accuracy.
Key Features of This Abaqus Model Package
- Fully implemented MJC viscoplastic model: Accounts for strain rate, temperature, and strain hardening
- Hershey yield surface integration: Enables realistic yielding predictions
- VUMAT subroutine: Custom material model implementation for precise control over material behavior
- Cutting plane method: The selected algorithm that updates the stress and internal variables every time step.
- 3D continuum elements: Suitable for a wide range of applications, from large-scale impact simulations to micro-scale material research
- Detailed documentation and support: Easy to integrate into your existing Abaqus projects with comprehensive instructions
Applications
Here are just a few of the many areas where this model can be applied:
- Crash Testing: Simulate car crashes to optimize safety features.
- Metal Forming: Predict how metals deform during hot or cold forming processes.
- Ballistics: Analyze the effects of high-speed impacts on protective materials.
This modeling package is not only for academic research but also for industrial applications where accurate prediction of material behavior can save time and reduce costs.
Conclusion
This Abaqus model package, features a VUMAT subroutine for the Modified Johnson Cook viscoplastic model and Hershey yield surface. It is a powerful tool for anyone needing high-precision material behavior simulations. It’s designed for ease of use in a range of applications, from crash testing to advanced manufacturing processes.
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It would be helpful to see Abaqus Documentation to understand how it would be hard to start an Abaqus simulation without any Abaqus tutorial.
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