Viscoplasticity Abaqus Simulation Using UMAT Subroutine | Perzyna Viscoplastic Model

Introduction to Viscoplasticity | Viscoplasticity Abaqus

Viscoplasticity is a branch of continuum mechanics that describes the behavior of solids that exhibit rate-dependent inelastic behavior.  This means that the deformation of a material depends on both the magnitude of the stress and how quickly that stress is applied. Materials that exhibit viscoplasticity are called viscoplastic materials. Viscoplasticity is an important concept in many engineering applications, such as the design of structures that are subjected to dynamic loads, the modeling of the behavior of soils during earthquakes, and the development of new materials with tailored mechanical properties (viscoplasticity Abaqus).

The role of numerical simulations in analyzing the behavior of viscoplastic materials

Numerical simulations are an essential tool for understanding, predicting, and optimizing the behavior of viscoplastic materials. They play a vital role in various engineering fields and contribute to the development of safe, efficient, and reliable structures and components.

For complex engineering problems involving viscoplastic materials, Abaqus is a powerful and versatile option. It allows users to define their desired material behavior through UMAT and VUMAT subroutines, even if they are not in the prebuilt Abaqus material library. However, writing UMAT or VUMAT codes requires valuable knowledge of programming in the Fortran language, experience in developing subroutines for Abaqus, and familiarity with the theoretical aspects of viscoplastic models. So, it is a challenging task. As many people may not be familiar with the prerequisites, we have covered them all in this tutorial.

Theoretical formulations | Perzyna Viscoplastic Model

Three well-known models to describe viscoplastic behavior in the numerical simulations are, Bingham–Maxwell, Bingham–Kelvi, and Overstress models of the Perzyna.

Bingham–Maxwell refers to an Elastic-Perfectly Viscoplastic model. In this model, plastic Strain Rate is a function of the initial yield stress, with no influence of hardening. So, it Exhibits a constant yielding stress when the elastic limit is exceeded. You can Use it to model materials that exhibit both elastic and perfectly viscoplastic behavior.

Bingham–Kelvin is another Elastic-Perfectly Viscoplastic Similar to the Bingham–Maxwell model but with a different arrangement of elements.

Perzyna Model (perzyna viscoplastic model) is a Classical Phenomenological Viscoplasticity that describes the viscoplastic behavior of materials, especially when the strain rate significantly influences the material’s response. In this model, Plastic Strain Rate is Dependent on the flow rule, yield function, and internal variables. Here, flow Rule: Defines the relationship between the plastic strain rate and the stress state. We can use it for modeling materials under conditions where strain rate effects are significant, such as in high-speed deformation processes. This model is our desired in this tutorial and we will show you how to use Abaqus subroutines to implement it. So let us provide more details on its formulation.

We use the Perzyna viscoplastic model to describe the viscoplastic behavior of materials, particularly when the strain rate is an important factor in the material’s response. In this model, a constitutive relation gives the plastic strain rate in the form of:

where  is a yield function,  is the Cauchy stress,  is a set of internal variables (such as the plastic strain  and   is a relaxation time. The Perzyna’s yield function  is often expressed as an equation consisting of some invariant of stress and a model for the yield stress (or plastic flow stress). An example is the von Mises yield criterion. Finally, the internal variables can include quantities like the plastic strain and backstress, which evolve over time and affect the material’s response. The relaxation time controls the rate at which the material transitions from elastic to plastic behavior.

Workshop

Numerical simulations are an essential tool for understanding, predicting, and optimizing the behavior of viscoplastic materials. They play a vital role in various engineering fields and contribute to the development of safe, efficient, and reliable structures and components. In the following we have discussed some benefits of the numerical simulation for predicting the viscoelastic behavior:

1-  Viscoplastic materials exhibit a complex interplay between elastic (recoverable deformation), viscous (rate-dependent dissipation of energy), and plastic (permanent deformation) responses.  Real-world experiments can be expensive, time-consuming, and limited in scope. Numerical simulations allow us to model these complex behaviors efficiently and explore a wider range of conditions.

2-  Engineers can use simulations to predict the performance of structures and components made from viscoplastic materials under various loading conditions, like temperature fluctuations or impact. This helps optimize designs for safety, durability, and efficiency.

3- Simulations can be used as a virtual prototyping tool.  Instead of building and testing physical prototypes, engineers can test different material properties and design configurations virtually.

4- By analyzing the simulation results, researchers can gain a deeper understanding of the mechanisms of viscoplastic behavior. You can use this knowledge to develop new material models and improve the accuracy of simulations.

5- Numerical simulations are valuable for safety analysis of structures and components made from viscoplastic materials. They can help predict potential failure modes and identify critical design features.

Abaqus Perzyna Model using UMAT subroutine

In this tutorial, we have implemented the Abaqus Perzyna model in Abaqus. It is a powerful tool that allows users to define custom material models not available by default. The Perzyna model is a strain rate-dependent viscoplasticity model, implemented using the UMAT subroutine. In the case of the Perzyna model, the UMAT subroutine relates the strain to the stress using specific constitutive relations from the Perzyna formulation. This process involves defining the plastic strain rate as a function of the stress state, internal variables, and relaxation time (viscoplasticity Abaqus).

Results

Our main focus has been on writing general UMAT codes for analyzing viscoplastic behavior in Abaqus. Therefore, our intention was not to focus on a specific problem. Consequently, the results we have obtained are general, such as stress fields, which are necessary for many engineering applications. However, you can extract the specific results you need from Abaqus based on your project.

Applications

You can use this tutorial to perform numerical simulations to address many engineering problems. For example, viscoplastic simulations are useful in calculating permanent deformations. They enable predicting how materials will permanently deform under different loading conditions. Moreover, they help us assess the point at which structures will fail due to plastic deformation. Analyzing the stability of structures under various loads and conditions is another benefit of such simulations. Modeling the behavior of materials and structures during impact or crash scenarios is another goal. Additionally, such simulations help you evaluate the performance of materials in high-temperature environments, such as turbines in engines or power plants. These applications are critical in fields such as aerospace, automotive, civil engineering, and the energy sector. We hope the tutorial benefits you and meets your needs.