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UMAT & VUMAT Comparison

UMAT and VUMAT: Advantages & Limitations

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Overview of UMAT and VUMAT Subroutines

The UMAT (User Material) and VUMAT (Vectorized User Material) subroutines are widely used in ABAQUS, a popular software suite for finite element analysis. These subroutines allow users to define custom material models and incorporate them into the simulation process. UMAT and VUMAT are user subroutines that allow users to implement their constitutive models in ABAQUS. They help when the ABAQUS library lacks accurate material models for the desired material behavior in modeling. In this essay, we will provide an introduction to UMAT and VUMAT, explore their similarities and differences, and discuss the advantages and limitations of each.

Understanding UMAT

Key Features and Functionality of UMAT

UMAT is an interface provided by ABAQUS that enables users to implement user-defined material models. It allows researchers and engineers to capture complex material behaviors, such as nonlinear elasticity, plasticity, and viscoelasticity. UMAT allows users to describe the constitutive equations governing the behavior of materials under various loading conditions. It provides hooks into ABAQUS solver routines, allowing users to define the stress-strain response and other material properties based on their specific requirements.

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A model developed with UMAT
A model developed with UMAT

Comparison of UMAT and VUMAT

Similarities between UMAT and VUMAT

Both UMAT and VUMAT aim to provide users with the flexibility to define custom material models. They share several similarities in terms of functionality and usage within ABAQUS. The following points highlight some common characteristics:

  • Interface: Both UMAT and VUMAT serve as interfaces between the material model and the ABAQUS solver. They receive inputs from the solver and return the corresponding outputs, including stresses, strains, and material tangent stiffness matrices.
  • Customization: With UMAT and VUMAT, users have the freedom to define their own material models according to their specific research or engineering requirements. This flexibility enables the simulation of a wide range of materials and material behaviors.

Differences between UMAT and VUMAT

The main difference between UMAT and VUMAT is that UMAT is for implicit analysis and VUMAT is for explicit analysis. This means that UMAT requires updating the material Jacobian or stiffness matrix at each time step, while VUMAT does not. UMAT also needs the deformation gradient as an input to calculate the global strain, while VUMAT uses the strain increment instead.

Distinctive Features of UMAT and VUMAT

While UMAT and VUMAT share similarities, they also differ in certain aspects. The key distinctions are as follows:

    • Programming Paradigm: UMAT is implemented using a serial programming paradigm, where the material model is defined and executed in a sequential manner. On the other hand, VUMAT utilizes vectorized programming techniques that take advantage of parallel processing capabilities offered by modern CPUs and GPUs. This enables VUMAT to achieve superior performance and computational efficiency.

    • Computational Efficiency: Due to its vectorized nature, VUMAT offers significant speed improvements over UMAT, especially for large-scale simulations involving numerous material points. VUMAT takes advantage of SIMD (Single Instruction, Multiple Data) instructions and parallel processing to efficiently compute material responses.

    • UMAT can handle both thermal and mechanical loading, while VUMAT is only for mechanical loading.

    • Code Structure: UMAT typically consists of a single subroutine, whereas VUMAT is composed of multiple subroutines that handle different aspects of the material model, such as stress update, tangent stiffness computation, and state variable evolution. This modular structure facilitates code organization and maintenance.
UMAT interface

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VUMAT Interface

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Comparison of UMAT and VUMAT interfaces


The finite element method uses the material tangent stiffness matrix, DDSDDE, to calculate the global stiffness matrix. It represents the rate of change of stress with respect to strain at a material point. It is also called the Jacobian matrix or the constitutive matrix.
In UMAT, DDSDDE is an output variable that you need to update at each time step, based on your material model and the current state of stress and strain. The Newton-Raphson iterative method solves the equilibrium equations for UMAT, which implicit analysis uses. Using the DDSDDE matrix, we form the global stiffness matrix and improve the convergence of the solution.
VUMAT does not require DDSDDE as an output variable because it uses a central difference integration scheme to solve the equilibrium equations in explicit analysis. We do not use the DDSDDE matrix to form the global stiffness matrix, but you can optionally calculate and store it for post-processing purposes.
The main difference between UMAT and VUMAT is that UMAT requires you to update the material Jacobian or stiffness matrix at each time step, while VUMAT does not. UMAT also needs the deformation gradient as an input to calculate the global strain, while VUMAT uses the strain increment instead.


The “nblock” is an input variable that represents the number of material points in the current block. It is passed as an argument to the VUMAT or UMAT subroutine. The value of “nblock” depends on the element type, the number of integration points per element, and the block size specified by the user.
The main difference between VUMAT and UMAT in terms of “nblock” is that VUMAT uses a vectorized scheme to pass multiple material points at once, while UMAT uses a single-point scheme to pass one material point at a time. This means that VUMAT can achieve higher computational efficiency by reducing the subroutine overhead, but it also requires more memory allocation and careful indexing of the variables.
When using C3D8R elements, which have one integration point per element, and specifying a block size of 1000, VUMAT will call “nblock” equal to 1000, while UMAT will be called 1000 times with “nblock” equal to 1.


According to the ABAQUS help source, the difference in the stress defining in UMAT and VUMAT subroutines is that UMAT uses Cauchy stress components (or true stress) in the local orientation, while VUMAT uses Cauchy stress components in the corotational coordinate system that rotates with the material point.
A Newton-Raphson iterative method solves the equilibrium equations using UMAT, an active user subroutine for implicit analysis. The UMAT aligns the stress components with the user-defined local axes at each material point. The stress components are in the global orientation if you do not use a local orientation.
UMAT’s stress components rely on deformation gradient, an input variable reflecting material point deformation from reference to the current configuration.
In VUMAT, a user subroutine for explicit analysis utilizes a central difference integration scheme to solve the equilibrium equations. The stress components in VUMAT are in the corotational coordinate system, which means that they rotate with the material point as it deforms. VUMAT stress components are independent of the deformation gradient but rely on the strain increments, describing strain changes in time.

Advantages and Limitations

Advantages of UMAT and VUMAT

When choosing between them, one should consider the advantages and limitations of both UMAT and VUMAT.

Advantages of UMAT:

  • Established Framework: Various applications have extensively used and tested UMAT, making it a well-established choice.
  • Ease of Implementation: UMAT’s sequential programming paradigm makes it relatively easier to implement and debug compared to the vectorized approach of VUMAT.

Advantages of VUMAT:

  • Computational Efficiency: VUMAT’s vectorized programming enables faster simulations, especially for large-scale analyses with a high number of material points.
  • Parallel Processing: VUMAT leverages parallel processing capabilities, making it highly suitable for multi-core CPUs and GPUs, resulting in reduced computation time. As industry trends shift towards parallel computing architectures, adopting VUMAT ensures compatibility with future hardware advancements.


  • Hardware Dependencies: VUMAT’s performance benefits are dependent on hardware capabilities, such as SIMD instructions and parallel processing support. In some cases, the hardware infrastructure may limit the advantages offered by VUMAT.


In conclusion, UMAT and VUMAT provide valuable tools within ABAQUS for the implementation of user-defined material models. The choice between these subroutines depends on specific requirements, including ease of implementation, computational efficiency, hardware dependencies, and of course the operating solver. Users can make informed decisions for effective simulation needs by understanding subroutine features, advantages, and limitations. UMAT and VUMAT add to ABAQUS, enhancing its versatility for engineers to analyze various material behaviors and phenomena during simulations.

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