VUMAT Subroutine: Shear Anisotropic Modified GTN Damage Model

Shear-Anisotropic Modified GTN Damage Abaqus VUMAT

The Gurson-Tvergaard-Needleman (GTN) damage model is one of the most widely recognized continuum damage theories for describing the behavior of ductile materials under large plastic deformations. By representing the accumulation of ductile damage through the nucleation, growth, and coalescence of micro-voids, the GTN model offers immense predictive power for porous metals and polymers.

However, the standard built-in Porous Metal Plasticity model in Abaqus/Standard and Abaqus/Explicit has fundamental limitations: it inherently relies on hydrostatic stress (stress triaxiality) to drive void growth and cannot accurately predict fracture under pure shear loading or highly anisotropic conditions.

To resolve these critical industrial challenges, BanuMusa R&D has developed the highly advanced Shear-Anisotropic Modified GTN Damage Abaqus VUMAT Subroutine. Based on the robust theoretical framework proposed by Gatea et al. (2017), this compiled Fortran subroutine extends the original GTN model by integrating plastic anisotropy and shear-driven void coalescence

Overcoming the Limitations of Standard Porous Metal Plasticity

In the standard GTN model, the yield function relies on a continuous internal state variable known as the void volume fraction (f). The damage evolution is entirely dependent on the development of hydrostatic stress. Consequently, under low stress triaxiality or pure shear conditions, the standard model incorrectly predicts infinite ductility without failure.

Our advanced VUMAT subroutine fundamentally upgrades this formulation:

1. Shear Loading Modification: By incorporating the Nahshon-Hutchinson shear mechanism, our VUMAT calculates the effect of shear stress invariants (via the Lode angle) to accelerate the void volume fraction increment. This dramatically improves the modeling accuracy of fracture propagation under pure shear and meridional tensile stress.

2. Plastic Anisotropy Integration: Drawing upon the constitutive equations proposed by Benzerga and Besson (2001), our model integrates the Hill Anisotropic Yield Function. By utilizing experimental Lankford coefficients, Abaqus application engineers can now evaluate materials that exhibit drastically different mechanical properties depending on the rolling and transverse directions.

(If you need to extract anisotropic yield parameters for this VUMAT, you can utilize our Anisotropy Calculator Abaqus Plugin to quickly fit your experimental test data).

Porous Metal Plasticity Material Model

The ductile damage model and Gurson damage model are the two most popular models used in FE simulation to model the ductile fracture of metal and polymeric materials. The Gurson-Tvergaard-Needleman model is a material plasticity model in which the accumulation of ductile damage is represented by the nucleation, growth, and coalescence of microvoids.
The basic yield function of the GTN model is:

The GTN damage model has a total of nine parameters, which need to be calibrated for a given material. The GTN model is just one model from a particular class of pressure-dependent plasticity models in which the response is dependent on the development of the hydrostatic stress as well as the deviatoric stress tensor. In the model, the micro-voids are represented by a continuous internal variable, the void volume fraction, f.

Implementation and Validation of Modified GTN Damage Abaqus VUMAT

The model has been implemented in ABAQUS finite element code via the VUMAT user subroutine. It supports fully the nucleation, growth, and coalescence of voids, and differs from the built-in porous plasticity model provided in ABAQUS/Standard. The modified GTN model has been implemented as a Fortran 90 VUMAT subroutine for use with the Abaqus/explicit.

It has several additional features and offers an alternative to the built-in porous plasticity model in ABAQUS. As well as predicting the void volume fraction, the model calculates the microscopic equivalent plastic strain in the fully dense material, the partitioning of the elastic and plastic strains, and the stress in the material. Integration of the constitutive equations is carried out using the backward Euler method. The incremental forms of the rate equations are nonlinear and coupled together, and robust numerical techniques are required to solve them.

Shear Loading  Effect in GTN Damage Abaqus VUMAT

This new advanced Gurson model is proposed, which is an extension of the original to take into account plastic anisotropy and shear loading conditions. The results showed that the modified GTN model improved the modeling accuracy of fracture over the original GTN model under shear loading conditions. Furthermore, the shear plays a role under meridional tensile stress to accelerate fracture propagation in processes such as single-point incremental forming (SPIF). 

In this work, a modified Gurson–Tvergaard-Needleman damage model based on Gatea et al. paper was developed with the consideration of shear to predict ductile fracture in the SPIF process due to void nucleation and coalescence with results compared with the original GTN model in SPIF.  the main motivation of this study is to develop a GTN-based model and to investigate its accuracy and effectiveness in predicting the ductile fracture in SPIF processing of typical truncated cone and pyramid shapes.

In the original GTN model, the increment of void volume fraction is measured based on the nucleation and growth of voids. In this study, the Nahshon-Hutchinson type shear mechanism was incorporated in the GTN model to take into account the effect of shear in the increment of void volume fraction.

Plastic Anisotropy for GTN Damage Abaqus VUMAT

One of the advantages of the Gurson model is its flexibility. Indeed this model can be extended to various mechanical behaviors of the matrix (hardening, plastic anisotropy,…), to many shapes of cavity (ellipsoidal, cylindrical), and several evolution laws of the void volume fraction. These different choices can be combined to generate an enriched or advanced Gurson model. Here, a new advanced model is proposed. This model takes into account plastic anisotropy of the dense matrix which is defined by the Hill anisotropic yield function.

The Hill anisotropic yield function is a mathematical equation used to describe the yield behavior of anisotropic materials. Anisotropic materials exhibit different mechanical properties in different directions, meaning their response to loading varies depending on the direction of applied stress.

Industrial Applications: From SPIF to Crashworthiness

The flexibility of our modified Gurson model makes it the ultimate predictive tool for complex manufacturing and structural integrity assessments:

• Single Point Incremental Forming (SPIF): Accurately predict ductile fracture, localized tearing, and void coalescence in SPIF processing of truncated cone and pyramid shapes where severe shear banding dominates the failure mechanism.

• Advanced Sheet Metal Forming: Predict edge-cracking and material tearing during deep drawing, blanking, and high-strength steel (AHSS) stamping operations.

• Crash & Impact Dynamics: Utilize the high-speed explicit integration of this VUMAT to simulate the progressive crushing and structural tearing of vehicle chassis components during dynamic collisions.

The Advantages of the Modified GTN Damage Model

• Incorporate plastic anisotropy into constitutive equations of the GTN damage model based on the Benzerga and Besson, 2001 paper by Lankford coefficient.
  
• Consideration of shear to predict ductile fracture and improved the modeling accuracy of fracture over the original GTN model under shear loading conditions based on Gatea et al..
  
• Abaqus application engineers can choose the Mises, Hill, or Barlat criterion independently.

What is Included in the GTN VUMAT Package?

By purchasing this product, you bypass months of complex Fortran coding and numerical debugging. This package provides a fully Verified & Validated (V&V) environment ready for immediate industrial application.

• Compiled Fortran Subroutines: Advanced VUMAT codes compatible with Abaqus/Explicit (Run on Windows and Linux).

• Abaqus Workshop Files: Complete *.cae, *.inp, *.jnl, and *.odb files for three distinct validation benchmarks:

  • Example 1: Damage prediction in a tensile test using the full Shear-Anisotropic Modified GTN damage model.

  • Example 2: Damage prediction using the Abaqus built-in GTN model for direct comparative analysis.

  • Example 3: Tensile test simulation using purely Anisotropic-Modified GTN without shear effects.

• Abaqus GTN Damage Parameters Database: To save you hundreds of hours of material calibration, this package includes a verified Microsoft Excel *.xls database containing precise GTN damage parameters for 14 engineering materials, including:

  • Al 6061-T6, Al 5182, Al 5754, AA 6016-T4, AA 6111-T4

  • Pure Titanium

  • Mild Steel, XES Steel, ULC/Ti, DC 06 Steel, DP 600 Steel

• Comprehensive Documentation: Step-by-step lecture notes (*.pdf) explaining the theoretical implementation, parameter calibration, backward Euler integration methodology, and how to define your material cards.

(Need access to a broader range of materials? Upgrade your simulation library with MatLib for Abaqus, featuring over 1,700 pre-calibrated material datasets).

Technical Support & Money-Back Guarantee

We stand by the numerical stability and accuracy of our codes. This package includes a 15-day money-back guarantee and free 24/7 online mentoring. If you encounter any compiler linking issues (Intel OneAPI / Visual Studio) or need assistance defining the yield function (Mises, Hill, or Barlat), our senior simulation engineers are ready to assist.

🎓 Attention Academic Researchers: Are you writing your MSc or PhD thesis on ductile fracture mechanics, void coalescence, or advanced metal forming processes? Verify your university status today and receive a 40% Academic Discount on this VUMAT package and our Introduction to VUMAT Subroutine Course. 👉 Apply for Your Academic Discount Here