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    <title language="eng">Integrating custom constitutive models into FEniCSx: A versatile approach and case studies</title>
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Since FEniCSx has become a powerful and popular open-source tool for solving partial differential equations, particularly due to its automatic computation of Hessians, we aim to develop a generalized interface to enhance its capability for constitutive modeling. This approach will address complex constitutive equations that require iterative solutions at the quadrature point level. Specific implementation challenges, such as using return-mapping procedures, can then be managed commonly. The provided interface for custom constitutive models offers a versatile way to implement them in various languages, including C++, Python, Rust, and Fortran. Finally, with UMATs for viscoplastic models as an example, we demonstrate how existing user subroutines can be incorporated into the interface and utilized within the FEniCSx framework.</abstract>
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Since FEniCSx has become a powerful and popular open-source tool for solving partial differential equations, particularly due to its automatic computation of Hessians, we aim to develop a generalized interface to enhance its capability for constitutive modeling. This approach will address complex constitutive equations that require iterative solutions at the quadrature point level. Specific implementation challenges, such as using return-mapping procedures, can then be managed commonly. The provided interface for custom constitutive models offers a versatile way to implement them in various languages, including C++, Python, Rust, and Fortran. Finally, using the example of UMATs for viscoplastic models, we demonstrate how available user subroutines can be incorporated into the interface while maintaining computational performance of FEniCSx comparable to that of Abaqus.</abstract>
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