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Automating derivative computations is essential for improving the efficiency, reliability, and maintainability of simulations in computational solid mechanics. This thesis investigates the application of Automatic Differentiation (AD) to constitutive modeling in both hyperelasticity and finite-strain elastoplasticity, focusing on integrating AD into high-performance, matrix-free finite element frameworks. By eliminating the need to derive and code complex tensor algebra manually, this approach enables material scientists to focus more on the underlying physics and material behavior rather than low-level implementation details.
Three AD tools, Enzyme, ADOL-C, and Tapenade, are benchmarked against hand-coded derivatives for Neo-Hookean materials in a lightweight test environment, ADBenchSolids. Among them, Enzyme offers the most favorable balance of performance, flexibility, and ease of integration. These findings are confirmed in a production-scale simulation code, Ratel, where both Enzyme and ADOL-C are used for automating derivatives in Neo-Hookean models.
The thesis also demonstrates an AD-based implementation of finite-strain von Mises plasticity with isotropic hardening using additive decomposition in logarithmic strain space. Unlike hyperplastic models, which depend solely on a strain energy functional, this formulation involves two arbitrary scalar inputs: the strain energy and a dissipation potential governing plastic flow. Leveraging Enzyme’s forward and reverse modes, the framework automates the computation of stress updates and consistent tangent moduli in models with evolving internal variables, significantly reducing the burden of manual derivative maintenance.
Together, these contributions advance the automation of constitutive modeling in solid mechanics, reducing manual implementation effort while maintaining accuracy, extensibility, and computational efficiency.
