TY - JOUR A1 - Rosenbusch, Sjard Mathis A1 - Balzani, D. A1 - Unger, Jörg F. T1 - Regularization of softening plasticity models for explicit dynamics using a gradient-enhanced modified Johnson–Holmquist model N2 - The behavior of concrete under high strain rates is often described by plasticity models with softening, which is modeled by a reduction of the yield surface as a function of the local equivalent plastic strain. Many of these models are local and therefore produce mesh-dependent results. In this contribution, the gradient-enhancement of such models is investigated to mitigate the mesh-dependency. First, the mesh-dependency of these local formulations based on the analysis with a modified JH2 model as a representative for these constitutive formulations is demonstrated using a one-dimensional benchmark example. In the benchmark, the width of the damaged zone decreases upon mesh-refinement and the dissipated plastic energy tends to zero. It is further shown that a significantly small safety factor for the critical time step is needed in order to achieve accurate results for the benchmark example. The first investigated gradient-enhancement approach replaces the equivalent local plastic strain with its nonlocal counterpart. The enhancement is based on the inclusion of inertia and damping to the additional Helmholtz equation which enables the use of the central difference method as an explicit solver. This method successfully distributes the damage over several elements, however, the local equivalent plastic strain still localizes into one cell. The inclusion of hardening with respect to the local equivalent plastic strain inhibits the localization and the dissipated plastic energy converges with mesh-refinement. This is further confirmed in a two-dimensional wedge-splitting experiment and a four-point bending test where the damage pattern produced by the local model is mesh-dependent as well and the dissipated plastic energy tends to zero with mesh-refinement. The proposed nonlocal model with hardening results in a consistent damage pattern and the dissipated plastic energy converges. Furthermore, the nonlocal model with hardening is less sensitive to time step refinement, such that computational efficiency can be improved compared to the local model. The numerical experiments are implemented using the free open source tool FEniCSx and have been made available on Zenodo. KW - Gradient plasticity KW - Explicit dynamics KW - JH2 model KW - Concrete modeling KW - FEniCS KW - Mesh convergence KW - Time step convergence PY - 2024 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-630453 DO - https://doi.org/10.1016/j.ijimpeng.2024.105209 SN - 1879-3509 VL - 198 SP - 1 EP - 18 PB - Elsevier Ltd. CY - Schweiz AN - OPUS4-63045 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - GEN A1 - Diercks, Philipp A1 - Robens-Radermacher, Annika A1 - Rosenbusch, Sjard Mathis A1 - Unger, Jörg F. A1 - Saif-Ur-Rehman, Saif-Ur-Rehman T1 - fenics-constitutive N2 - This software enables the use of nonlinear constitutive models with FEniCSx. KW - Constitutive models KW - FEniCSx KW - Fenics-constitutive PY - 2024 DO - https://doi.org/10.5281/zenodo.13364955 PB - Zenodo CY - Geneva AN - OPUS4-62114 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - GEN A1 - Rosenbusch, Sjard Mathis A1 - Diercks, Philipp A1 - Kindrachuk, Vitaliy A1 - Unger, Jörg F. T1 - Integrating custom constitutive models into FEniCSx: A versatile approach and case studies N2 - The development and integration of user-defined constitutive relationships into finite element (FE) tools using standardized interfaces play a pivotal role in advancing the capabilities of FE solvers for structural mechanics applications. While commercial FE solvers like Abaqus and Ansys have designed their interfaces to provide custom stresses, tangents, and updated history variables, the open-source solver FEniCSx remains efficient only when the constitutive update has an analytical representation. This restricts the application of FEniCSx for non-linear structural mechanics. 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. KW - Finite element method KW - Constitutive models KW - FEniCSx KW - UMAT KW - Rust KW - Python KW - C++ PY - 2024 DO - https://doi.org/10.5281/zenodo.13980988 PB - Zenodo CY - Geneva AN - OPUS4-62112 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Rosenbusch, Sjard Mathis T1 - Gradient-enhanced models in blast simulations of concrete structures N2 - Blast experiments on reinforced concrete structures are often limited to small structures and therefore simple shock waves. Such experiments are carried out at the Bundesanstalt für Materialforschung und -prüfung (BAM) and the structural response is investigated using several measuring methods. Complex load scenarios that occur as a result of reflection of the shock wave in larger structures are harder to realize in practice. Numerical simulations for the propagation of the shock wave and the structural response can therefore be an alternative method for the investigation of blast loads on complex structures. For the simulation of concrete under impact and blast loads, several local constitutive models exist that are formulated as plasticity models with softening taken into account by introducing a scalar damage field. Local damage models however often lead to mesh-dependent results which do not converge with mesh refinement. In order to achieve meaningful predictions from numerical experiments, independence from the mesh is needed. In this contribution, the Johnson-Holmquist model (JH2) for brittle damage [2] has been implemented for the free open source software FEniCSx and is investigated in a high strain rate benchmark simulation. Mesh-convergence analyses show that displacements as well as the dissipated plastic energy do not converge with mesh-refinement. Following the gradient-enhancement approach by [1], a gradient-enhanced JH2 model which can be efficiently solved with explicit solvers is introduced and its advantages over the local models are discussed. Since many damage models for concrete share the damage mechanism of the JH2 model, the application of the regularization methods to more complex material models, like the RHT model [3], is also discussed. Advantages of a gradient-enhanced formulation to simulate dynamic strength increase of concrete, as suggested in [1], is discussed as well. T2 - ECCOMAS CONGRESS 2024 CY - Lisbon, Portugal DA - 03.06.2024 KW - Concrete Modeling KW - Explicit Dynamics KW - Gradient-Damage KW - Mesh Convergence PY - 2024 AN - OPUS4-64613 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - GEN A1 - Rosenbusch, Sjard Mathis A1 - Balzani, Daniel A1 - Unger, Jörg F. T1 - Regularization of softening plasticity models for explicit dynamics using a gradient-enhanced modified Johnson-Holmquist model N2 - The behavior of concrete under high strain rates is often described by plasticity models with softening, which is modeled by a reduction of the yield surface as a function of the local equivalent plastic strain. Among these are the RHT model, the K\&C model and the Johnson-Holmquist concrete model. These models are however local and therefore produce mesh-dependent results. In this contribution, the gradient-enhancement of such models is investigated. First, the mesh-dependency of these local formulations based on the analysis with a modified JH2 model as a representative for these constitutive formulations is demonstrated using a one-dimensional benchmark example. The central difference method is used as solver with a diagonal mass matrix obtained from a Gauß-Lobatto integration. In the benchmark, the width of the damaged zone decreases upon mesh-refinement and the dissipated plastic energy tends to zero. It is further shown that a significantly small safety factor for the critical time step is needed in order to achieve accurate results for the benchmark example. Next, two gradient-enhancement approaches are investigated. The enhancement is based on the inclusion of inertia and damping to the additional Helmholtz equation which enables the use of the central difference method as an explicit solver. In the first formulation, the yield surface and therefore the softening is formulated in terms of a nonlocal equivalent plastic strain. In the second approach, a hardening term which depends on the local equivalent plastic strain is introduced to the modified JH2 model in addition to the nonlocal softening. This approach is inspired by results from gradient plasticity in quasi-static loading scenarios. It is shown that the approach without hardening can still lead to mesh-dependent results while the model that includes hardening successfully inhibits strain localization and leads to a converging dissipated plastic energy. This is further confirmed in a two-dimensional wedge-splitting experiment where the damage pattern produced by the local model is mesh-dependent as well and the dissipated plastic energy tends to zero with mesh-refinement. The proposed nonlocal model with hardening results in a consistent damage pattern and the dissipated plastic energy converges. Furthermore, the nonlocal model with hardening is less sensitive to time step refinement, such that computational efficiency can be improved compared to the local model. The numerical experiments are implemented using the free and open-source tool FEniCSx. KW - Concrete modeling KW - Explicit Dynamics KW - FEniCS KW - Gradient plasticity KW - JH2 model KW - Mesh convergence PY - 2024 DO - https://doi.org/10.5281/zenodo.13983859 PB - Zenodo CY - Geneva AN - OPUS4-65083 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -