A mortar-type finite element approach for embedding 1D beams into 3D solid volumes
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ORIGINAL PAPER
A mortar-type finite element approach for embedding 1D beams into 3D solid volumes Ivo Steinbrecher1 · Matthias Mayr1 · Maximilian J. Grill2 · Johannes Kremheller2 · Christoph Meier2 · Alexander Popp1 Received: 9 December 2019 / Accepted: 17 August 2020 © The Author(s) 2020
Abstract In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with 3D continuum (solid) elements. An embedded mortar-type approach is employed to enforce the kinematic coupling constraints between the beam elements and solid elements on non-matching meshes. This allows for very flexible mesh generation and simple material modeling procedures in the solid, since it can be discretized without having to account for the reinforcements, while still being able to capture complex nonlinear effects due to the embedded fibers. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method, as well as its applicability to rather complex fiber-reinforced structures of practical relevance. Keywords Beam-to-solid coupling · 1D-3D coupling · Finite element method · Nonlinear beam theory · Mortar methods
1 Introduction Embedding fiber reinforcements into a solid matrix material is a commonly used approach to improve the mechanical behavior of engineering structures. In many cases, the reinforcements can be considered as being one-dimensional (1D), i.e. one dimension is much larger than the other two. Applications can be found in different fields, such as civil engineering, where steel reinforcements are embedded into concrete to improve its low tensile strength. In mechanical engineering, fiber-reinforced composites take advantage of fibers with high stiffness by embedding them inside a softer matrix material. This results in lightweight structures that are used in various applications, such as spacecrafts, boats, or sports equipment. Last but not least, also nature exploits the benefits of fiber-reinforced materials, as can be
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Ivo Steinbrecher [email protected]
1
Institute for Mathematics and Computer-Based Simulation, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
2
Institute for Computational Mechanics, Technical University of Munich, Boltzmannstrasse 15, 85748 Garching b. München, Germany
seen for example in arterial wall tissue with collagen fibers. Numerical simulation of such engineering and biomechanical structures is of high importance during the development and design phase, but it is also quite challenging. Different modeling techniques exist to create a numerical model of the reinforced materials, almost all of them being based on the finite element method. From a mechanical point of view the m
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