A 3D benchmark problem for crack propagation in brittle fracture L. Hug * 1 , S. Kollmannsberger 1 , Z. Yosibash 2 , and E. Rank 1,3 1 Chair for Computation in Engineering, Technische Universit¨ at M¨ unchen, Arcisstr. 21, 80333 M¨ unchen, Germany 2 School of Mechanical Engineering, Tel-Aviv University, 69978 Ramat-Aviv, Israel 3 Institute for Advanced Study, Technische Universit¨ at M¨ unchen, Lichtenbergstr. 2a, 85748 Garching, Germany Abstract We propose a full 3D benchmark problem for brittle fracture based on experiments as well as a validation in the context of phase-field models. The example consists of a series of four-point bending tests on graphite specimens with sharp V-notches at different inclination angles. This simple setup leads to a mixed mode (I + II + III) loading which results in complex yet stably reproducible crack surfaces. The proposed problem is well suited for benchmarking numerical methods for brittle fracture and allows for a quantitative comparison of failure loads and propagation paths as well as initiation angles and the fracture surface. For evaluation of the crack surfaces image-based 3D models of the fractured specimen are provided along with experimental and numerical results. In addition, measured failure loads and computed load-displacement curves are given. To demonstrate the applicability of the benchmark problem, we show that for a phase-field model based on the Finite Cell Method and multi-level hp-refinement the complex crack surface as well as the failure loads can be well reproduced. Keywords: Brittle fracture, benchmark, verification and validation, phase-field modeling, multi-level hp-adaptivity, Finite Cell Method Contents 1 Introduction 2 2 The Benchmark: V-notched Specimen 3 2.1 Experimental Setup ..................................... 3 2.2 Comparison Quantities .................................... 4 2.2.1 Failure Loads ..................................... 4 2.2.2 Fracture Initiation Angles .............................. 4 2.2.3 Fracture Surface ................................... 5 2.3 Provided Data for Benchmarking .............................. 6 3 Phase-Field Formulation 6 3.1 Energy Functional and Variational Problem ........................ 7 3.2 Governing Equations ..................................... 8 3.2.1 The Hybrid Model .................................. 8 3.2.2 Dynamic Fracture .................................. 9 * [email protected], Corresponding Author Preprint submitted to Some Journal October 16, 2019 arXiv:1910.06691v1 [cs.CE] 15 Oct 2019
A 3D benchmark problem for crack propagation in brittle fracture
May 23, 2023
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Related Documents
