Phase-field analysis of finite-strain plates and shells including element subdivision

• Published in: Computer methods in applied mechanics and engineering 2016-12, Vol.312, p.322-350
• Main Authors: Areias, P., Rabczuk, T., Msekh, M.A.
• Format: Article
• Language: English
• Subjects: Algorithms; Clamping; Cylinders; Damage; Elasto-plastic constitutive laws; Fracture; Mathematical models; Phase-field model; Plates; Regularization; Robustness (mathematics); Shells; Strain; Two independent phase fields
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2016.01.020

With the theme of fracture of finite-strain plates and shells based on a phase-field model of crack regularization, we introduce a new staggered algorithm for elastic and elasto-plastic materials. To account for correct fracture behavior in bending, two independent phase-fields are used, corresponding to the lower and upper faces of the shell. This is shown to provide a realistic behavior in bending-dominated problems, here illustrated in classical beam and plate problems. Finite strain behavior for both elastic and elasto-plastic constitutive laws is made compatible with the phase-field model by use of a consistent updated-Lagrangian algorithm. To guarantee sufficient resolution in the definition of the crack paths, a local remeshing algorithm based on the phase-field values at the lower and upper shell faces is introduced. In this local remeshing algorithm, two stages are used: edge-based element subdivision and node repositioning. Five representative numerical examples are shown, consisting of a bi-clamped beam, two versions of a square plate, the Keesecker pressurized cylinder problem, the Hexcan problem and the Muscat-Fenech and Atkins plate. All problems were successfully solved and the proposed solution was found to be robust and efficient.