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

By Pedro Areias, Timon Rabczuk, M. A. Msekh. 2016

304 citations recorded by the source corpus.

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.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b859f585d8ea1485364c9d7d8c34c82596042890

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

High-accuracy phase-field models for brittle fracture based on a new family of degradation functions (2017, background): “…since the problem of regularizationdependent material response is not solved in the alternative formulations previously mentioned, and furthermore is not only confined to brittle fracture as demonstrated in the numerical results of Areias et al. (2016) on cracking in elastoplastic materials.”
Phase field modelling of crack propagation, branching and coalescence in rocks (2018, unknown): “Gradient models (Thai et al. 2016), non-local models (Pijaudier-Cabot et al. 2004), models based on the screend-poisson equation (Areias et al. 2016a) and also phase field models are typical continuous approaches to fracture.”
Phase-field description of brittle fracture in plates and shells (2016, background): “[24] presented an approach for finite-strain plates and shells, where they assume two independent phase fields, corresponding to the lower and upper face of the shell, in order to correctly account for the fracture behavior in bending.”
Revisiting the problem of a crack impinging on an interface: A modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model (2017, background): “Recent studies have further extended this modeling strategy to shell structures in geometrically linear [55] and nonlinear [56,57] frameworks, ductile fracture [58,59], cohesive-based failure [60], dynamic fracture [61,62], and multi-physics applications [63,64], to quote some of the most notable st”