Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formulation and finite element implementation
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Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models.
KeywordsShells Fracture mechanics Phase field fracture Finite elements Mixed formulation
MP and JR gratefully acknowledge financial support of the European Research Council (ERC), Grant No. 306622 through the ERC Starting Grant “Multi-field and multi-scale Computational Approach to Design and Durability of PhotoVoltaic Modules” - CA2PVM. JR is also grateful to the support of the Spanish Ministry of Economy and Competitiveness (Projects MAT2015-71036-P and MAT2015-71309-P) and Andalusian Government (Project of Excellence No. TEP-7093).
- 19.Rabczuk T, Areias PMA (2006) A meshfree thin shell for arbitrary evolving cracks based on an extrinsic basis. Comput Model Eng Sci 16:115–130Google Scholar
- 25.Ambrosio L, Tortorelli VM (1992) On the approximation of free discontinuity problems. Boll Un Mat Italy B(7)6(1):105–123Google Scholar
- 41.Keip MA, Kiefer B, Schröder J, Linder C (2016) Special Issue on Phase Field Approaches to Fracture. In: Memory of Professor Christian Miehe (1956–2016). Comput Methods Appl Mech Eng 312:1–2Google Scholar
- 44.Ambati M, De Lorenzis L (2016) Phase-field modeling of brittle and ductile fracture in shells with isogeometric NURBS-based solid-shell elements. Comput Methods Appl Mech Eng 312:351–373Google Scholar
- 45.Areias P, Rabczuk T, Msekh MA (2016) Phase-field analysis of finite-strain plates and shells including element subdivision. Comput Methods Appl Mech Eng 312:322–350Google Scholar
- 62.Zienkiewicz OC, Taylor RL (2000) The finite element method. Butterworth–Heinemann, Woburn, 5th ed, Vol. I. ISBN: 0750650494Google Scholar