A meshfree thin shell method for non‐linear dynamic fracture

TLDR

The authors develop a meshfree thin‑shell formulation that handles finite strains and arbitrary evolving cracks without requiring a mesh. The method employs a C1‑continuous meshfree approximation with cubic or quartic polynomial basis functions, eliminating the need to discretize the director field and simplifying crack incorporation. The formulation satisfies the C1 displacement continuity, removes membrane locking, and yields accurate results on several elastic and elasto‑plastic benchmark tests. © 2007 John Wiley & Sons, Ltd.

Abstract

Abstract A meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The C 1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto‐plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straightforward. Copyright © 2007 John Wiley & Sons, Ltd.