Dynamic fracture modeling in shell structures based on XFEM
Journal article, 2010

Through-the-thickness crack propagation in thin-walled structures is dealt with in the paper. The formulation is based on the cohesive zone concept applied to a kinematically consistent shell model enhanced with an XFEM–based discontinuous kinematical representation. The resulting formulation comprises the representation of continuous deformation, represented by midsurface placement, director and thickness inhomogeneous fields, and discontinuous deformation, represented by discontinuous placement and director fields. The shell model is implemented both for the implicit static analysis and in the context of explicit dynamic integration pertinent to impact loading, and the implementation results in a 7-parameter solid-shell element based on a 6-noded triangular element. In order to properly formulate the dynamic fracture characteristics, a rate-dependent cohesive zone model is employed with respect to e.g. limiting crack speeds as observed experimentally. In the final example, this model has been applied to a blast loaded pressure vessel that has been experimentally tested. The results indicate that the right crack speed as well as fracture characteristics are relatively well captured. Furthermore, it appears that the discontinuous model exhibits the expected properties with respect to critical time step size in the dynamic analysis and convergence behavior towards the analytical static solution.

Dynamic fracture

Cohesive zones

Higher order thickness strain

Discontinuous XFEM kinematics

Shell theory


Ragnar Larsson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Jesus Mediavilla

Netherlands Organisation for Applied Scientific Research (TNO)

Martin Fagerström

Chalmers, Applied Mechanics, Material and Computational Mechanics

International Journal for Numerical Methods in Engineering

0029-5981 (ISSN) 1097-0207 (eISSN)

Vol. 86 4-5 499-527

Subject Categories

Mechanical Engineering

Applied Mechanics

Areas of Advance



Materials Science



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