# Mesh refinement strategies without mapping of non-linear solutions for the generalized and standard FEM analysis of 3-D cohesive fractures¶

This page describes the ABAQUS simulation of a delamination problem in a bonded double cantilever beam (DCB) specimen which is presented in Section 5.2 of the paper Mesh refinement strategies without mapping of non-linear solutions for the generalized and standard FEM analysis of 3-D cohesive fractures by J. Kim, A. Simone and C. A. Duarte [1].

The domain is discretized by bilinear four-node quadrilateral elements and the debonding process is captured using four-node cohesive elements inserted along a pre-defined discontinuity path. Rather than performing a simulation with a fixed mesh for all load steps, the simulation is split into six sub-simulations, where a single adaptively refined mesh is employed for each sub-simulation [2, 3]. As depicted below, the original stress field at the last load step of each sub-simulation (left) is well recovered in the next sub-simulation (right). A simplified strategy, described in Section 4 of the paper, is employed to circumvent the transfer of material state information between sub-simulations.

The load-displacement curves reported below illustrate that the solution computed using adaptive meshes over sub-simulations is in excellent agreement with the reference data obtained using a heavily refined fixed mesh for the whole simulation. The results shown in this figure can be drawn using a MATLAB script which is extracted from ABAQUS output files. The relevant input and output files for the ABAQUS simulation are available for download here.

## References¶

[1] J. Kim, A. Simone, and C. A. Duarte. Mesh refinement strategies without mapping of non-linear solutions for the generalized and standard FEM analysis of 3-D cohesive fractures. International Journal for Numerical Methods in Engineering, in press, 2016.

[2] Z. Shabir. Role of microstructural geometry in the deformation and failure of polycrystalline materials, PhD Thesis, Delft University of Technology. 27 March 2012. ISBN 978-94-6191-222-0.

[3] L. Ponson, Z. Shabir, E. Van der Giessen, and A. Simone. Brittle intergranular fracture of two-dimensional disordered solids as a random walk. in preparation, 2016.

Created by Jongheon Kim, Angelo Simone, and C. Armando Duarte | Last updated 22 July 2015