Quasi-static crack propagation simulation by an enhanced nodal gradient finite element with different enrichments

- Enhanced nodal gradient 4-node quadrilateral elements are used for quasi-static crack growth simulation.
- Different enrichments for crack-tip with ramp functions for crack growth are presented.
- XCQ4 possesses the continuous nodal gradients and continuous nodal stresses without smoothing operation.
- XCQ4 offers high accuracy in simulation of quasi-static crack propagation.

The recently developed consecutive-interpolation local enriched partition-of-unity method based on 4-node quadrilateral element (XCQ4) is used to study quasi-static crack propagation in 2-dimensional solids. For some of these problems numerical results have also been calculated with the standard extended finite element (XQ4), provided that the two approaches have the same number of degrees of freedom. In addition, two different versions of enrichment functions capturing the crack tip fields are taken into account, integrating into either the XCQ4 or XQ4. In each case, results have been computed with both settings and compared between each other. It is found that the numerical solution using the XCQ4 element has better accuracy than that found with the XQ4, and these solutions agree well with reference solutions available in literature. The underlying difference between the consecutive-interpolation basis functions and those for the traditional XQ4 is that the former approximation functions constructed by incorporating both nodal values and averaged nodal gradients obtained from linear shape function as interpolation conditions, enhancing and smoothing the stress fields and stress intensity factors. Additionally, the conditioning issue of the developed method is also numerically examined.