Abstract
AbstractSharp interface material models can be related to phase field models by introducing an order parameter, whose value is assigned to the different phases of a material. The elastic material law is coupled to the evolution equation of the order parameter and cracking is addressed as a phase transition problem instead of a moving boundary value problem. A regularization parameter ϵ controls the width of the diffuse cracks represented by the order parameter and the underlying sharp interface model can be recovered from the phase field model by the limit ϵ → 0. However, in numerical simulations using standard finite elements with linear shape functions, the minimum value of ϵ is restricted by the grid size and therefore the discretization of the crack field requires extensive mesh refinement for small values of ϵ. In this work, we construct special 2d shape functions which take into account the exponential character of the crack field and its dependence on the parameter ϵ. Especially in simulations with small values of ϵ and a rather coarse mesh, the elements with exponential shape functions perform significantly better than standard linear elements. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.