Crack propagation involves the creation of new internal surfaces of a priori unknown paths. A first challenge for modeling and simulation of crack propagation is to identify the location of the crack initiation accurately, a second challenge is to follow the crack paths accurately. Phase-field models address both challenges in an elegant way, as they are able to represent arbitrary crack paths by means of a damage parameter. Moreover, they allow for the representation of complex crack patterns without changing the computational mesh via the damage parameter—which however comes at the cost of larger spatial systems to be solved. Phase-field methods have already been proven to predict complex fracture patterns in two and three dimensional numerical simulations for brittle fracture. In this paper, we consider phase-field models and their numerical simulation for conchoidal fracture. The main characteristic of conchoidal fracture is that the point of crack initiation is typically located inside of the body. We present phase-field approaches for conchoidal fracture for both, the linear-elastic case as well as the case of finite deformations. We moreover present and discuss efficient methods for the numerical simulation of the arising large scale non-linear systems. Here, we propose to use multigrid methods as solution technique, which leads to a solution method of optimal complexity. We demonstrate the accuracy and the robustness of our approach for two and three dimensional examples related to mussel shell like shape and faceted surfaces of fracture and show that our approach can accurately capture the specific details of cracked surfaces, such as the rippled breakages of conchoidal fracture. Moreover, we show that using our approach the arising systems can also be solved efficiently in parallel with excellent scaling behavior.
Meccanica – Springer Journals
Published: Aug 28, 2017
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera