| 论文简介 |
The numerical manifold method is a cover-based method using mathematical covers that are
independent of the physical domain. As the unknowns are defined on individual physical covers, the
numerical manifold method is very suitable for modeling discontinuities. This paper focuses on
modeling complex crack propagation problems containing multiple or branched cracks. The
displacement discontinuity across crack surface is modeled by independent cover functions over
different physical covers, while additional functions, extracted from the asymptotic near tip field, are
incorporated into cover functions of singular physical covers to reflect the stress singularity around the
crack tips. In evaluating the element matrices, Gaussian quadrature is used over the sub-triangles of
the element, replacing the simplex integration over the whole element. First, the method is validated by
evaluating the fracture parameters in two examples involving stationary cracks. The results show good
agreement with the reference solutions available. Next, three crack propagation problems involving
multiple and branched cracks are simulated. It is found that when the crack growth increment is taken
to be 0.5hrdar0.75h, the crack growth paths converge consistently and are satisfactory. |
(创新港)
