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A higher-order scheme for two-dimensional quasi-static crack growth simulations. (English) Zbl 1173.74470
Summary: An efficient scheme for the simulation of quasi-static crack growth in two-dimensional linearly elastic isotropic specimens is presented. The crack growth is simulated in a stepwise manner where an extension to the already existing crack is added in each step. In a local coordinate system each such extension is represented as a polynomial of some, user specified, degree,$n$. The coefficients of the polynomial describing an extension are found by requiring that the mode II stress intensity factor is equal to zero at certain points of the extension. If a crack grows from a pre-existing crack so that a kink develops, the leading term describing the crack shape close to the kink will, in a local coordinate system, be proportional to ${x}^{3/2}$. We therefore allow the crack extensions to contain such a term in addition to the monomial terms. The discontinuity in the crack growth direction at a kink, the kink angle, is determined by requiring that the mode II stress intensity factor should be equal to zero for an infinitesimal extension of the existing crack. To implement the scheme, accurate values of the stress intensity factors and $T$-stress are needed in each step of the simulation. These fracture parameters are computed using a previously developed integral equation of the second kind.
##### MSC:
 74S30 Other numerical methods in solid mechanics 74R10 Brittle fracture 74H35 Singularities, blowup, stress concentrations (dynamical problems in solid mechanics)