Energy conservation during remeshing in the analysis of dynamic fracture

Abstract

Summary The analysis of (dynamic) fracture often requires multiple changes to the discretisation during crack propagation. The state vector from the previous time step must then be transferred to provide the initial values of the next time step. A novel methodology based on a least‐squares fit is proposed for this mapping. The energy balance is taken as a constraint in the mapping, which results in a complete energy preservation. Apart from capturing the physics better, this also has advantages for numerical stability. To further improve the accuracy, Powell‐Sabin B‐splines, which are based on triangles, have been used for the discretisation. Since scriptC1 continuity of the displacement field holds at crack tips for Powell‐Sabin B‐splines, the stresses at and around crack tips are captured much more accurately than when using elements with a standard Lagrangian interpolation, or with NURBS and T‐splines. The versatility and accuracy of the approach to simulate dynamic crack propagation are assessed in two case studies, featuring mode‐I and mixed‐mode crack propagation.

Coupling of non‐ordinary state‐based peridynamics and finite element method with reduced boundary effect

“…where K(x PD i ) is the shape tensor of peridynamic node i obtained from Equation (6), and K(x PD 2 ) and K(x PD 3 ) are equal to 2AΔx 3 . In contact-coupling (CT-coupling), the coupling force exerted by embedded peridynamic node 2 is fully applied to finite element node 3, and the net force R applied to finite element node 3 is expressed as…”

“…However, the displacement fields are usually discontinuous if a crack tip or crack surfaces exist. A remeshing technique might be required to prevent discontinuous fields within meshes, 2,3 notably in nonlinear analysis. In the framework of the FEM, the extended FEM (XFEM) was proposed to deal with the spatial derivatives on either the crack tip or crack surfaces 4,5 .…”

The use of Powell-Sabin B-Splines in a higher-order phase-field model for crack kinking

“…Ψ r ). Due to the non-interpolatory property of Powell-Sabin B-splines, a least-squares fit is employed to carry out the mapping [37]:…”

Convergence in non‐associated plasticity and fracture propagation for standard, rate‐dependent, and Cosserat continua

“…If the fracture had been propagated by locally reducing from a  2 to a  −1 continuity, the control points of the mesh would have changed location, necessitating a remap not only of the displacements, but also a recalculation of the history variables at the new control points. 46 To prevent this, and to eliminate a source of potential errors, we have pre-inserted a  0 continuity along a predetermined fracture path. Mesh line insertion to reduce the continuity from  0 to  −1 results in only a duplication of the control point at the interface, without altering the location of this or any other control point.…”