Mesh refitting approach: a simple method to model mixed-mode crack propagation in nonlinear elastic solids

Abstract

We devise a finite element methodology to trace quasi-static through-thickness crack paths in nonlinear elastic solids. The main feature of the proposed method is that it can be directly implemented into existing large scale finite element solvers with minimal effort. The mesh topology modifications that are essential in propagating a crack through the finite element mesh are accomplished by utilizing a combination of a mesh refitting procedure and a nodal releasing approach. The mesh refitting procedure consists of two steps: in the first step, the nodes are moved by solving the elastostatic equations without touching the connectivity between the elements; in the next step, if necessary, quadrilateral elements attached to crack tip nodes are split into triangular elements. This splitting of elements allows the straightforward modification of element connectivity locally, and is a key step to preserve the quality of the mesh throughout the simulation. All the geometry related operations required for crack propagation are addressed in detail with full emphasis on computer implementation. Solving several examples involving single and multiple cracks, and comparing them with experimental or other numerical approaches indicate that the proposed method captures crack paths accurately.

A strongly coupled partitioned approach for fluid‐structure‐fracture interaction

“…J−integral quantifies the energy release rate from the crack tip, and hence, the crack driving force. In this work, as in Ma and Korsunsky 25 and Sudhakar and Wall, 26 we compute the crack propagation direction using the maximum energy release rate criterion, which states that the crack propagates along the direction of the vector J−integral. The crack propagation criterion 25 states that the crack in a material propagates when the crack driving force exceeds the fracture toughness (given by critical J−integral J c ), which is considered to be a material property.…”

“…26 The nonlinear system of equations resulting from the FE weak form can be written as The first step is to solve the governing equations of the structure.…”

“…The complete crack propagation algorithm, together with the appropriate mesh modifications are already elaborated in the framework of a mesh refitting approach, 26 and the relevant details are summarized here. The complete crack propagation algorithm, together with the appropriate mesh modifications are already elaborated in the framework of a mesh refitting approach, 26 and the relevant details are summarized here.…”

“…where c J is the part of the crack surface falling on the J−integral domain, P is the first Piola-Kirchhoff stress tensor, W is the strain energy per unit volume, q is the support function as defined in Sudhakar and Wall, 26 and t c is the externally applied traction acting on the crack surfaces; here, t c = − f · n f . The first term, as in Moran and Shih, Shivakumar and Raju, Dolbow and Devan, and Legrain et al, [44][45][46][47] is obtained after applying the divergence theorem to convert the contour form given in Equation 4 into the domain form and performing the pull-back operations; the second term accounts for the external traction on the crack faces.…”

“…That is, the crack propagates when |J| ≥ J c . In this work, as in Ma and Korsunsky 25 and Sudhakar and Wall, 26 we compute the crack propagation direction using the maximum energy release rate criterion, which states that the crack propagates along the direction of the vector J−integral.…”