Adaptive analysis of yield line patterns in plates with the arbitrary Lagrangian–Eulerian method

Remeshing techniques for r-adaptive and combined h/r-adaptive analysis with application to 2D/3D crack propagation

“…Too large elements in the elastic regions can significantly delay or disturb the crack initiation and crack propagation processes [6,15,16]. Therefore, it should be ensured that element sizes are small enough in regions where cracking is about to occur.…”

“…The ratio ε eq /κ 0 denotes how close an element is to damage initiation [6,15], while the power n allows for a progressive decrease of the desired element size in the elastic regime [6]. Note that for damage initiation, i.e.…”

“…(14) can be solved by means of relaxation. Discretisation yields [6,7] −A x + b = Q ∂x ∂τ (15) where A and b are the same as in Eq. (12) and with (14).…”

“…It has been argued that taking the pseudo-time step ∆τ < h 2 2 leads to stable solutions with the Forward Euler scheme [6]. After the new nodal coordinates have been found, the stresses, strains and internal variables are transported to the new mesh using a Godunov algorithm [5,15,23,24]. For elements with one integration point, the value of a state variable component after remeshing η new is related to the value before remeshing η old via…”

“…(15). Extenstion towards elements with multiple integration points is straightforward [5,15,23,24]. Note that the computer costs involved with Eq.…”