[ \mathcalF[\mathbfu,\phi] = \int_\Omega \left[ g(\phi) \psi^+(\mathbfu) + \psi^-(\mathbfu) \right] ,d\Omega
where (g(\phi)=(1-\phi)^2), (\ell) is the regularization length, (G_c) the critical fracture energy, and (c_w=4/3). i--- Comsol 6.1 Download Crack
| Quantity | Analytical | COMSOL 6.1 | Error | |----------|------------|------------|-------| | Critical load (P_cr) | (2\sqrtE' G_c a / \pi) | 9.82 kN | 2.3 % | | Crack‑tip opening displacement (CTOD) | (\delta = \fracK_I^2E' \sigma_y) | 0.154 mm | 1.9 % | | Step | COMSOL Action | Reason |
Funding agencies, lab facilities, and any collaborators. (\ell) is the regularization length
| Step | COMSOL Action | Reason | |------|----------------|--------| | 1 | Create 2‑D rectangle (L = 100 mm, H = 20 mm). | Benchmark geometry (center‑cracked plate). | | 2 | Insert a pre‑existing crack as a thin line (width ≈ 0 mm). | Initiate crack propagation. | | 3 | Use Free Triangular mesh with size = 0.5 mm (global) and size = 0.1 mm near crack tip (boundary layer). | Resolve stress singularity and phase‑field gradient. | | 4 | Enable Mesh refinement based on (\phi) gradient (adaptive). | Automatic refinement as crack grows. |
Finite‑Element Simulation of Crack Initiation and Propagation in Heterogeneous Solids Using COMSOL Multiphysics 6.1
(Alternative: “Phase‑Field Modelling of Fracture in Composite Materials with COMSOL 6.1”)