5.1 A homogeneous plate subjected to tension
A two-dimensional homogeneous plate with dimensions of\(1\ \times\ 1\) mm is discretized by one element. The computation is performed by \(u=1\ \) mm for 1000 steps. The following material properties are chosen: The Young’s modulus \(E=71\) GPa, Poisson’s ratio \(\vartheta=0.3\) and critical fracture energy density\(\mathcal{G}_{c}=9.310\) kN/mm. As the characteristic size of the element is \(1\) mm, the length scale parameter is set to \(l=2\) mm.
Setting the crack surface gradient to zero, corresponding to the homogeneous case \((\nabla\varphi=0)\). Thus, the axial stress can be calculated as\(\mathbf{\sigma}\left(\mathbf{u}\mathrm{,}\varphi\right)=g\left(\varphi\right)\frac{\partial\psi_{e}\left(\mathbf{\varepsilon}\right)}{\partial\mathbf{\varepsilon}}=g\left(\varphi\right)\mathbb{C:}\mathbf{\varepsilon}\), with \(\psi_{e}\left(\mathbf{\varepsilon}\right)\) =\({\psi_{e}}^{+}\left(\mathbf{\varepsilon}\right)\) and\({\psi_{e}}^{-}\left(\mathbf{\varepsilon}\right)=0\) because of the pure tension loading. Dimension and boundary conditions for numerical examples are listed in Table 3.
Table . Dimension and boundary conditions for all of the tested specimens