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