Zusammenfassung
This paper shows a new approach to estimate the critical traction for Mode I
crack opening before crack growth by numerical simulation. For quasi-static
loading, Linear Elastic Fracture Mechanics predicts the critical traction
before crack growth. To simulate the crack growth, we used bond-based
peridynamics, a non-local generalization of continuum mechanics. We discretize
the peridynamics equation of motion with a collocation by space approach, the
so-called EMU nodal discretization. As the constitutive law, we employ the
improved prototype micro brittle material model. This bond-based material model
is verified by the Young's modulus from classical theory for a homogeneous
deformation for different quadrature rules. For the EMU-ND we studied the
behavior for different ratios of the horizon and nodal spacing to gain a robust
value for a large variety of materials. To access this wide range of materials,
we applied sparse grids, a technique to build high-dimensional surrogate
models. Sparse grids significantly reduce the number of simulation runs
compared to a full grid approach and keep up a similar approximation accuracy.
For the validation of the quasi-static loading process, we show that the
critical traction is independent of the material density for most material
parameters. The bond-based IPMB model with EMU nodal discretization seems very
robust for the ratio \$$\backslash$delta/$\backslash$Delta X=3\$ for a wide range of materials, if an
error of 5$\backslash$\% is acceptable.
Nutzer
