The enhanced Craig–Bampton (ECB) method is a novel extension of the original Craig–Bampton (CB) method, which has been widely used for component mode synthesis (CMS). The ECB method, using residual modal compensation that is neglected in the CB method, provides dramatic accuracy improvement of reduced matrices without an increasing number of eigenbasis. However, it also needs additional computational requirements to treat the residual flexibility. In this paper, an efficient parallelization of the ECB method is presented to handle this issue and accelerate the applicability for large-scale structural vibration problems. A new ECB formulation within a substructuring strategy is derived to achieve better scalability. The parallel implementation is based on OpenMP parallel architecture. METIS graph partitioning and Linear Algebra Package (LAPACK) are used to automated algebraic partitioning and computational linear algebra, respectively. Numerical examples are presented to evaluate the accuracy, scalability, and capability of the proposed parallel ECB method. Consequently, based on this work, one can expect effective computation of the ECB method as well as accuracy improvement.

Three-dimensional (3D) simulations via molecular dynamics (MD) show that the brittle or ductile behavior of the atomistic samples with the edge crack (001)[110] (crack plane/crack front) depend on size of the self-similar atomistic crystals. Since the basic continuum predictions concerning cracks do not consider the random thermal atomic motion, we are restricted in this study to MD simulations with initial temperature of 0 K. For all samples tested, the crack initiation is brittle. However, the subsequent crack growth can be inhibited by twin formation on oblique planes {112}, crack branching along {011} planes and new dislocation emissions on {123} slip planes and the final fracture can also be then ductile, which depends predominantly on the thickness of the atomistic sample. The representative quantity, the atomistic fracture toughness initially increases with increasing sample thickness and later saturates near Griffith level for plane strain state along the crack front. The tested loading rates are equivalent to a cross head speed of 0.833 · 10⁻⁴ m s⁻¹ used in one our previous experiment. These new MD results comply with the stress analysis performed by the anisotropic linear fracture mechanics (LFM) and with some experimental observations.