A robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures. This class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small-sized critical regions. The proposed approach is based on the division of a simulation into a suitable number of sub-simulations where adaptive mesh refinement is performed only once based on refinement window(s) around crack front process zone(s). The initialization of Newton-Raphson nonlinear iterations at the start of each sub-simulation is accomplished by solving a linear problem based on a secant stiffness, rather than a volume mapping of nonlinear solutions between meshes. The secant stiffness is evaluated using material state information stored/read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework. Moreover, a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software. Data transfer between sub-simulations is not required in the simplified strategy. The computational efficiency, accuracy, and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3-D.

This paper reviews radar architectures that employ multiple transmit and multiple receive channels to improve the performance of synthetic aperture radar (SAR) systems. These advanced architectures have been dubbed multiple-input multiple-output SAR (MIMO-SAR) in analogy to MIMO communication systems. Considerable confusion arose, however, with regard to the selection of suitable waveforms for the simultaneous transmission via multiple antennas. In this paper, it is shown that the mere use of orthogonal waveforms is insufficient for the desired performance improvement in view of most SAR applications. As a solution to this fundamental MIMO-SAR problem we had previously suggested to exploit the special data acquisition geometry of a side-looking imaging radar equipped with multiple receiver channels in addition to appropriately designed waveforms transmitted by multiple antennas. Here, we extend this approach to a more general set of radar waveforms with special correlation properties that satisfy a short-term shift-orthogonality condition. We show that the echoes from simultaneously transmitted pulses can be separated if the short-term shift orthogonality is combined with digital beamforming on receive in elevation. This enables the implementation of a fully functional MIMO-SAR without correlation noise leakage for extended scattering scenarios.