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A B S T R A C T Several fracture codes have been developed in recent years to perform analyses of dynamic crack propagation in arbitrary directions. However, general-purpose, commercial finiteelement software which have capabilities to do fracture analyses are still limited in their use to stationary cracks and crack propagation along trajectories known a priori. In this paper, we present an automated fracture procedure implemented in the large-scale, nonlinear, explicit, finite-element code DYNA3D which can be used to simulate dynamic crack propagation in arbitrary directions. The model can be used to perform both generationand application-phase simulations of self-similar as well as non-self-similar dynamic crack propagation in linear elastic structures without user intervention. It is developed based on dynamic fracture mechanics concepts and implemented for three-dimensional solid elements. Energy approach is used in the model to check for crack initiation/propagation. Dynamic energy release rate and stress intensity factors are determined from far-field finite-element field solutions using finite-domain integrals. Fracture toughness is input as a function of crack-tip velocity, and when the criterion for crack growth is satisfied, an element deletion-and-replacement re-meshing procedure is used along with a gradual nodal release technique to update the crack geometry and model the crack propagation. Direction of crack propagation is determined using the maximum circumferential stress criterion. Numerical simulations of experiments involving non-self-similar crack propagation are performed, and results are presented as verification examples.

Flexible Circuit Boards (FCB) are ubiquitous in most electronic devices used today. These are utilized in mobile phones, display cables in laptops, cameras, smart watches, robotic arms and more. They are mainly used in applications where space, flexibility and construction constraints limit the usage of conventional Printed Circuit Board (PCB). While FCBs offer numerous advantages over traditional PCBs, like enhanced reliability, capabilities, reduced weight, and lesser space utilization, on the other hand, they present different set of challenges like assembly, installation, and difficulty in repairing and reworking after installation. The flexes are generally bent at several points before conforming to the installed state which induces stresses before the actual operation or the working phase. These stresses are further magnified during the cyclic loading which can lead to breakage of these flexes. Due to intricacies involved in FCBs, numerical modeling of these components is challenging. In this work, a methodology is developed in Ansys Mechanical™ to model the installation and operating phase of the FCB. Stresses generated in both the phases are calculated and fatigue life is computed after the operational phase. Two different models are analyzed. The first model is a Rigid Flex PCB, where a FCB connects with the rigid PCBs. The second model is a standalone FCB cable. For both the models, shell elements are used to mesh the FCBs, which are typically thin structures and experience a large amount of rotation and bending loads. Trace mapping feature is used to accurately model the large number of intricate features such as copper traces, vias and other Electronic-CAD data. The trace mapping feature simplifies the model by modeling the geometry as dielectric layers and includes the effect of traces by mapping the metal fraction onto the dielectric layers. The loop forming capability of both the models is analyzed where they are subjected to a 180° bend. The fatigue induced due to this bending load is calculated for both the models. For the FCB cable case, the work is extended to study the stresses developed in the installation phase as it impacts the overall fatigue life of the FCB. Here the rigid surface bodies are used to push/deform the FCB cable to its final installation stage. Lastly, a detailed High-Performance Computing (HPC) scalability study is performed in-order to find the best balance between the number of cores and solution time.