Thermosonic wire bonding is a common fabrication process for connecting devices in electronic packaging. However, when the free air ball (FAB) is compressed onto the I/O pad of the chip during bonding procedure, chip cracking may occur if the contact pressure is too large. This study proposes an effective simulation technique that can predict the wire ball geometry after bonding in an accurate range. The contact force obtained in the simulation can be used for possible die cracking behavior evaluation. The simulation in this study used the explicit time integration scheme to deal with the time marching problem, and the second-order precision arbitrary Lagrangian-Eulerian (ALE) algorithm was used to deal with the large deformation of the wire ball during the bonding process. In addition, the equilibrium smoothing algorithm in LS-DYNA can make the contact behavior and geometry of the bonding wire almost the same as the experiment, which can also significantly reduce the distortion of the mesh geometry after remeshing.

We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration scheme allows us to recover conservation of energy, and thus stability over long time simulations. These theoretical results are illustrated by numerical simulations of test cases involving large displacements.

We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG)methods. The output of this detector is a reliably scaled, element-wise smoothnessestimate which is suited as a control input to a shock capture mechanism. Using anartificial viscosity in the latter role, we obtain a DG scheme for the numerical solutionof nonlinear systems of conservation laws. Building on work by Persson and Peraire, wethoroughly justify the detector’s design and analyze its performance on a number ofbenchmark problems. We further explain the scaling and smoothing steps necessary to turnthe output of the detector into a local, artificial viscosity. We close by providing anextensive array of numerical tests of the detector in use.