In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element exterior calculus and domain decomposition to interconnect two systems with dual input-output behavior. The spatial domain is split into two parts by introducing an arbitrary interface. Each subdomain is discretized with a mixed finite element formulation that introduces a uniform boundary condition in a natural way as the input. In each subdomain the finite element spaces are selected from a finite element subcomplex to obtain a stable discretization. The two systems are then interconnected together by making use of a feedback interconnection. This is achieved by discretizing the boundary inputs using appropriate spaces that couple the two formulations. The final systems include all boundary conditions explicitly and do not contain any Lagrange multiplier. Time integration is performed using the implicit midpoint or Störmer-Verlet scheme. The method can also be applied to semilinear systems containing algebraic nonlinearities. The proposed strategy is tested on different examples: geometrically exact intrinsic beam model, the wave equation, membrane elastodynamics and the Mindlin plate. Numerical tests assess the conservation properties of the scheme, the effectiveness of the methodology and its robustness against shear locking phenomena.

In this work, the Material Point Method (MPM) is reviewed for application in the microelectronics industry. Microelectronic processes often involve large deformations, evolving interfaces, multiphysics coupling, and complex geometries that challenge conventional mesh-based methods such as the finite element method (FEM). Meshless methods provide an alternative solution that avoids these issues. A comparison is made between Smoothed Particle Hydrodynamics (SPH), Element Free Galerkin (EFG), peridynamics, Radial Basis Function–Finite Difference (RBF-FD), and MPM, evaluated with respect to convergence, consistency and stability, boundary enforcement, adaptivity, coupling, and industrial applicability. Based on this assessment, MPM and its main variants (BSMPM, GIMP, CPDI, and TLMPM) are examined in depth. The method’s ability to address large deformations, moving interfaces, contact, history-dependent material behavior, and multiphysics interactions is examined. The underfill process is used as a representative use case to illustrate challenges such as free surface flow, void formation, thermomechanical coupling, and residual stress. Overall, MPM shows strong potential, although further benchmarking and validation are required for widespread industrial adoption.

A meshless method is used to simulate the Fluid-Structure Interaction (FSI) in a micropump intended to treat nerve injury. Conventional meshbased methods can suffer from mesh deformation and quality issues, and find it difficult to track the fluid-structure interface. The Material Point Method (MPM) combines Lagrangian material points with an Eulerian computational grid, thereby avoiding any mesh related problems. To simulate the valve dynamics in the micropump, MPM was used to analyze the effect of the valve length on the behaviour of the pump. A longer valve length takes longer to open, as it sticks to the valve seat, meaning the pump needs to generate more pressure to open the valve. This contribution shows that MPM simulations can be used to optimize the valve design for implantable micropumps.

Underfill has an important role in the reliability of flip-chips, but voids formed during manufacturing can initiate fractures. Simulations can be used to predict when and where the fracture takes place. However, traditional mesh-based methods suffer from mesh distortions, require remeshing, and have long preprocessing times. In this work, the Material Point Method (MPM) is used to study the effect of the void size and relative distance on fracturing in the underfill. We find MPM can predict crack propagation without prior knowledge of the path, reduce preprocessing time, and eliminate remeshing. Therefore, this work aims to show MPM makes for an effective and efficient alternative to traditional simulation methods. Simulations are performed with MPM to investigate the effect of void size and distance between voids on crack propagation in the underfill. The results show that fractures occur later when the distance between voids is larger, but the rate of damage is significantly faster once a crack is formed. Larger void sizes increase the rate of damage, but no significant effect on crack initiation was found. These results show that the meshless material point method is a promising alternative for simulating fractures in the underfill.

The demand for rapid advancement in AI, mobile and automotive markets is pushing the boundaries of electronic packaging, including heterogeneous integration, high-power packages, and large-die packaging. Against this backdrop, machine learning technologies emerge as dynamic tools for correlation building and classification, revolutionizing the traditional approaches to design, manufacturing, and testing in electronic packaging, as well as the Design for Reliability (DfR) methodologies.This paper reviews the most recent AI-assisted approach for electronic packaging and then focuses on the AI-assisted DfR (AI-DfR) approaches. Our examination reveals that AI methods have been adapted to meet the specific needs of electronic packaging. The industry’s anticipation for AI-DfR stems from its potential to address prevailing reliability design challenges, yet its multidisciplinary essence poses hurdles to swift progress. This review proposes future directions for AI-DfR’s development, spotlighting critical areas such as the quality and efficiency of finite element modeling, design and optimization of training models, selection of AI models, and maintenance and value enhancement strategies.

The ability to accurately predict the reliability and lifetime of electronics is of great importance to the industry. The failure of the solder joint is of particular interest for these predictions, because of their susceptibility to failure under thermo-mechanical stress. However, the experimental or even conventional simulation techniques employed to estimate the lifetime of a solder joint are often too expensive or time consuming to be of practical use. Therefore, this work introduces a physics-informed Long Short-Term Memory (LSTM) to predict the plastic strain in the critical area of the solder joint. The predicted values are in agreement with the values gained from finite elements, thereby demonstrating the advantage of applying the proposed methodology.