Two-dimensional Equivalent Model Research Articles

High temperature viscoplastic deformation behavior of sintered nanocopper paste used in power electronics packaging: Insights from constitutive and multi-scale modelling

As a promising technology for high-power and high-temperature power electronics packaging, nanocopper (nanoCu) paste sintering has recently received increasing attention as a die-attachment. The high-temperature deformation of sintered nanoCu paste and its underlying mechanisms challenge the reliability of high-power electronics packaging. In this study, the tensile deformation behaviors of sintered nanoCu paste were firstly characterized by high-temperature tensile tests performed at various temperatures and strain rates ranging from 180 °C to 360 °C, 1 × 10−4 s−1 to 1 × 10−3 s−1 respectively. It was found that the elastic modulus and tensile strength decreased at the higher tensile temperature while the ductility increased accordingly. The highest elastic modulus and tensile strength results were 12.15 GPa and 46.97 MPa, respectively. Second, failure analysis was conducted based on the fracture surface after tensile testing. Recrystallization was revealed as the main factor for ductility improvement. Subsequently, an Anand model was fitted by stress-strain curves to describe the tensile constitutive behavior of the sintered nanoCu paste. Multi-scale modelling techniques also investigated the impact of tensile temperature and strain rate on the tensile response. Molecular dynamics simulation was implemented using a hemispherical Cu nanoparticle model to reveal the properties from an atomistic perspective. In addition, a two-dimensional equivalent model was further established by using a stochastically distributed void morphology. The multi-scale modelling techniques successfully describe the evolution of tensile response to the different tensile temperatures and strain rates. Besides, the equivalent model with random void morphology was demonstrated as the finite element simulation results were highly consistent with the high-temperature tensile experiments.

Free vibration behavior of Ti-6Al-4V sandwich beams with corrugated channel cores: Experiments and simulations

Free vibration of ultralight all-metallic (Ti-6Al-4V alloy) sandwich beams with corrugated channel cores was investigated by experiments and finite element (FE) simulations. The natural frequencies and mode shapes were measured and compared with simulations from both three-dimensional model (3D model) and two-dimensional equivalent model (2D model). Predictions of the 2D model agreed well with results obtained from the 3D model and experiments. It was found that for sandwich beams, the topological change from corrugated core to corrugated channel core eliminates the anisotropy of the structural stiffness and suppresses the local modes of vibration. The effect of geometrical parameters on the first natural frequency was also explored. In addition, preliminary assessment of the influence induced by varying the core topology was carried out. The first natural frequency of sandwich beams with corrugated channel cores having an inclination angle θ > 45° is higher than those of sandwich beams constructed with competing core topologies, including tetrahedral, Kagome and pyramidal trusses and hexagonal honeycombs.

Homogenization of a Sandwich Structure and Validity of the Corresponding Two-dimensional Equivalent Model

The aim of this paper is to present a method allowing us to obtain the three-dimensional (3D) modeling of sandwich structures by a two-dimensional (2D) equivalent plate-type model. This modeling is carried out by using the homogenization method of periodic media based on the technique of asymptotic expansions. We propose a new method of identifying the 2D equivalent model parameters that are required by most well-known softwares. The validity of the 2D models obtained is studied by comparing the 3D and 2D calculation results through the definition of two error indicators in terms of displacement and stress.

Yang-Mills theory as a deformation of topological field theory, dimensional reduction, and quark confinement

We propose a reformulation of Yang-Mills theory as a perturbative deformation of a novel topological (quantum) field theory. We prove that this reformulation of four-dimensional QCD leads to quark confinement in the sense of an area law of the Wilson loop. First, Yang-Mills theory with a non-Abelian gauge group G is reformulated as a deformation of a novel topological field theory. Next, a special class of topological field theories is defined by both Becchi-Rouet-Stora-Tyupin (BRST) and anti-BRST exact actions corresponding to the maximal Abelian gauge leaving the maximal torus group Hof G invariant. Then we find topological field theory $(D>2)$ has a hidden supersymmetry for a choice of maximal Abelian gauge. As a result, the D-dimensional topological field theory is equivalent to the $(D\ensuremath{-}2)$-dimensional coset $G/H$ nonlinear sigma model in the sense of the Parisi-Sourlas dimensional reduction. After maximal Abelian gauge fixing, the topological property of the magnetic monopole and antimonopole of four-dimensional Yang-Mills theory is translated into that of an instanton and anti-instanton in a two-dimensional equivalent model. It is shown that the linear static potential in four dimensions follows from the instanton--anti-instanton gas in the equivalent two-dimensional nonlinear sigma model obtained from the four-dimensional topological field theory by dimensional reduction, while the remaining Coulomb potential comes from the perturbative part in four-dimensional Yang-Mills theory. The dimensional reduction opens a path for applying various exact methods developed in two-dimensional quantum field theory to study the nonperturbative problem in low-energy physics of four-dimensional quantum field theories.