Fracture mechanics parameters of many adhesive joints are obtained by the finite element method. When the adhesive can be regarded as an elastic body, the energy release rate is usually used as a fracture mechanics parameter. However, it is necessary to consider the non-linearity of the stress-strain curve of the adhesive layer for recent highly toughened adhesives. The J-integral is used as the fracture mechanics parameter for adhesive joints joined by such adhesives. In this review, after explaining the outline of the J-integral, the analysis method of the J-integral by the finite element method was explained by giving a concrete example.

In this article we discuss about molecular simulation methods to analyze the interface phenomena such as adhesion. First we discuss about the origin of complexity of the surface modeling. Then we show the all-atom molecular dynamics simulation with parameter fitting methods and simulation tools. The molecualar dynamics simulation including chemical reaction is now growing area and it is important for analyzing adhesion. Coarsegrained molecular simulations are then shown to analyze polymer based system. At last we show the mesoscale treatment in micron scale to analyze the realistic surface with roughness, heat transfer and phase transition.

In recent years, the importance of numerical analysis of adhesively bonded parts is increasing with increasing demand for adhesive joints. Cohesive zone model（ CZM） is one of the promising methods to evaluate the crack propagation and strength prediction of the adhesive joints. Using the cohesive element in the finite element method（ FEM）, the fracture process of the adhesive layer can be numerically analyzed. However, a clear understanding of CZM parameters and the input of the appropriate values are essential to creating correct numerical models. In this paper, a traction-separation law was explained based on its physical mechanism. Then, the meaning of the CZM parameters and determination processes of them were explained. Additionally, recent researches of adhesively bonded joints using CZM analysis were reviewed.

General introduction to molecular orbital（ MO） method is afforded with emphasis of the actual utilizations. In this respect, the density functional theory（ DFT） method is mainly employed here in particular among other MO calculation methods such as Hartree-Fock（ HF） and the post HF ones. The way of preparation of the environment for the MO calculation, actually available softwares, and the way of inputs are to be first explained. Several examples revealing the utility of MO calculations are also mentioned: these include achievement of the energetically optimized molecular structure, its geometrical parameters, vibration analyses including the IR and the Raman scattering absorption intensities, thermochemical analyses including the temperature corrections, analyses of the MO patterns, the total electron density, atomic net charge, bond order, and spin densities. Furthermore, estimation of the NMR chemical shift and description of the singlet excitation spectrum are also afforded. Especially in the last part of the article, the theme concerning the adhesion is mentioned and importance of the long-range interaction between molecules as well as the calculation method for which is also to be described.

We introduced the Self-Organizing Map（ SOM） as a visualization tool utilized for a multi-objective material optimization. The SOM, one of un-supervised machine learning techniques, enables to locate and cluster materials on a low-dimensional space according to similarity of multi-objective functions. In this paper, we showed the effectiveness of the SOM through applications to structural materials such as composite and thermosetting resins.