The densification process during pressure sintering has been analyzed using finite element analysis. This analysis uses an iterative solution algorithm. With this the densification process in complex geometries with complex boundary conditions can be analyzed and this technique is particularly suited for tackling material nonlinearity. Evolution of dense structures with gradual closure of pores is described for two typical geometries.

Based on the physical interpretation of the linear equation of state (EOS) of dense solids under shock loading, which relates particle and shock speeds asU_s=C_b+gU_p, the EOS for porous solids has been developed and is expressed asU_s*=ΨC_b*+g*U_p whereC_b* andg* are effective bulk sound speed and effective inverse ultimate volume strain respectively. Ψ is a pore collapse function introduced specially to differentiate loading and unloading behaviour.C_b* andg* are derived theoretically whereas Ψ is established empirically as Ψ=f(U_p,C_b). This EOS does not call for any experimentally established material constant to describe the effect of porosity. Also its ability to describe the unloading behaviour distinguishes it from the presently available equations of state.

An equation for contact area between powder particles in a powder compact, in terms of the porosity, has been derived using a geometry representing spherical voids of different sizes distributed in a material matrix. This equation is verified using experimental data as well as results obtained from computer simulation of powder compaction using a finite element method.

A set of analytical expressions which can be used for estimating the effective speed of sound in porous materials is presented along with a brief description of the micromechanical origins of the analytical equations. These equations are validated and the accuracies are compared using published experimental data corresponding to four different ceramic materials.

The paper presents a ballistic performance index for metallic armour materials in terms of the commonly determined mechanical properties such as strength and modulus. The index is derived using an energy-balance approach, where the kinetic energy of the projectile is assumed to be absorbed by the elastic and the plastic deformation involved in the penetration process as well as the kinetic energy imparted to the target material during deformation. The derivation assumes two distinct stages to exist during the penetration of the projectile. At the striking face of the armour, the material is assumed to flow radially in a constrained deformation region but longitudinally at the rear surface leading to typically observed bulging of the armour without constraint. The index is validated using the available experimental and empirical data obtained in the case of small arm projectiles for an impact velocity of about 800 m/sec. This index is expected to facilitate the development of metallic armour, since the number of the ballistic experiments can be reduced significantly and only the promising materials need to be considered.

The paper presents an overview of the analytical methods as well as finite element method employed by the author in a few earlier investigations pertaining to modelling and simulation of deformation at microscopic scale. The following case-studies are considered for illustrations: deformation of a set of powder particles during hot isostatic pressing; effective properties of a typical particulate metal matrix composite and porous material; constitutive behaviour of a material exhibiting transformation-induced plasticity; shear band formation in polycrystalline material.

The paper describes certain generalized techniques for constructing the microstructural geometries, assigning material properties and imposing boundary conditions. The concept of generating two-phase geometries using a master mesh and the generalized plane strain approach to handle two-dimensional approximations used in the above studies are also reviewed. In contrast to the commonly employed unit cell models based on certain regular geometries, the present method uses the actually observed microstructural geometries. This method accommodates more realistic and complex conditions compared to those supported by the well-explored analytical methods. Although, only homogeneous and isotropic systems have been discussed in this paper, this method can be easily extended to inhomogeneous and anisotropic cases as well. In general, the technique is emerging as a suitable numerical tool for designing materials for specific applications.

The paper presents a brief overview of different types of modelling and simulation along with the distinguishing features between the two. Spatial as well as temporal size scales with a special reference to multiscale modelling are explained with illustrations. The paper includes a discussion on numerical experiments and their validation based on the authors’ work on FEM simulation of crack-tip blunting during ductile fracture. Attention is drawn to the use of a 3P technique involving integrated simulation of deformation (property) at microstructural level, the process at macroscopic level and the performance at the product level.