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This paper focuses on studying different numerical models to simulate a solid-state sintering process with grain boundary diffusion for the components made of pure aluminium powders. A continuum model based on the linear viscous law is introduced to describe the mechanical behavior during sintering. To identify the parameters in the constitutive law (shear and bulk viscosity moduli in addition to sintering stress), various macroscopic models were utilized. Beside the mass conservation equation which regulates the densification process, Kang's model based on Herring's scale law, which takes into account the role of grain boundaries and diffusion area in densification, is also used to describe the densification process. These numerical models have been implemented in FORTRAN subroutine UMAT and solved using the FE-software ABAQUS/Standard. Finally, the densification behavior of each model is compared to each other.

In injection and compression molding simulation, orientation tensors provide an efficient way with less computational effort to calculate flow-induced fiber orientations. In these flow calculations, the solution of any even-ordered orientation tensor needs the following even higher-ordered orientation tensor. Therefore, a closure is used in order to approximate the higher-ordered orientation tensor as a function of the components of the lower-ordered orientation tensors. There exist many closures of the fourth-order orientation tensor in terms of the second-order orientation. This paper gives a review with mathematical details for different closure approximations including simple closures, composite closures, eigenvalue-based orthotropic closures, invariant-based closures, and neural-network-based closures. Moreover, a new closure approximation that assumes an orthotropic stiffness tensor was suggested in this work. The results of the closure approximations were validated through the comparison of Young moduli between the closure approximations and the experimental results for both short-and long-fiber-reinforced composites.

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Contact mechanics models based on linearity assumptions, often using the viscoelastic half space theory and numerically implemented with the boundary element method, are known to provide accurate results for small mean square slope of the surface roughness. For large mean square slope, models accounting for finite deformations, often implemented with the non-linear finite element method, are more accurate but lead to a prohibitive computational cost. We propose a new hybrid multiscale approach able to account for the finite deformations arising due to large mean square slope, while keeping a computational cost similar to that associated to linear approaches. The basic strategy is a decomposition of the surface roughness power spectrum into a discrete number of waves, whose spectral range is partitioned into a high mean square slope range and a low mean square slope range. The contact mechanics in the former is accurately solved with the kinematically non-linear model and the results averaged out at the larger wavelength scale in terms of an effective interface interaction law. This law is then applied in the linear simulation involving the scales within the low mean square slope range. The proposed approach is a more accurate alternative to fully linear and a computationally faster alternative to fully non-linear contact mechanics approaches.