SUMMARYComputer simulations of atomic scale processes in solids are often associated with the issue of spurious reflection of elastic waves at the boundaries of a molecular dynamics domain. In this paper, we propose an approach to emulate non-reflecting boundary conditions in atomistic simulations of crystalline solids. Harmonic response of the outer, non-simulated, region is accurately represented by a memory function, related to the lattice dynamics Green's function. The outward wave flow is cancelled due to work done by the corresponding response forces. Performance of method, dependent on a series of method parameters, is illustrated on a benchmark problem.

Three different models with increased complexity to study the effects of hybridization on the tensile failure of hybrid composites are proposed. The first model is a model for dry bundles of fibres based on the statistics of fibre strength. The second is a model for composite materials based on the multiple fragmentation phenomenon. Lastly, a micromechanical numerical model is developed that considers a random distribution of fibres and takes into account the stochastic nature of fibre strength. This study aims to understand the controlling factors that lead to pseudo-ductility, as well as establish the sequence of failure mechanisms in hybrid composites under tensile loadings.

Reproducing Kernel Particle Methods (RKPM) with a built-in feature of multiresolution analysis are addressed. Some fundamental concepts such as reproducing conditions, and correction function are constructed to systematize the framework of RKPM. In particular, Fourier analysis, as a tool, is exploited to further elaborate RKPM in the frequency domain. Furthermore, we address error estimation and convergence properties. We present several applications which con®rm the widespread applicability of multiresolution RKPM.

An experimentally validated micro-scale analysis of the visco-thermo-mechanical behavior of polymer matrix composites under different loads is proposed. A new constitutive law for the matrix material is developed taking into account the pressure dependence of the material as well as strain-rate and temperature dependence. Capturing the matrix behavior under multi-axial stress states is concluded to be essential to accurately predict the composite material behavior, even when considering simple load cases such as transverse compression and/or shear. Without any calibration procedure at the composite level, good agreement with the experimental data is observed for different loading conditions, including strain-rate dependency. Using this validated micro-scale model, a three-dimensional simulation of the formation of a kink band under longitudinal compression of the composite is conducted. A new evidence at micro-scale is found supporting the hypothesis that shear stresses transferred between fibers and matrix are particularly important in the formation of the kink band.

Microforming using a small machine (or so-called desktop machine) is an alternative new approach to those using full-size heavy equipment for manufacturing microparts. Microparts are commonly defined as parts or structures with at least two dimensions in the submillimeter range, which are used extensively in electronics and micromechanical products. However, when scaling down a conventional forming process to microscale, the influence of the so-called size effect needs to be considered. The individual microstructure (size, shape, and orientation of grains) and the interfacial conditions show a significant effect on the process characteristics. In this paper, the process of extrusion is investigated to establish it as a viable process for microforming. A forming assembly is fabricated and used in conjunction with a loading substage to extrude micropins with a final diameter of 1 mm. The effect of grain size is investigated by using workpieces heat treated to produce grain sizes varying from 32 μm up to 211 μm. Two extrusion dies with different roughness are used to study the effect of surface finish. While experiments lead to interesting questions and new discoveries, theoretical or numerical solutions are necessary tools for process optimization. Here, knowing the limits of the current widely used numerical simulation tools [i.e., the Finite Element Method (FEM)], a new method, the Reproducing Kernel Element Method (RKEM), has recently been developed to address the limitations of the FEM (for example, remeshing issue), while maintaining FEM’s advantages, e.g., the polynomial reproducing property and function interpolation property. The new RKEM method is used to simulate the microextrusion problem. Its results are compared with that obtained from the FEM and the experiment result. Satisfactory results were obtained. Future directions on the experimental and simulation work are addressed.