arXiv subjects

K. Mikeš

Publications and source records attributed to K. Mikeš.

2 recordsLinked to original sources

arXiv2021

Comparative study of multiscale computational strategies for materials with discrete microstructures

The evolution of local defects such as dislocations and cracks often determines the performance of engineering materials. For a proper description and understanding of these phenomena, one needs to descend to a very small scale, at which the discreteness of the material emerges. Fully-resolved discrete numerical models often suffer from excessive computing expenses when used for application-scale considerations. More efficient multiscale simulation procedures are thus called for, capable of capturing the most significant microscopic phenomena while being computationally tractable. Two broad classes of methods are available in the literature. The first class considers the fully-resolved discrete system, which is subsequently reduced through suitable mathematical tools such as projection and reduced integration. The second class first homogenizes the discrete system into an equivalent continuum formulation, into which the main phenomena are added through specific enrichments. This paper provides a thorough comparison of the two different modeling philosophies in terms of their theory, accuracy, and performance. To this goal, two typical representatives are adopted: the Quasicontinuum method for the first class, and an effective continuum with an embedded cohesive zone model for the second class. Two examples are employed to demonstrate capabilities and limitations of both approaches: dislocation propagation and pile-up against a coherent phase boundary, and a three-point bending test of a concrete specimen with crack propagation. In both cases, the accuracy of the two methods is compared against the fully-resolved discrete reference model. It is shown that whereas continuum models with embedded cohesive zones offer good performance to accuracy ratios, they might fail to capture unexpected mechanical behavior. The Quasicontinuum method offers more flexibility at a higher computational cost.

cond-mat.soft↗

arXiv2020

The Peierls--Nabarro FE model in two-phase microstructures -- a comparison with atomistics

This paper evaluates qualitatively as well as quantitatively the accuracy of a recently proposed Peierls--Nabarro Finite Element (PN-FE) model for dislocations by a direct comparison with an equivalent molecular statics simulation. To this end, a two-dimensional microstructural specimen subjected to simple shear is considered, consisting of a central soft phase flanked by two hard-phase regions. A hexagonal atomic structure with equal lattice spacing is adopted, the interactions of which are described by the Lennard--Jones potential with phase specific depths of its energy well. During loading, edge dislocation dipoles centred in the soft phase are introduced, which progress towards the phase boundaries, where they pile up. Under a sufficiently high external shear load, the leading dislocation is eventually transmitted into the harder phase. The homogenized PN-FE model is calibrated to an atomistic model in terms of effective elasticity constants and glide plane properties as obtained from simple uniform deformations. To study the influence of different formulations of the glide plane potential, multiple approaches are employed, ranging from a simple sinusoidal function of the tangential disregistry to a complex model that couples the influence of the tangential and the normal disregistries. The obtained results show that, qualitatively, the dislocation structure, displacement, strain fields, and the dislocation evolution are captured adequately. The simplifications of the PN-FE model lead, however, to some discrepancies within the dislocation core. Such discrepancies play a dominant role in the dislocation transmission process, which thus cannot quantitatively be captured properly. Despite its simplicity, the PN-FE model proves to be an elegant tool for a qualitative study of edge dislocation behaviour in two-phase microstructures, although it may not be quantitatively predictive.

cond-mat.mtrl-sci↗