Micromechanics

About: Micromechanics is a research topic. Over the lifetime, 6000 publications have been published within this topic receiving 162635 citations.

Homogenization Techniques and Micromechanics. A Survey and Perspectives

Abstract: In this paper, we present a critical survey on homogenization theory and related techniques applied to micromechanics. The validation of homogenization results, the characterization of composite materials and the optimal design of complex structures are issues of great technological importance and are viewed here as a combination of mathematical and mechanical homogenization. The mathematical tools for modeling sequentially layered composites are explained. The influence of initial and boundary conditions on the effective properties in nonlinear problems is clarified and the notion of stability by homogenization is analyzed. Multiscale micromechanics methods are outlined and the classical as well as the emerging analytical and computational techniques are presented. Computation of effective static and dynamical properties of materials with linear or nonlinear constitutive equations is closely related to the development of generalized theories such as the strain-gradient mechanics. Selected applications of these techniques are outlined. Moreover, the extension of kinetic techniques in homogenization and the related inverse imaging problem are presented.

A comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites

Abstract: This paper describes an approximate, yet comprehensive, closed form micromechanics model for estimating the effective elastic modulus of carbon nanotube-reinforced composites. The model incorporates the typically observed nanotube curvature, the nanotube length, and both 1D and 3D random arrangement of the nanotubes. The analytical results obtained from the closed form micromechanics model for nanoscale representative volume elements and results from an equivalent finite element model for effective reinforcing modulus of the nanotube reveal that the reinforcing modulus is strongly dependent on the waviness, wherein, even a slight change in the nanotube curvature can induce a prominent change in the effective reinforcement provided. The micromechanics model is also seen to produce reasonable agreement with experimental data for the effective tensile modulus of composites reinforced with multi-walled nanotubes (MWNTs) and having different MWNT volume fractions.

Micromechanics of crack nucleation during indentations

Abstract: An analysis for the nucleation of microcracks from the inhomogeneous flow lines in soda-lime glass under Vickers indentations is considered. The minimum loads for crack nucleation are shown to depend on the hardness,H, and the critical stress intensity factor,K IC. Unlike the Lawn and Evans analysis, the present model does not require the presence of any fortuitous flaws of critical dimensions in the material, since the flaws are nucleated by the deformation in the deformed zone.

Micromechanical models to guide the development of synthetic ‘brick and mortar’ composites

Abstract: This paper describes a micromechanical analysis of the uniaxial response of composites comprising elastic platelets (bricks) bonded together with thin elastic perfectly plastic layers (mortar). The model yields closed-form results for the spatial variation of displacements in the bricks as a function of constituent properties, which can be used to calculate the effective properties of the composite, including elastic modulus, strength and work-to-failure. Regime maps are presented which indicate critical stresses for failure of the bricks and mortar as a function of constituent properties and brick architecture. The solution illustrates trade-offs between elastic modulus, strength and dissipated work that are a result of transitions between various failure mechanisms associated with brick rupture and rupture of the interfaces. Detailed scaling relationships are presented with the goal of providing material developers with a straightforward means to identify synthesis targets that balance competing mechanical behaviors and optimize material response. Ashby maps are presented to compare potential brick and mortar composites with existing materials, and identify future directions for material development.