Unlike classical methods, the present approach applies to any loading case and an arbitrary number of layers with arbitrary stiffness tetrads, and can be considered as the explicit analytical solution of the multi-layer homogenization in linear elasticity.
A layer-wise homogenization method is proposed to solve the one-way coupled heat conduction equation with variable coefficients.
But since current experimental investigations of the wave behavior in undamaged CFRP structures reveal an effect called "quasi-continuous mode conversion", which can not be reproduced with this layer-wise homogenization procedure, an improved material model for the finite element analysis of the Lamb wave propagation is presented in this work.
Starting from the observation that a continuous grid preserves the periodicity of the internal masonry layer, rigid-plastic homogenization is applied directly on a multi-layer heterogeneous representative element of volume (REV) constituted by bricks, finite thickness mortar joints and external FRP grids.
The tomography results indicate that the pores nucleate near the interface between the Ni Cr core and β-NiAl(Cr) reaction layer that develops upon homogenization.
The artificial microstructures are, a priori, generated in a periodic manner and, therefore, possible boundary layer effects during computational homogenization are minimized.
Finally, a level set method is applied to evolve the shape and topology of the microstructure for each layer, with the numerical homogenization method to evaluate the effective properties of the microstructures.
After an initial centrifugation at 5000× g for 15 min, most of the supernatant was removed and the yellow-brown portion (approximately the upper one-third) of the pellet was suspended in homogenization buffer, layered over 2.7 ml of 1.2 M sucrose and spin for 30 min at 100,000× g in a swinging bucket rotor (SW50.1).
The homogenization of material parameters layer by layer is a mostly sufficient method for the simulation of Lamb wave propagation in carbon fiber reinforced plastics.
Following Wood and Johnson (1978) two broad soil-forming processes can be recognised – horizonation, represented here by the deposition of a layer of volcanic ash, and homogenization, pedoturbation or soil mixing produced by subsequent burial of the tephra layer.
The topology optimization involves two scales: firstly, macrostructural design using SIMP to generate an overall multilayered layout with free material distribution involving intermediate densities; and secondly, microstructural design to produce periodic cellular composite for each layer, by integrating the numerical homogenization into a level set approach.
