Analysing composite materials through efficient higher-order homogenization techniques requires accurate simulations of highly heterogeneous domains. However the validity of the homogenization response in regions with highly localized variations is still questionable. A scale adaptation strategy is developed for a more accurate analysis of generally inelastic macrostructures, where a transition from a homogenized description to an explicit micro-structural resolution is pursued. The designated zones of interest are indicated through two different methods of error estimation. First for mesh refinement approaches, the discretization error is estimated using an indicator developed by Zienkiewicz-Zhu and studying L2 norm. Furthermore a second adaptation zone is identified based on a post-processing step on the homogenized solution and corresponds to regions with high strain-gradients, the gradient of the deformation gradient. In the designated sub-domains a micro-structure representation will replace the homogenized area. The introduced scale-adaptivity method returns an inexpensive and more accurate analysis of composite materials.
To guarantee excellent work piece quality for the machining of compound materials characteristic interactions between the components have to be considered in the process design. Especially by parallel compounds, where the different components are processed in an alternating manner, the machinability of the compound differs considerably from the machinability of each homogeneous component. Depending on the compound partner the surface topography of a component can vary considerably. Rotationally symmetric compound work pieces primary hold radius and transition deviations. In addition to unequal tool and workpiece deflection the radius deviations results from the different topographies in each component. The surface topography and its measurement methods as well as the process parameters and their influence on the process forces have to be considered for a proper process design.
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