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Abstract
In this paper, a multiscale approach to capture the behavior of material layers that possess a micromorphic mesostructure is presented. To this end, we seek to obtain a macroscopic traction-separation law based on the underlying meso and microstructure. At the macro level, a cohesive interface description is used, whereas the underlying mesostructure is resolved as a micromorphic representative volume element. The micromorphic continuum theory is particularly well-suited to account for higher-order and size-dependent effects in the material layer. On considering the height of the material layer, quantities at different scales are related through averaging theorems and the Hill condition. An admissible scale-transition is guaranteed via the adoption of customized boundary conditions, which account for the deformation modes in the interface. On the basis of this theoretical framework, computational homogenization is embedded within a finite-element approach, and the capabilities of the model are demonstrated through numerical examples.
Acknowledgements
The authors gratefully acknowledge financial support from the German Science Foundation (DFG) within the International Research Training Group 1131 ‘Visualization of large and unstructured data sets. Applications in geospatial planning, modeling, and engineering’.
Notes
Note
1. The following auxiliary relations are commonly utilized to convert the averaging theorems from volume to surface integrals (e.g. Citation35,Citation36)
