Size effects in nonlinear periodic materials exhibiting reversible pattern transformations

• Published in: Mechanics of materials Vol. 124; pp. 55 - 70
• Main Authors: Ameen, M.M., Rokoš, O., Peerlings, R.H.J., Geers, M.G.D.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2018
• Subjects: Auxetic materials; Elastic instability; Low scale separation; Mechanical metamaterials; Microfluctuations; Size effects; Low scale separation; Size effects; Microfluctuations; Elastic instability; Auxetic materials; Mechanical metamaterials
• ISSN: 0167-6636; 1872-7743
• DOI: 10.1016/j.mechmat.2018.05.011

highlights•Size effects in elastic periodic metamaterials significantly influence overall behaviour.•Induced size effects cannot be captured by conventional homogenization schemes.•Deviations of overall solutions from homogenized limits exceed 40% at small scale ratios.•Relative magnitudes of fluctuations in nominal quantities induced by spatial positioning of a microstructure reach 50%. This paper focuses on size effects in periodic mechanical metamaterials driven by reversible pattern transformations due to local elastic buckling instabilities in their microstructure. Two distinct loading cases are studied: compression and bending, in which the material exhibits pattern transformation in the whole structure or only partially. The ratio between the height of the specimen and the size of a unit cell is defined as the scale ratio. A family of shifted microstructures, corresponding to all possible arrangements of the microstructure relative to the external boundary, is considered in order to determine the ensemble averaged solution computed for each scale ratio. In the compression case, the top and the bottom edges of the specimens are fully constrained, which introduces boundary layers with restricted pattern transformation. In the bending case, the top and bottom edges are free boundaries resulting in compliant boundary layers, whereas additional size effects emerge from imposed strain gradient. For comparison, the classical homogenization solution is computed and shown to match well with the ensemble averaged numerical solution only for very large scale ratios. For smaller scale ratios, where a size effect dominates, the classical homogenization no longer applies.