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Computational aspects of morphological instabilities in multi-layered systems

Graduate Researcher(s): 
Berkin Dortdivanlioglu (berkin@stanford.edu), Emma Lejeune (elejeune@stanford.edu)
Faculty Advisor/PI: 
Christian Linder
Collaborators: 
Ali Javili, Johannes Weickenmeier, Ellen Kuhl

When a thin stiff film adhered to a compliant substrate is subject to compressive stresses, the film will experience a geometric instability and buckle out of plane. For perfectly attached bi-layer systems with high film/substrate stiffness ratios, the primary mode of instability is sinusoidal wrinkling. In this research, wrinkling is studied from two different angles. First, we develop a computational framework to provide quantitative and accurate predictions of instability onset. The framework is initially developed for standard finite element analysis (FEA) and used to compare the eigenvalue analysis approach to the perturbation approach and study the performance of multiple element types. The framework is then extended from FEA to isogeometric analysis (IGA), and used to investigate period-doubling, a secondary instability. Second, we use our computational framework to investigate wrinkling in multi-layer systems. In contrast to bi-layer systems, multi-layer systems are not well understood. By developing and verify an analytical solution for predicting instability onset in tri-layer systems, and then extending it to general multi-layer systems, we are able to better understand the instability behavior of multi-layer structures ranging from the developing cerebellum, to poorly adhered thin films, to epidermal electronics, to fault-related folding. 

 

Upper left: summary of tri-layer models; Lower left: schematic illustration of multi-layer wrinkling; Upper right: agreement between the numerical and analytical solution for critical strain; Lower right: agreement between the numerical and analytical solution for critical wave number.

 

Left: comparing the performance of FEA and IGA via relative error in predicted critical growth; Right: instability mode phase transition diagram with respect to growth and film/substrate stiffness ratio.

 

 

Publications: 

Javili, A., Dortdivanlioglu, B., Kuhl, E., & Linder, C. (2015). Computational aspects of growth-induced instabilities through eigenvalue analysis. Computational Mechanics, 56(3), 405-420. doi: 10.1007/s00466-015-1178-6
 
Lejeune, E., Javili, A., & Linder, C. (2016). Understanding geometric instabilities in thin films via a multi-layer model. Soft matter, 12(3), 806-816. doi: 10.1039/C5SM02082D
 
Lejeune, E., Javili, A., & Linder, C. (2016). An algorithmic approach to multi-layer wrinkling. Extreme Mechanics Letters, 7, 10-17. doi: 10.1016/j.eml.2016.02.008
 
Lejeune, E., Javili, A., Weickenmeier, J., Kuhl, E., & Linder, C. (2016). Tri-layer wrinkling as a mechanism for anchoring center initiation in the developing cerebellum. Soft matter. doi: 10.1039/C6SM00526H
 
Dortdivanlioglu, B., Javili, A., & Linder, C. (2016). Computational aspects of morphological instabilities using isogeometric analysis. Computer Methods in Applied Mechanics and Engineering. doi: 10.1016/j.cma.2016.06.028