Structural and Multidisciplinary Optimization

, Volume 58, Issue 3, pp 1067–1080 | Cite as

Optimizing microstructure for toughness: the model problem of peeling

  • Chun-Jen Hsueh
  • Kaushik Bhattacharya


We consider the problem of peeling an adhesive thin film from a substrate that has a non-uniform distribution of adhesive. When the length scale of the non-uniformity is small compared to the overall dimensions of the film being peeled, it is possible to describe the overall peeling behavior with an effective adhesive strength. In this paper, we seek to find the distributions of adhesive strength at the microscale that optimize various aspects of the effective adhesive strength at the macroscale. We do so using both analytic bounds and topology optimization. We formulate the problem of peeling as a free boundary problem, and the effective strength as a maximum principle over the trajectory. For topology optimization, we replace the maximum with an integral norm, and use an adjoint method for the sensitivity. The problem of peeling may be viewed as a model problem in fracture mechanics where the crack (peel) front is confined to a plane, and thus our analysis as a first step toward studying the more general problem of optimizing microstructure for toughness.


Fracture Toughness Adhesion 



This work draws from the thesis of Chun-Jen Hsueh at the California Institute of Technology. We gratefully acknowledge discussions with Ole Sigmund and Blaise Bourdin, and the financial support of the the US Air Force Office of Scientific Research through the MURI grant “Managing the Mosaic of Microstructure” (FA9550-12-1-0458) as well as the U.S. National Science Foundation through Award No. DMS-1535083 under the Designing Materials to Revolutionize and Engineer our Future (DMREF) Program.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Division of Engineering and Applied SciencesCalifornia Institute of TechnologyPasadenaUSA

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