Date of download: 5/31/2016 Copyright © ASME. All rights reserved. From: Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface J. Appl. Mech. 2015;82(5): doi: / (a) Film–substrate system with periodic interfacial microstructures and (b) a finite element method (FEM) model. The insets in (b) show the amplified mesh in the finite element simulations. (c) The system has stress concentration near the interfacial corners, where the elastic moduli μf=80μs=80 MPa, the film lengths L¯1=L¯2/8=0.7, and the compressive strain is 15%. The legend indicates the maximal principal stress Smax. Figure Legend:

Date of download: 5/31/2016 Copyright © ASME. All rights reserved. From: Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface J. Appl. Mech. 2015;82(5): doi: / Six wrinkling patterns observed in FEM simulations: (a) sinusoidal wrinkles, (b) periodic tilted sawteeth, (c) slope–sine pattern consisting of rotated thick films and wrinkled thin films, (d) alternating upward–downward arcs, (e) sinusoidal wrinkles separated by shallow arcs, and (f) folded thin films separated by unbuckled thick films. The legend denotes the Lagrange strain in the x-direction. Figure Legend:

Date of download: 5/31/2016 Copyright © ASME. All rights reserved. From: Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface J. Appl. Mech. 2015;82(5): doi: / Phase diagram of six wrinkling patterns with respect to the film lengths, where the modulus ratio is in the range of 70 < μf/μs < 1000 Figure Legend:

Date of download: 5/31/2016 Copyright © ASME. All rights reserved. From: Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface J. Appl. Mech. 2015;82(5): doi: / Phase diagram of the buckling modes in the thick film regions. The diamonds, triangles, and circles represent the results of finite element simulations for the sinusoidal wrinkling, Euler buckling, and rigid rotation modes, respectively. Figure Legend:

Date of download: 5/31/2016 Copyright © ASME. All rights reserved. From: Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface J. Appl. Mech. 2015;82(5): doi: / (a) Theoretical model of a film–substrate system with a finite-length L1, (b) FEM model with L1 = 40 μm, (c) equivalent stiffnesses Kw, Kr, and Ke as functions of Es* when L1 = 20 μm, and (d) equivalent stiffnesses Kw, Kr, and Ke as functions of L1 when Es* = 1.3 MPa Figure Legend:

Date of download: 5/31/2016 Copyright © ASME. All rights reserved. From: Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface J. Appl. Mech. 2015;82(5): doi: / (a) Schematic of the sinusoidal wrinkling morphology of the film in a thick region and (b) the finite element simulation result for the surface morphology of pattern VI. The legend denotes the Lagrange strain in the x-direction. Figure Legend:

Date of download: 5/31/2016 Copyright © ASME. All rights reserved. From: Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface J. Appl. Mech. 2015;82(5): doi: / The critical strains ɛ c for the occurrence of the sinusoidal wrinkling, Euler buckling, and rigid rotation modes, where Ef*/Es* is taken as 100. The magnitude of Ef*/Es* does not affect the critical lengths L¯1crot and L¯1csin. Figure Legend:

Date of download: 5/31/2016 Copyright © ASME. All rights reserved. From: Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface J. Appl. Mech. 2015;82(5): doi: / (a) Schematic of the Euler buckling mode of a film, and the finite element simulation results for the surface morphologies of: (b) pattern V and (c) pattern IV. The legend denotes the Lagrange strain in the x-direction. Figure Legend:

Date of download: 5/31/2016 Copyright © ASME. All rights reserved. From: Surface Wrinkling Patterns of Film–Substrate Systems With a Structured Interface J. Appl. Mech. 2015;82(5): doi: / (a) Schematic of the pure rotation mode of a film, and the finite element simulation results for the surface morphologies of: (b) pattern I, (c) pattern III, and (d) pattern II. The legend denotes the Lagrange strain in the x-direction. Figure Legend: