Hierarchical folding of elastic membranes under biaxial compressive stress.
نویسندگان
چکیده
Mechanical instabilities that cause periodic wrinkling during compression of layered materials find applications in stretchable electronics and microfabrication, but can also limit an application's performance owing to delamination or cracking under loading and surface inhomogeneities during swelling. In particular, because of curvature localization, finite deformations can cause wrinkles to evolve into folds. The wrinkle-to-fold transition has been documented in several systems, mostly under uniaxial stress. However, the nucleation, the spatial structure and the dynamics of the invasion of folds in two-dimensional stress configurations remain elusive. Here, using a two-layer polymeric system under biaxial compressive stress, we show that a repetitive wrinkle-to-fold transition generates a hierarchical network of folds during reorganization of the stress field. The folds delineate individual domains, and each domain subdivides into smaller ones over multiple generations. By modifying the boundary conditions and geometry, we demonstrate control over the final network morphology. The ideas introduced here should find application in the many situations where stress impacts two-dimensional pattern formation.
منابع مشابه
Finite Difference Method for Biaxial and Uniaxial Buckling of Rectangular Silver Nanoplates Resting on Elastic Foundations in Thermal Environments Based on Surface Stress and Nonlocal Elasticity Theories
In this article, surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (FDM). The uniform temperature change is utilized to study thermal effect. The surface energy effects are taken into account using the Gurtin-Murdoch’s theory. Using the principle of virtual work, the...
متن کاملAcoustic phonon propagation in ultra-thin Si membranes under biaxial stress field
We report on stress induced changes in the dispersion relations of acoustic phonons propagating in 27 nm thick single crystalline Si membranes. The static tensile stress (up to 0.3GPa) acting on the Si membranes was achieved using an additional strain compensating silicon nitride frame. Dispersion relations of thermally activated hypersonic phonons were measured by means of Brillouin light scat...
متن کاملFinite Plate with Circular and Square Hole under Partial Loading
In this paper a general analytical solution is obtained to find stress distribution in a finite elastic plate with a circular or square hole subjected to arbitrary biaxial partial loading using modified boundary condition by assuming plane stress conditions. The method employed is based on solution of circular hole in finite rectangular plate. This plate is mapped to circular ones and the parti...
متن کاملSmall Scale Effect on the Vibration of Orthotropic Plates Embedded in an Elastic Medium and Under Biaxial In-plane Pre-load Via Nonlocal Elasticity Theory
In this study, the free vibration behavior of orthotropic rectangular graphene sheet embedded in an elastic medium under biaxial pre-load is studied. Using the nonlocal elasticity theory, the governing equation is derived for single-layered graphene sheets (SLGS). Differential quadrature method (DQM) has been used to solve the governing equations for various boundary conditions. To verify the a...
متن کاملBiaxial Buckling Analysis of Symmetric Functionally Graded Metal Cored Plates Resting on Elastic Foundation under Various Edge Conditions Using Galerkin Method
In this paper, buckling behavior of symmetric functionally graded plates resting on elastic foundation is investigated and their critical buckling load in different conditions is calculated and compared. Plate governing equations are derived using the principle of minimum potential energy. Afterwards, displacement field is solved using Galerkin method and the proposed process is examined throug...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Nature materials
دوره 10 12 شماره
صفحات -
تاریخ انتشار 2011