Nonlocal wrinkling instabilities in bilayered systems using peridynamics

Abstract

Wrinkling instabilities occur when a stiff thin film bonded to an elastic substrate undergoes compression. Regardless of the nature of compression, this phenomenon has been extensively studied through local models based on classical continuum mechanics. However, the experimental behavior is not yet fully understood and the influence of nonlocal effects remains largely unexplored. The objective of this paper is to fill this gap from a computational perspective by investigating nonlocal wrinkling instabilities in a bilayered system. Peridynamics (PD), a nonlocal continuum formulation, serves as a tool to model nonlocal material behavior. This manuscript presents a methodology to precisely predict the critical conditions by employing an eigenvalue analysis. Our results approach the local solution when the nonlocality parameter, the horizon size, approaches zero. An experimentally observed influence of the boundaries on the wave pattern is reproduced with PD simulations which suggests nonlocal material behavior as a physical origin. The results suggest that the level of nonlocality of a material model has quantitative influence on the main wrinkling characteristics, while most trends qualitatively coincide with predictions from the local analytical solution. However, a relation between the film thickness and the critical compression is revealed that is not existent in the local theory. Moreover, an approach to determine the peridynamic material parameters across a material interface is established by introducing an interface weighting factor. This paper, for the first time, shows that adding a nonlocal perspective to the analysis of bilayer wrinkling by using PD can significantly advance our understanding of the phenomenon.

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

“…If only one-neighbor interactions are present, different kinds of mixture rules can be implemented to determine the property of a bond across the interface. 29 For multi-neighbor interactions, however, the behavior is additionally characterized by the ratio of the material parameters. For instance, in two dimensions, Poisson-like effects are described by the ratio C 2 ∕C 1 .…”

“…Since peridynamic material parameters describe the properties of an interaction between points, rather than the properties of a point itself, interactions between points of different materials are not characterized explicitly. If only one‐neighbor interactions are present, different kinds of mixture rules can be implemented to determine the property of a bond across the interface 29 . For multi‐neighbor interactions, however, the behavior is additionally characterized by the ratio of the material parameters.…”

“…[18][19][20][21][22][23][24] In most real-world problems, materials are heterogeneous. Numerous fields of applications of PD are concerned with modeling heterogeneous media, such as micro-structured materials, 6,7 functionally graded materials, [25][26][27][28] or bilayers, 29 to name a few. This requires methodological approaches on how to treat material interfaces that are inherently nonlocal within a peridynamic model.…”

“…Meanwhile, a couple of contributions introduced more freely selectable weighting factors. 29,39,40 Recently, Ahmadi et al 41 determined the parameters by considering both the distance to the interface and the number of neighboring points of dissimilar material. Behera et al 37 employed a Heaviside function to assign the parameters.…”

“…Cheng et al 26 used the proportion of the material coefficients to identify a weighting factor. Meanwhile, a couple of contributions introduced more freely selectable weighting factors 29,39,40 . Recently, Ahmadi et al 41 determined the parameters by considering both the distance to the interface and the number of neighboring points of dissimilar material.…”