Morphological instabilities and surface wrinkling of soft materials such as gels and biological tissues are of growing interest to a number of academic disciplines including soft lithography, metrology, flexible electronics, and biomedical engineering. In this paper, we review some of the recent progresses in experimental and theoretical investigations of instabilities that lead to the emergence and evolution of surface wrinkling, folding and creasing under various geometrical constraints (e.g., thin films, sheets, fibers, particles, tubes, cavities, vesicles and capsules) and loading stimuli (e.g., mechanical forces, growth, atrophy, swelling, shrinkage, van der Waals interactions). Some representative theoretical and numerical approaches aimed at modelling the onset of instabilities as well as the postbuckling evolution involving multiple bifurcations and symmetry-breakings are discussed along with the main characteristics and some possible applications of this rich phenomenon.

The three-dimensional patterns of surface wrinkling on a core-shell soft sphere are investigated through buckling and postbuckling analyses under differential tissue growth or shrinkage. With increasing deformation, the sphere first exhibits a buckyball-like wrinkling pattern and then undergoes a wrinkle-to-fold transition into labyrinth folded patterns, in agreement with experimental observations. This transition involves dynamic movement, rotation, and coalescence of polygons formed during the initial buckling.

Determining the macroscopic mechanical properties of composites with complex microstructures is a key issue in many of their applications. In this Letter, a machine learning-based approach is proposed to predict the effective elastic properties of composites with arbitrary shapes and distributions of inclusions. Using several data sets generated from the finite element method, a convolutional neural network method is developed to predict the effective Young's modulus and Poisson's ratio of composites directly from a window of their microstructural image. Through numerical experiments, we demonstrate that the trained network can efficiently provide an accurate mapping between the effective mechanical property and the microstructures of composites with complex structures. This study paves a way for characterizing heterogeneous materials in big data-driven material design.

Solitary, persistent wave packets called solitons hold potential to transfer information and energy across a wide range of spatial and temporal scales in physical, chemical, and biological systems. Mechanical solitons characteristically emerge either as a single wave packet or uncorrelated propagating topological entities through space and/or time, but these are notoriously difficult to control. Here, we report a theoretical framework for programming static periodic topological solitons into a metamaterial, and demonstrate its implementation in real metamaterials computationally and experimentally. The solitons are excited by deformation localizations under quasi-static compression, and arise from buckling-induced kink-antikink bands that provide domain separation barriers. The soliton number and wavelength demonstrate a previously unreported size-dependence, due to intrinsic length scales. We identify that these unanticipated solitons stem from displacive phase transitions with periodic topological excitations captured by the well-known $${\varphi }^{4}$$φ 4 theory. Results reveal pathways for robust regularizations of stochastic responses of metamaterials.