Transition of surface-interface creasing in bilayer hydrogels

Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution

We review our recent contributions to anisotropic soft matter models for liquid crystal interfaces, drops and membranes, emphasizing validations with experimental and biological data, and with related theory and simulation literature. The presentation aims to illustrate and characterize the rich output and future opportunities of using a methodology based on the liquid crystal-membrane shape equation applied to static and dynamic pattern formation phenomena. The geometry of static and kinetic shapes is usually described with dimensional curvatures that co-mingle shape and curvedness. In this review, we systematically show how the application of a novel decoupled shape-curvedness framework to practical and ubiquitous soft matter phenomena, such as the shape of drops and tactoids and bending of evolving membranes, leads to deeper quantitative insights than when using traditional dimensional mean and Gaussian curvatures. The review focuses only on (1) statics of wrinkling and shape selection in liquid crystal interfaces and membranes; (2) kinetics and dissipative dynamics of shape evolution in membranes; and (3) computational methods for shape selection and shape evolution; due to various limitations other important topics are excluded. Finally, the outlook follows a similar structure. The main results include: (1) single and multiple wavelength corrugations in liquid crystal interfaces appear naturally in the presence of surface splay and bend orientation distortions with scaling laws governed by ratios of anchoring-to-isotropic tension energy; adding membrane elasticity to liquid crystal anchoring generates multiple scales wrinkling as in tulips; drops of liquid crystals encapsulates in membranes can adopt, according to the ratios of anchoring/tension/bending, families of shapes as multilobal, tactoidal, and serrated as observed in biological cells. (2) Mapping the liquid crystal director to a membrane unit normal. The dissipative shape evolution model with irreversible thermodynamics for flows dominated by bending rates, yields new insights. The model explains the kinetic stability of cylinders, while spheres and saddles are attractors. The model also adds to the evolving understanding of outer hair cells in the inner ear. (3) Computational soft matter geometry includes solving shape equations, trajectories on energy and orientation landscapes, and shape-curvedness evolutions on entropy production landscape with efficient numerical methods and adaptive approaches.

Modeling Tunable Fracture in Hydrogel Shell Structures for Biomedical Applications

Hydrogels are nowadays widely used in various biomedical applications, and show great potential for the making of devices such as biosensors, drug- delivery vectors, carriers, or matrices for cell cultures in tissue engineering, etc. In these applications, due to the irregular complex surface of the human body or its organs/structures, the devices are often designed with a small thickness, and are required to be flexible when attached to biological surfaces. The devices will deform as driven by human motion and under external loading. In terms of mechanical modeling, most of these devices can be abstracted as shells. In this paper, we propose a mixed graph-finite element method (FEM) phase field approach to model the fracture of curved shells composed of hydrogels, for biomedical applications. We present herein examples for the fracture of a wearable biosensor, a membrane-coated drug, and a matrix for a cell culture, each made of a hydrogel. Used in combination with experimental material testing, our method opens a new pathway to the efficient modeling of fracture in biomedical devices with surfaces of arbitrary curvature, helping in the design of devices with tunable fracture properties.

Magttice: a lattice model for hard-magnetic soft materials

Magnetic actuation has emerged as a powerful and versatile mechanism for diverse applications, ranging from soft robotics, biomedical devices to functional metamaterials. This highly interdisciplinary research calls for an easy to use and efficient modeling/simulation platform that can be leveraged by researchers with different backgrounds. Here we present a lattice model for hard-magnetic soft materials by partitioning the elastic deformation energy into lattice stretching and volumetric change, so-called 'magttice'. Magnetic actuation is realized through prescribed nodal forces in magttice. We further implement the model into the framework of a large-scale atomic/molecular massively parallel simulator (LAMMPS) for highly efficient parallel simulations. The magttice is first validated by examining the deformation of ferromagnetic beam structures, and then applied to various smart structures, such as origami plates and magnetic robots. After investigating the static deformation and dynamic motion of a soft robot, the swimming of the magnetic robot in water, like jellyfish's locomotion, is further studied by coupling the magttice and lattice Boltzmann method (LBM). These examples indicate that the proposed magttice model can enable more efficient mechanical modeling and simulation for the rational design of magnetically driven smart structures.

Soft Nucleation of an Elastic Crease

Creasing instability is ubiquitous in soft solids; however, its inception remains enigmatic as it cannot be captured by the standard linearization techniques. It also does not fit the conventional picture of a barrier-crossing nucleation, and instead carries some features of a second order phase transition. Here we show that despite its fundamentally nonlinear nature, creasing has its origin in marginal stability which is, however, obscured by the dominance of long-range elastic interactions. We argue that despite its supercritical (soft) character, creasing bifurcation can be identified by the condition that the (generalized) driving force acting on an incipient stress singularity degenerates. The analytic instability criterion, obtained in this way, shows an excellent agreement with both physical experiments and direct numerical simulations.

Surface Instability of Bilayer Hydrogel Subjected to Both Compression and Solvent Absorption

The bilayered structure of hard thin film on soft substrate can lose stability and form specific patterns, such as wrinkles or creases, on the surface, induced by external stimuli. For bilayer hydrogels, the surface morphology caused by the instability is usually controlled by the solvent-induced swelling/shrinking and mechanical force. Here, two important issues on the instability of bilayer hydrogels, which were not considered in the previous studies, are focused on in this study. First, the upper layer of a hydrogel is not necessarily too thin. Thus we investigated how the thickness of the upper layer can affect the surface morphology of bilayer hydrogels under compression through both finite element (FE) simulation and theoretical analysis. Second, a hydrogel can absorb water molecules before the mechanical compression. The effect of the pre-absorption of water before the mechanical compression was studied through FE simulations and theoretical analysis. Our results show that when the thickness of the upper layer is very large, surface wrinkles can exist without transforming into period doublings. The pre-absorption of the water can result in folds or unexpected hierarchical wrinkles, which can be realized in experiments through further efforts.