Curvature-Regulated Multiphase Patterns in Tori.

Biological functions in living systems are closely related to their geometries and morphologies. Toroidal structures, which widely exist in nature, present interesting features containing positive, zero, and negative Gaussian curvatures within one system. Such varying curvatures would significantly affect the growing or dehydrating morphogenesis, as observed in various intricate patterns in abundant biological structures. To understand the underlying morphoelastic mechanism and to determine the crucial factors that govern the patterning in toroidal structures, we develop a core-shell model and derive a scaling law to characterize growth- or dehydration-induced instability patterns. We find that the eventual patterns are mainly determined by two dimensionless parameters that are composed of stiffness and curvature of the system. Moreover, we construct a phase diagram showing the multiphase wrinkling pattern selection in various toroidal structures in terms of these two parameters, which is confirmed by our experimental observations. Physical insights into the multiphase transitions and existence of bistable modes are further provided by identifying hysteresis loops and the Maxwell equal-energy conditions. The universal law for morphology selection on core shell structures with varying curvatures can fundamentally explain and precisely predict wrinkling patterns of diverse toroidal structures, which may also provide a platform to design morphology-related functional surfaces.

Modelling transport of reactive tracers in a heterogeneous crystalline rock matrix.

A numerical reactive transport model for crystalline rocks is developed and evaluated. The model is based on mineral maps generated by X-ray micro computed tomography (X-µCT); the maps used have a resolution of approximately 30 µm and the rock samples are on the cm scale. A computational grid for the intergranular space is generated and a micro-DFN (Discrete Fracture Network) model governs the grid properties. A particle tracking method (Time Domain Random Walk) is used for transport simulations. The basic concept of the model can now be formulated as follows; "when a particle is close to a reactive mineral surface it has a certain probability to get sorbed during a certain time span. Once sorbed it will remain so a certain time". The model requires a number of input parameters that represent the sorption properties of the reactive minerals. Attempts are made to relate the parameters to traditional distribution parameters. The model is evaluated by comparisons with recent laboratory experimental data. These experiments consider two rock types (veined gneiss and pegmatitic granite) and two radionuclides (cesium and barium). It is concluded that the new reactive transport model can simulate the experimental data in a consistent and realistic way.

A Multiscale Analysis on the Superelasticity Behavior of Architected Shape Memory Alloy Materials.

In this paper, the superelasticity effects of architected shape memory alloys (SMAs) are focused on by using a multiscale approach. Firstly, a parametric analysis at the cellular level with a series of representative volume elements (RVEs) is carried out to predict the relations between the void fraction, the total stiffness, the hysteresis effect and the mass of the SMAs. The superelasticity effects of the architected SMAs are modeled by the thermomechanical constitutive model proposed by Chemisky et al. 2011. Secondly, the structural responses of the architected SMAs are studied by the multilevel finite element method (FE 2 ), which uses the effective constitutive behavior of the RVE to represent the behavior of the macroscopic structure. This approach can truly couple the responses of both the RVE level and structural level by the real-time information interactions between two levels. Through a three point bending test, it is observed that the structure inherits the strong nonlinear responses-both the hysteresis effect and the superelasticity-of the architected SMAs at the cellular level. Furthermore, the influence of the void fraction at the RVE level to the materials' structural responses can be more specifically and directly described, instead of using an RVE to predict at the microscopic level. Thus, this work could be referred to for optimizing the stiffness, the hysteresis effect and the mass of architected SMA structures and extended for possible advanced applications.

Pattern Transitions in a Soft Cylindrical Shell.

Instability patterns of rolling up a sleeve appear more intricate than the ones of walking over a rug on floor, both characterized as systems of uniaxially compressed soft film on stiff substrate. This can be explained by curvature effects. To investigate pattern transitions on a curved surface, we study a soft shell sliding on a rigid cylinder by experiments, computations and theoretical analyses. We reveal a novel postbuckling phenomenon involving multiple successive bifurcations: smooth-wrinkle-ridge-sagging transitions. The shell initially buckles into periodic axisymmetric wrinkles at the threshold and then a wrinkle-to-ridge transition occurs upon further axial compression. When the load increases to the third bifurcation, the amplitude of the ridge reaches its limit and the symmetry is broken with the ridge sagging into a recumbent fold. It is identified that hysteresis loops and the Maxwell equal-energy conditions are associated with the coexistence of wrinkle-ridge or ridge-sagging patterns. Such a bifurcation scenario is inherently general and independent of material constitutive models.

Quantitative predictions of diverse wrinkling patterns in film/substrate systems.

A basic characteristic of stiff film/soft substrate systems is their ability to experience large deformation under compressive stresses, which inevitably leads to formation of patterns on the surface. Such pattern formation is the result of loss of stability and symmetry breaking. Knowledge on how such instabilities arise and evolve is essential to describe, understand, predict, and ultimately to design complex functional materials and structures, for example the fabrication of stretchable electronic devices and micro/nano-scale surface patterning control. In this paper, quantitative predictions of various instability pattern formations and evolutions, which involve highly nonlinear deformation and multiple bifurcations, will be presented based on advanced mechanical models and methods, from planar to curved geometry. The results can provide further insight into fundamental understanding in a whole view of a variety of surface patterning morphology and imply a potential way to facilitate the design of functional materials and structures by quantitatively harnessing surface instabilities.