Tiling a tubule: How increasing complexity improves the yield of self-limited assembly

The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of systems with self-limited length scales is that thermal fluctuations can lead to the assembly of nearby, off-target states. We investigate strategies for limiting off-target assembly by using multiple types of subunits. Using simulations and energetics calculations, we explore this concept by considering the assembly of tubules built from triangular subunits that bind edge to edge. While in principle, a single type of triangle can assemble into tubules with a monodisperse width distribution, in practice, the finite bending rigidity of the binding sites leads to the formation of off-target structures. To increase the assembly specificity, we introduce tiling rules for assembling tubules from multiple species of triangles. We show that the selectivity of the target structure can be dramatically improved by using multiple species of subunits, and provide a prescription for choosing the minimum number of subunit species required for near-perfect yield. Our approach of increasing the system’s complexity to reduce the accessibility of neighboring structures should be generalizable to other systems beyond the self-assembly of tubules.

A Finite Strain Analytical Solution for Stress-Softening of Hyperelastic Materials Under Cyclic Bending

In this paper, a new approach for stress-softening of an isotropic, incompressible, hyperelastic and rectangular beam that undergoes cyclic bending-unbending deformation, is presented. Employing an exponential softening function, damage response of the hyperelastic beam due to cyclic finite bending is investigated. The stress-softening phenomenon occurs in elastomeric materials when they deform for the first time. Under the same deformation, the stress required in reloading is smaller than the initial loading stage. This is known as the Mullins effect. To verify the accuracy of the proposed solution, finite element analysis of the same problem is carried out. In this study, a principal stretch-based strain energy function i.e., Ogden model and an invariant-based function such as a newly introduced Exp–Exp model are used for all bending, unbending and re-bending procedures. The proposed method needs a much shorter time compared to FEM simulations. Thus, in design and optimization of the structures under bending that requires a large number of analyses, the proposed semi-analytical solution can be considered as an efficient tool for studying the effects of different material and geometrical parameters.

FE Analyses of Hyperelastic Solids under Large Bending: The Role of the Searle Parameter and Eulerian Slenderness

A theoretical model concerning the finite bending of a prismatic hyperelastic solid has been recently proposed. Such a model provides the 3D kinematics and the stress field, taking into account the anticlastic effects arising in the transverse cross sections also. That model has been used later to extend the Elastica in the framework of finite elasticity. In the present work, Finite Element (FE) analyses of some basic structural systems subjected to finite bending have been carried out and the results have been compared with those provided by the theoretical model performed previously. In the theoretical formulation, the governing equation is the nonlinear local relationship between the bending moment and the curvature of the longitudinal axis of the bent beam. Such a relation has been provided in dimensionless form as a function of the Mooney–Rivlin constitutive constants and two kinematic dimensionless parameters termed Eulerian slenderness and compactness index of the cross section. Such parameters take relevance as they are involved in the well-known Searle parameter for bent solids. Two significant study cases have been investigated in detail. The results point out that the theoretical model leads to reliable results provided that the Eulerian slenderness and the compactness index of the cross sections do not exceed fixed threshold values.

Finite Bending and Straightening of Hyperelastic Materials: Analytical Solution and FEM

In this research, an incompressible, isotropic, nonlinear elastic rectangular block and a circular cylindrical sector are studied under bending and straightening moments, respectively. Analytical approaches are presented on implementing of the left Cauchy–Green tensor and Cauchy stresses. In addition, finite element analysis of both problems is carried out using UHYPER user-defined subroutine in ABAQUS to verify the analytical methods. Four different invariant-based strain energy functions, including neo-Hookean, Mooney–Rivlin, Arruda–Boyce, and recently proposed polynomial Exp-Exp models, are examined, and the results are compared. Material parameters of silicon rubber for the strain energy functions are identified by applying an optimization procedure. Finite element method results confirmed the analytical approach with great compatibility. Results showed that the length of the unbent beam does not affect the stress. Likewise, the initial angle of curved structure does not affect the unbending moment and stresses. Moreover, the Exp-Exp model had a slightly different result rather than other strain energies, which means that this model is more conservative than its counterparts. Furthermore, the Exp-Exp strain energy function is calibrated for tissue-like phantom and is compared with experimental data.

A combined analytical–numerical analysis on multidirectional finite bending of functionally graded temperature-sensitive hydrogels

Recently, temperature-sensitive hydrogels have been employed widely in various applications such as switches and actuators. Considering the discontinuity in the stresses and deformation fields of multilayers, in this article, we developed a new analytical method to study the swelling-induced finite bending of temperature-sensitive functionally graded hydrogels under plane-strain condition. The cross-linked density distribution along strip thickness varies linearly or exponentially which causes the switch to bend in response to temperature variation. To clarify the actuation mechanism and probe the various effects of parameters on switches’ thermomechanical response, a semi-analytical approach is developed. Finite element method is employed to validate the deformation of functionally graded temperature-sensitive hydrogel layer results. The stresses and deformation fields, bending curvature, and semi-angle are investigated using semi-analytical and numerical methods for several cases in one-directional and bidirectional bending switches. The continuous stresses and deformation fields and multiple neutral axes are illustrated which have crucial role in designing switches.