Importance of Mullins effect in commercial silicone elastomer formulations for soft robotics

Silicone elastomers are used in a wide range of applications, including artificial muscles, biomedical devices, and soft robotics, for which chemical, thermal, and mechanical stability are important requirements that these elastomers must fulfill. However, to ensure that silicone elastomers' properties and performance remain constant under long-term deployment, it is necessary to examine and account for the Mullins effect, which has the potential to significantly alter certain elastomer properties of interest. In this article, the mechanical properties of soft and hard commercial silicone elastomers and two blends of commercial silicone elastomers are investigated—specifically their softening behavior due to the Mullins effect. Ultimate stresses, ultimate strains, and Young's moduli are obtained from uniaxial tensile tests. Results show that the point of softening greatly depends on both the elastomer type and its strain history. Furthermore, a significant permanent set is observed in the softest commercial formulations.     

Upcycling by grafting onto semi-crystalline polymers using supercritical CO2

The creation of graft copolymers by selectively grafting a second polymer to the amorphous fraction of a semi-crystalline polymer in supercritical CO₂ is demonstrated herein. The graft copolymer is synthesized by free radical polymerization of a vinyl monomer within the semi-crystalline polymer below its melt temperature. Such conditions afford selective grafting on the amorphous regions (block “B”) while leaving the crystalline domains (block “A”) unmodified. Accordingly, unique A-B, A-B-A, A-B-A-B-A, and so forth. block structures are formed. In this work, styrene is polymerized within polyamide 6, polyethylene terephthalate, and isotactic polypropylene. Purification of these material is performed to remove the un-grafted homopolymer, allowing for determination of the graft yield, the portion of polymer which covalently bonds to the semi-crystalline matrix. Grafting yields achieved in polyamide 6, polyethylene terephthalate, and isotactic polypropylene were 98%, 59%, and 15%, respectively. Property enhancements were observed upon further characterization of polystyrene-polyamide 6 copolymers, including high glass transition temperatures, the ability to be remelted, and tunable grafting molecular weight. Additionally, hydrophobicity is controlled by varying polystyrene composition. The remarkable range of accessed properties demonstrates this as a potential route to upcycling plastics.     

Microstructure and mechanical properties of laser solid formed 30Cr–Mn–Si–Ni–2A ultra-high-strength steel

ABSTRACT

Microstructure and mechanical properties of laser solid formed 30Cr–Mn–Si–Ni–2A steel are investigated. The deposits consist of epitaxial columnar grains, equiaxed grains or direction changed dendrites can be observed in the bulk specimens. The microstructure at the bottom of deposits is mainly composed of tempered martensite; the middle to top zone of the deposits are characterised by martensite and bainite. With the increasing of deposition height, the volume fraction of bainite increases, the size of martensite laths increases but its volume fraction decreases. The microhardness shows a decrease from the bottom zone to the middle–upper zone, and then a significant increase at the top of the deposits. Anisotropic and unevenly distributed tensile properties are observed for the deposits. Samples after heat treatment demonstrate tensile strength of 1720?MPa and elongation rate of 8.7%.     

Dual–primal proximal point algorithms for extended convex programming

This paper presents a class of dual–primal proximal point algorithms (PPAs) for extended convex programming with linear constraints. By choosing appropriate proximal regularization matrices, the application of the general PPA to the equivalent variational inequality of the extended convex programming with linear constraints can result in easy proximal subproblems. In theory, the sequence generated by the general PPA may fail to converge since the proximal regularization matrix is asymmetric sometimes. So we construct descent directions derived from the solution obtained by the general PPA. Different step lengths and descent directions are chosen with the negligible additional computational load. The global convergence of the new algorithms is proved easily based on the fact that the sequences generated are Fejér monotone. Furthermore, we provide a simple proof for the O(1/t) convergence rate of these algorithms.     

A new high accuracy method for two-dimensional biharmonic equation with nonlinear third derivative terms: application to Navier–Stokes equations of motion

In this paper, we propose a new compact fourth-order accurate method for solving the two-dimensional fourth-order elliptic boundary value problem with third-order nonlinear derivative terms. We use only 9-point single computational cell in the scheme. The proposed method is then employed to solve Navier–Stokes equations of motion in terms of streamfunction–velocity formulation, and the lid-driven square cavity problem. We describe the derivation of the method in details and also discuss how our streamfunction–velocity formulation is able to handle boundary conditions in terms of normal derivatives. Numerical results show that the proposed method enables us to obtain oscillation-free high accuracy solution.     

Compact difference method for solving the fractional reaction–subdiffusion equation with Neumann boundary value condition

In this paper, we derive a high-order compact finite difference scheme for solving the reaction–subdiffusion equation with Neumann boundary value condition. The L1 method is used to approximate the temporal Caputo derivative, and the compact difference operator is applied for spatial discretization. We prove that the compact finite difference method is unconditionally stable and convergent with order O(τ^2?α+h⁴) in L₂ norm, where τ, α, and h are the temporal step size, the order of time fractional derivative and the spatial step size, respectively. Finally, some numerical experiments are carried out to show the effectiveness of the proposed difference scheme.     

Numerical solution of nonlinear system of Klein–Gordon equations by cubic B-spline collocation method

A technique to approximate the solutions of nonlinear Klein–Gordon equation and Klein–Gordon-Schrödinger equations is presented separately. The approach is based on collocation of cubic B-spline functions. The above-mentioned equations are decomposed into a system of partial differential equations, which are further converted to an amenable system of ODEs. The obtained system has been solved by SSP-RK54 scheme. Numerical solutions are presented for five examples, to show the accuracy and usefulness of proposed approach. The approximate solutions of both the equations are computed without using any transformation and linearization. The technique can be applied with ease to solve linear and nonlinear PDEs and also reduces the computational work.