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A novel numerical approach employing a meshless technique with molecular dynamics is proposed for coupled length-scale simulations spanning continuum to atomistic regions. In this multiscale simulation, the meshless Element-Free Galerkin (EFG) method is employed in the continuum region, and in the atomistic region, molecular dynamics (MD) is used for refined level simulation. This is the first instance whereby this meshless technique has been deployed for continuum/MD multiscale analysis. Another contribution of this work is the development of a handshaking algorithm, under the coupled EFG/MD framework, for the compatibility of both displacements and stresses on the interface region between the continuum and atomistic regions. This seamless coupling of the continuum to statistical mechanics is validated by several numerical examples, and the developed source codes were found to be robust and efficient in the implementation. [ABSTRACT FROM AUTHOR]

Abstract: In this work, a novel true meshless numerical technique is proposed. It is termed the Hermite–Cloud method and is based on the classical reproducing kernel particle method except that a fixed reproducing kernel approximation is used instead. Another distinction is that the point collocation technique is used for the discretization of the governing partial differential equations. In this method, the Hermite theorem is employed for the construction of the interpolation functions. Through the constructed Hermite-type interpolation functions, we are able to generate the expressions of approximate solutions of both the unknown functions and the first-order derivatives, in a direct manner. A set of auxiliary conditions have also been developed so as to construct a complete set of PDEs with mixed Dirichlet and Neumann boundary conditions. Through several structural analysis examples, it is shown that the numerical results at the scattered discrete points generated by the Hermite–Cloud method are distinctly improved, for both the approximate solutions as well as the first-order derivatives. [Copyright &y& Elsevier]

It is very difficult for traditional numerical methods to simulate the problems of water mitigation which has been increasingly used to reduce blast effects. This paper studies water mitigation problems by using smoothed particle hydrodynamics (SPH), which is a meshless, Lagrangian method appealing in treating large deformation explosion events with significant inhomogeneities. Numerical verifications considering high explosive detonation and underwater explosion shock waves have demonstrated the effectiveness of the SPH method, the solution procedure and the code. Contact and non-contact water mitigation simulations have been carried out and are compared with the case without mitigation. For either contact or non-contact water shield, the peak shock pressure and the equilibrium gas pressure are reduced to different levels according to the relevant geometry of the system setup. An optimum contact water shield thickness is found to produce the best mitigation effect for a given high explosive charge, while the non-contact water shield, if properly designed, can result in further reduction of the peak shock pressure and the equilibrium gas pressure. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a well-developed meshless numerical technique, local Kriging (LoKriging) method, is used to develop the LoKriging formulation for the large deformation problems, which are geometrically nonlinear. This is the first work for the geometrically nonlinear analyses by this meshless local weak-form method. In the LoKriging method, the Kriging interpolation is employed to construct the meshless shape functions. The spline function with high continuity is used as the weight function. The discrete equations of the large deformation analysis for two-dimensional solids are obtained using the local weak-forms, and based on the total Lagrangian (TL) approach. The presently developed LoKriging method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak-form. Several numerical examples of the two-dimensional geometrically nonlinear analysis are presented to illustrate the performance of the present LoKriging method. The present nonlinear LoKriging formulation is also used for the large deformation analysis of the microelectromechanical systems (MEMS) device. The numerical results are compared with the experimental results. Very good results are obtained. All these applications have demonstrated that the present LoKriging method is very effective for the large deformation analyses, because it avoids all mesh distortion issues. [Copyright &y& Elsevier]

This paper presents a novel meshless approach to study the dynamic responses of structures. It is called Local Kriging (LoKriging) method, where the Kriging interpolation is employed to construct the field approximation function and meshless shape functions, and the local weak form of partial differential governing equations is derived by the weighted residual technique. Since the shape functions constructed by this interpolation possess the delta function property even for a set of randomly distributed points, the essential boundary condition can be easily imposed. In implementation of local weak form, the spline function with high continuity is used as the weight function. No mesh is required either for integration of the local weak form, or for construction of the shape functions. Thus the present LoKriging method is a truly meshless method. Several numerical examinations for the free/forced vibrational analysis of structures and the dynamic performance of microelectromechanical systems (MEMS) device are carried out to demonstrate the accuracy and efficiency of the LoKriging method. The numerical results show that the presently developed method is quite easy to implement, very accurate and highly efficient for the problems considered. [Copyright &y& Elsevier]

Based on a multi-phasic mixture theory with consideration of ionic diffusion and convection, a multi-physic model, called the multi-effect-coupling electric-stimulus (MECe) model, is developed for simulation of responsive behavior of the electric-sensitive hydrogels when they are immersed into a bathing solution subject to an externally applied electric field. In the developed model, with chemo-electro-mechanical coupling effects, the convection–diffusion equations for concentration distribution of diffusive ions incorporate the influence of electric potential. The electroneutrality condition is replaced by the Poisson equation for distribution of electric potential. The steady and transient analyses of hydrogel deformation are easily carried out by the continuity and momentum equations of the mixture phase. Further, the computational domain of the present model covers both the hydrogel and the surrounding solution. In order to solve the present mathematical model consisting of multi-field coupled nonlinear partial differential governing equations, a hierarchical iteration technique is proposed and a meshless Hermite–Cloud method (HCM) is employed. The steady-state simulation of the electric-stimulus responsive hydrogel is numerically conducted when it is subjected to an externally applied electric field. The hydrogel deformation and the ionic concentrations as well as electric potentials of both the hydrogel and external solution are investigated. The parameter influences on the swelling behaviors of the hydrogel are also discussed in detail. The simulating results are in good agreement with the experimental data and they validate the presently developed model. [Copyright &y& Elsevier]

Abstract: In this paper, the kinetics of polymer-based electric-stimulus-responsive hydrogels is investigated numerically. The studied hydrogels are mainly composed of three phases, i.e. the interstitial water, mobile ions and a three-dimensional networked structure of hydrophilic polymer-chains crosslinked to each other. With consideration of the chemo-electro-mechanical coupling effect and the multi-phasic (water, ion and polymer-based solid phases) interactions, a newly developed mathematical model, called the multi-effect-coupling electric-stimulus (MECe) model, is briefly presented to simulate the responsive behaviors of electric-sensitive hydrogels immersed into a bath solution under an externally applied electric field. The full formulation of the MECe model is expressed by a set of nonlinear partial differential equations, consisting of the Nernst–Plank equations for the concentration distributions of diffusive ionic species, the Poisson equation for the pattern of electric potential, and the continuum mechanical equation for the mechanical deformation of hydrogels. In order to solve the complex MECe model, a novel meshless Hermite-Cloud method is used in numerical implementations. The simulations in this paper focus on the one-dimensional transient analysis for the kinetics of the hydrogels. After the validation of the developed MECe model by comparing the steady-state numerical results with the experiments, this paper presents the transient simulations for variations of the ionic concentration and average curvature of hydrogels. The simulating results of the kinetic hydrogel indicate that the electric-sensitive hydrogels respond rapidly to the external electric-stimulus before a critical time and then no significant further response occurs after the critical time. [Copyright &y& Elsevier]

Through higher-order Hermite construction of the interpolation functions, a novel true meshless numerical technique—the Hermite-Cloud method is developed for the analysis of nonlinear fluid-structure interaction of near-bed submarine pipelines under a current. Following the development of the discrete point collocation technique throughout the computational domains, the present method constructs the approximations of both the unknown functions and their first-order derivatives based on the classical reproducing kernel particle method, except that a fixed reproducing kernel approximation is employed instead. For partial differential equations with boundary conditions, certain auxiliary conditions are required due to the use of the Hermite theorem. After validation of the presently developed Hermite-Cloud method by several two-dimensional elasticity examples, the method is used for the failure analysis of a near-bed submarine pipeline under a horizontal current with consideration of a nonlinear fluid–structure interaction effect. The numerical result indicates that the distance from the pipelines to seabed and the current velocity have remarkable influences on the deformation behavior of the pipelines. It also shows that various critical current velocities corresponding to different failure patterns exist, and the presently simulated relation of the critical velocities agrees with the results in the previous publications. [Copyright &y& Elsevier]