Related papers: Moving Mesh simulation of contact sets in two dime…
The dynamics of a free boundary problem for electrostatically actuated microelectromechanical systems (MEMS) is investigated. The model couples the electric potential to the deformation of the membrane, the deflection of the membrane being…
A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves…
Mainstream numerical Partial Differential Equation (PDE) solvers require discretizing the physical domain using a mesh. Mesh movement methods aim to improve the accuracy of the numerical solution by increasing mesh resolution where the…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
In Part I of this two part series, we presented a multi-neighbor dependent contact model for adhesive elastic-plastic particles built upon the method of dimensionality reduction that is valid for the elastic and fully-plastic contact…
Shear transformations (i.e., localised rearrangements of particles resulting in the shear deformation of a small region of the sample) are the building blocks of mesoscale models for the flow of disordered solids. In order to compute the…
Fluid-structure interactions are a widespread phenomenon in nature. Although their numerical modeling have come a long way, the application of numerical design tools to these multiphysics problems is still lagging behind. Gradient-based…
Immersed finite element (IFE) methods are a group of long-existing numerical methods for solving interface problems on unfitted meshes. A core argument of the methods is to avoid mesh regeneration procedure when solving moving interface…
Based on the superposition of incremental frictional surface tractions that, in the case of an incompressible elastic half-space, correspond to a rigid tangential translation of a circular contact domain, the stress and displacement fields…
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to…
Soft slender structures are ubiquitous in natural and artificial systems and can be observed at scales that range from the nanometric to the kilometric, from polymers to space tethers. We present a practical numerical approach to simulate…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
We introduce a mathematical model with a mesh-free numerical method to describe contact-line motion in lubrication theory. We show how the model resolves the singularity at the contact line, and generates smooth profiles for an evolving,…
A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The…
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of…
Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to…
The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces…
This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…