Related papers: Simulation of thin hyperelastic shells with the Ma…
Mesh-free Lagrangian methods are widely used for simulating fluids, solids, and their complex interactions due to their ability to handle large deformations and topological changes. These physics simulators, however, require substantial…
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…
In this paper we derive a new finite element method for nonlinear shells. The Hellan-Herrmann-Johnson (HHJ) method is a mixed finite element method for fourth order Kirchhoff plates. It uses convenient Lagrangian finite elements for the…
We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test…
Taylor impacts tests were originally devised to determine the dynamic yield strength of materials at moderate strain rates. More recently, such tests have been used extensively to validate numerical codes for the simulation of plastic…
Performing shell model calculations for heavy nuclei is a long-standing problem in nuclear physics. The shell model truncation in the configuration space is an unavoidable step. The Projected Shell Model (PSM) truncates the space under the…
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the…
Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…
The geometrically rigorous nonlinear analysis of elastic shells is considered in the context of finite, but small, strain theory. The research is focused on the introduction of the full shell metric and examination of its influence on the…
Thin surfaces, such as the leaves of a plant, pose a significant challenge for implicit surface reconstruction techniques, which typically assume a closed, orientable surface. We show that by approximately interpolating a point cloud of the…
We investigate a specific finite element model to study the thermoelastic behavior of an elastic body within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic…
Existing numerical methods for modeling magnetization in thin type-II superconducting films have mostly been developed for flat films. This work introduces an efficient spectral method for axisymmetric magnetization problems involving…
Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a…
A buckled sheet offers a reservoir of material that can be unfurled at a later time. For sufficiently thin yet stiff materials, this geometric process has a striking mechanical feature: when the slack runs out, the material locks to further…
The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of…
We present a mathematical model of polymer bilayers that undergo large bending deformations when actuated by non-mechanical stimuli such as thermal effects. The simple model captures a large class of nonlinear bending effects and can be…
We present a new method for real-time physics-based simulation supporting many different types of hyperelastic materials. Previous methods such as Position Based or Projective Dynamics are fast, but support only limited selection of…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…