Daniel Aubram | Searcharxiv

arXiv2017

Notes on rate equations in nonlinear continuum mechanics

The paper gives an introduction to rate equations in nonlinear continuum mechanics which should obey specific transformation rules. Emphasis is placed on the geometrical nature of the operations involved in order to clarify the different concepts. The paper is particularly concerned with common classes of constitutive equations based on corotational stress rates and their proper implementation in time for solving initial boundary value problems. Hypoelastic simple shear is considered as an example application for the derived theory and algorithms.

physics.class-ph↗

arXiv2014

Optimization-based smoothing algorithm for triangle meshes over arbitrarily shaped domains

This paper describes a node relocation algorithm based on nonlinear optimization which delivers excellent results for both unstructured and structured plane triangle meshes over convex as well as non-convex domains with high curvature. The local optimization scheme is a damped Newton's method in which the gradient and Hessian of the objective function are evaluated exactly. The algorithm has been developed in order to continuously rezone the mesh in arbitrary Lagrangian-Eulerian (ALE) methods for large deformation penetration problems, but it is also suitable for initial mesh improvement. Numerical examples highlight the capabilities of the algorithm.

math.NA↗