Space-time variational material modeling

Numerical simulations for the wave equation with velocity initial and final time condictions

authored by: Philipp Junker, Julian Roth, Thomas Wick
Abstract: In this work, we consider one key component, namely the wave equation, of a recently proposed space-time variational material model. The overall model is derived from a thermodynamically consistent Hamilton functional in the space-time cylinder in which mechanics, temperature and internal variables couple. Through the derivation, rather unusual end time conditions for the second-order in time wave equation arise. In order to understand their behavior better, we solely focus on the wave equation (neglecting temperature and internal variables) and formulate a Galerkin finite element discretization in time and space. Based on this discretization and the corresponding implementation, some numerical simulations are conducted. Therein, both traditional initial conditions for the displacements and the velocities are considered, as well as our newly proposed conditions for initial time and final time acting on the velocity variable only.
Organisation(s): Institute of Continuum Mechanics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
Institute of Applied Mathematics
Type: Conference contribution
No. of pages: 12
Publication date: 21.07.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mechanical Engineering
Electronic version(s): https://doi.org/10.23967/wccm.2024.036 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@inproceedings{7ab9ffd6222a4829b56ba1eafe3110d7,
title = "Space-time variational material modeling: Numerical simulations for the wave equation with velocity initial and final time condictions",
abstract = "In this work, we consider one key component, namely the wave equation, of a recently proposed space-time variational material model. The overall model is derived from a thermodynamically consistent Hamilton functional in the space-time cylinder in which mechanics, temperature and internal variables couple. Through the derivation, rather unusual end time conditions for the second-order in time wave equation arise. In order to understand their behavior better, we solely focus on the wave equation (neglecting temperature and internal variables) and formulate a Galerkin finite element discretization in time and space. Based on this discretization and the corresponding implementation, some numerical simulations are conducted. Therein, both traditional initial conditions for the displacements and the velocities are considered, as well as our newly proposed conditions for initial time and final time acting on the velocity variable only.",
keywords = "Galerkin finite elemendiscretization, Space-time, variational material modeling, wave equation",
author = "Philipp Junker and Julian Roth and Thomas Wick",
note = "Publisher Copyright: {\textcopyright} 2024, Scipedia S.L. All rights reserved.; 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics, WCCM-PANACM 2024 ; Conference date: 21-07-2024 Through 26-07-2024",
year = "2024",
month = jul,
day = "21",
doi = "10.23967/wccm.2024.036",
language = "English",
series = "World Congress in Computational Mechanics and ECCOMAS Congress",
publisher = "International Centre for Numerical Methods in Engineering, CIMNE",
editor = "A. Korobenko and M. Laforest and S. Prudhomme and R. Vaziri",
booktitle = "16th World Congress in Computational Mechanics (WCCM)",
}