Energy-Conserving Time Discretization of Abstract Dynamic Problems with Applications in Continuum Mechanics of Solids. (2nd September 2017)

• Record Type: Journal Article
• Authors: Roubíček, Tomáš; Panagiotopoulos, Christos G.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 9(2017)
• Page Start: 1143
• Page End: 1172
• Publication Date: 2017-09-02
• Subjects: Computational simulations -- Crank Nicolson formula -- damage -- evolution variational inequalities -- fractional-step splitting -- inelastic processes -- inertia -- numerical approximation -- plasticity -- standard solids with internal parameters; 35Q74 -- 35R45 -- 37N15 -- 65K15 -- 65P99 -- 74C05 -- 74H15 -- 74J99 -- 74M10 -- 74N30 -- 74R05 -- 90C20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1318915
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: An abstract second-order evolution equation or inclusion is discretized in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or "slightly perturbed" quadratic. Specific applications in continuum mechanics of solids possibly with various internal variables cover vibrations or waves in linear viscoelastic materials at small strains, coupled with some inelastic processes as plasticity, damage, or phase transformations, and also some surface variants related to contact mechanics. The applicability is illustrated by numerical simulations of vibrations interacting with a frictional contact or waves emitted by an adhesive contact of a two-dimensional viscoelastic body.