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An approach to nonlinear viscoelasticity via metric gradient flows

Title	An approach to nonlinear viscoelasticity via metric gradient flows
Author	Mielke, A., Ortner, C., Şengül, Yasemin
Publication Date:	2014
Publication Place	- SIAM
Subject	Nonlinear viscoelasticity, Gradient flow, Dissipative distance, Generalized geodesics
Type	Periodical
Language	English
Digital	Yes
Manuscript	No
Library:	Özyeğin University
Library Asset ID	0036-1410
Record ID	c3c23280-c89b-497e-9556-fc8d1a11ec88
Library Location	Natural and Mathematical Sciences
Date	2014
Notes	DFG ; ERC ; Leverhulme Trust
Sample Text	We formulate quasistatic nonlinear finite-strain viscoelasticity of rate type as a gradient system. Our focus is on nonlinear dissipation functionals and distances that are related to metrics on weak diffeomorphisms and that ensure time-dependent frame indifference of the viscoelastic stress. In the multidimensional case we discuss which dissipation distances allow for the solution of the time-incremental problem. Because of the missing compactness the limit of vanishing timesteps can be obtained only by proving some kind of strong convergence. We show that this is possible in the one-dimensional case by using a suitably generalized convexity in the sense of geodesic convexity of gradient flows. For a general class of distances we derive discrete evolutionary variational inequalities and are able to pass to the time-continuous limit in a specific case.
DOI	10.1137/130927632
Cilt	46

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Özyeğin University

An approach to nonlinear viscoelasticity via metric gradient flows

Author Mielke, A., Ortner, C., Şengül, Yasemin

Publication Date 2014

Publication Place - SIAM

Subject Nonlinear viscoelasticity, Gradient flow, Dissipative distance, Generalized geodesics

Type Periodical

Language English

Digital Yes

Manuscript No

Library Özyeğin University

Library Asset ID 0036-1410

Record ID c3c23280-c89b-497e-9556-fc8d1a11ec88

Library Location Natural and Mathematical Sciences

Date 2014

Notes DFG ; ERC ; Leverhulme Trust

Sample Text We formulate quasistatic nonlinear finite-strain viscoelasticity of rate type as a gradient system. Our focus is on nonlinear dissipation functionals and distances that are related to metrics on weak diffeomorphisms and that ensure time-dependent frame indifference of the viscoelastic stress. In the multidimensional case we discuss which dissipation distances allow for the solution of the time-incremental problem. Because of the missing compactness the limit of vanishing timesteps can be obtained only by proving some kind of strong convergence. We show that this is possible in the one-dimensional case by using a suitably generalized convexity in the sense of geodesic convexity of gradient flows. For a general class of distances we derive discrete evolutionary variational inequalities and are able to pass to the time-continuous limit in a specific case.

DOI 10.1137/130927632

Cilt 46