An approach to nonlinear viscoelasticity via metric gradient flows

Name: An approach to nonlinear viscoelasticity via metric gradient flows
Author: Mielke, A., Ortner, C., Şengül, Yasemin

İsim	An approach to nonlinear viscoelasticity via metric gradient flows
Yazar	Mielke, A., Ortner, C., Şengül, Yasemin
Basım Tarihi:	2014
Basım Yeri	- SIAM
Konu	Nonlinear viscoelasticity, Gradient flow, Dissipative distance, Generalized geodesics
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0036-1410
Kayıt Numarası	c3c23280-c89b-497e-9556-fc8d1a11ec88
Lokasyon	Natural and Mathematical Sciences
Tarih	2014
Notlar	DFG ; ERC ; Leverhulme Trust
Örnek Metin	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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An approach to nonlinear viscoelasticity via metric gradient flows

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

Basım Tarihi 2014

Basım Yeri - SIAM

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

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0036-1410

Kayıt Numarası c3c23280-c89b-497e-9556-fc8d1a11ec88

Lokasyon Natural and Mathematical Sciences

Tarih 2014

Notlar DFG ; ERC ; Leverhulme Trust

Örnek Metin 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