Abstract
AbstractWe consider generalized gradient systems with rate-independent and rate-dependent dissipation potentials. We provide a general framework for performing a vanishing-viscosity limit leading to the notion of parametrized and true Balanced-Viscosity solutions that include a precise description of the jump behavior developing in this limit. Distinguishing an elastic variable u having a viscous damping with relaxation time $$\varepsilon ^\alpha $$
ε
α
and an internal variable z with relaxation time $$\varepsilon $$
ε
we obtain different limits for the three cases $$\alpha \in (0,1)$$
α
∈
(
0
,
1
)
, $$\alpha =1$$
α
=
1
and $$\alpha >1$$
α
>
1
. An application to a delamination problem shows that the theory is general enough to treat nontrivial models in continuum mechanics.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Mathematics (miscellaneous),Analysis
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