We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the fact that damage is favoured in regions where the cumulation of the elastic strain (or other relevant variables, depending on the model) is higher. To prove the existence of a quasistatic evolution, we follow a vanishing viscosity approach based on two steps: we first let the time step τ of the time discretisation and later the viscosity parameter ε go to zero. As τ→ 0 , we find ε-approximate viscous evolutions; then, as ε→ 0 , we find a rescaled approximate evolution satisfying an energy-dissipation balance.

Fatigue Effects in Elastic Materials with Variational Damage Models: A Vanishing Viscosity Approach / Alessi, R.; Crismale, V.; Orlando, G.. - In: JOURNAL OF NONLINEAR SCIENCE. - ISSN 0938-8974. - 29:3(2019), pp. 1041-1094. [10.1007/s00332-018-9511-9]

Fatigue Effects in Elastic Materials with Variational Damage Models: A Vanishing Viscosity Approach

Crismale V.;
2019

Abstract

We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the fact that damage is favoured in regions where the cumulation of the elastic strain (or other relevant variables, depending on the model) is higher. To prove the existence of a quasistatic evolution, we follow a vanishing viscosity approach based on two steps: we first let the time step τ of the time discretisation and later the viscosity parameter ε go to zero. As τ→ 0 , we find ε-approximate viscous evolutions; then, as ε→ 0 , we find a rescaled approximate evolution satisfying an energy-dissipation balance.
2019
Fatigue; gradient damage models; vanishing viscosity approach; variational methods
01 Pubblicazione su rivista::01a Articolo in rivista
Fatigue Effects in Elastic Materials with Variational Damage Models: A Vanishing Viscosity Approach / Alessi, R.; Crismale, V.; Orlando, G.. - In: JOURNAL OF NONLINEAR SCIENCE. - ISSN 0938-8974. - 29:3(2019), pp. 1041-1094. [10.1007/s00332-018-9511-9]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1485805
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