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Identifying processes governing damage evolution in quasi-static elasticity: Part 1- Analysis
University of Bremen, DEU.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
2021 (English)In: Advances in Mathematical Sciences and Applications, E-ISSN 1343-4373, Vol. 30, no 2, p. 305-334Article in journal (Refereed) Published
Abstract [en]

We present a quasi-static elasticity model that accounts for damage evolution. We show well-posedness of the resulting strongly nonlinear system of differential equations. The specific feature is the connection of dis-placements to damage evolution via a Nemytskii- or superposition- operator. From a material modelling perspective, the shape of this operator defines the afforementioned connection. The novelty in this work is the presentation of an inverse problem to identify the shape of this Nemytskii-operator. We establish the Fréchet-derivative of the forward operator as well as the adjoint of the derivative and characterize both via systems of linear differential equations. We prove ill-posedness of the inverse problem and provide asufficient condition for the classical nonlinear Landweber method to converge.

Place, publisher, year, edition, pages
GAKKO TOSHO , 2021. Vol. 30, no 2, p. 305-334
Keywords [en]
damage mechanics, inverse problems, partial differential equations, parameter identification
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-85475Scopus ID: 2-s2.0-85125026445OAI: oai:DiVA.org:kau-85475DiVA, id: diva2:1579757
Available from: 2021-07-10 Created: 2021-07-10 Last updated: 2022-10-18Bibliographically approved

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Muntean, Adrian

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