2021/07/02 by Simon Grützner, Adrian Muntean, Grützner, Simon +1
Computer Science · Engineering · Mathematics · #35R30 #74A45 #74G75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems #Topology Optimization in Engineering #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2107.01082
openalex publication_date 2021/07/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We present a quasi-static elasticity model that accounts for damage evolution\nbased on the ideas of Kachanov 1958 and and Rabotnov 1968. We analyze the\nresulting strongly nonlinear system of differential equations in view of\nwell-posedness. The specific feature is that the displacements are connected to\nthe damage evolution equation via a Nemytskii- or superposition- operator. The\nnovelty in this work is that we present an inverse problem in a parameter\nidentification setting, in which we are able to identify the shape of this\nNemytskii-operator. From the material modelling point of view, the relation of\nmaterial damage and displacements is modelled by the shape of this operator. We\nestablish the Fr 'echet-derivative of the forward operator as well as the\nadjoint of the derivative and characterize both via systems of linear\ndifferential equations. We prove ill-posedness of the inverse problem and\nprovide a sufficient condition for the classical nonlinear Landweber method to\nconverge.\n