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Singularity sets of constant principal strain deformations. (English) Zbl 1007.74007

Summary: We show that if \(f\) is a mapping with constant principal strains (cps-mapping) of a planar domain of the form \(D\setminus S\), where \(D\) is itself a domain and \(S\) is a closed subset of \(D\) with linear measure \(0\), then \(f\) has an extension to a cps-mapping of \(D\setminus S'\), where \(S'\subset S\) has no accumulation points in \(D\). The proof uses properties of cps-mappings attributable to the nonlinear hyperbolic nature of the underlying system of partial differential equations as well as results about their behavior in neighborhoods of isolated singularities.

MSC:

74A05 Kinematics of deformation
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