On Timoshenko thin elastic inclusions inside elastic bodies

Khludnev AM, Leugering G (2015)

Publication Status: Published

Publication Type: Journal article

Publication year: 2015


Publisher: SAGE Publications (UK and US)

Book Volume: 20

Pages Range: 495-511

Journal Issue: 5

DOI: 10.1177/1081286513505106


The paper concerns the analysis of equilibrium problems for 2D elastic bodies with thin inclusions modeled in the framework of Timoshenko beams. The first focus is on the well-posedness of the model problem in a variational setting. Then delaminations of the inclusions are considered, forming a crack between the elastic body and the inclusion. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. The corresponding variational formulations together with weak and strong solutions are discussed. The model contains various physical parameters characterizing the mechanical properties of the inclusion, such as flexural and shear stiffness. The paper provides an asymptotic analysis of such parameters. It is proved that in the limit cases corresponding to infinite and zero rigidity, we obtain rigid inclusions and cracks with the non-penetration conditions, respectively. Finally, exemplary networks of Timoshenko beams are considered as inclusions as well.

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Khludnev, A.M., & Leugering, G. (2015). On Timoshenko thin elastic inclusions inside elastic bodies. Mathematics and Mechanics of Solids, 20(5), 495-511. https://doi.org/10.1177/1081286513505106


Khludnev, A. M., and Günter Leugering. "On Timoshenko thin elastic inclusions inside elastic bodies." Mathematics and Mechanics of Solids 20.5 (2015): 495-511.

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