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Journal of Elasticity

, Volume 135, Issue 1–2, pp 375–397 | Cite as

The State of Stress and Strain Adjacent to Notches in a New Class of Nonlinear Elastic Bodies

  • Vojtěch Kulvait
  • Josef Málek
  • K. R. RajagopalEmail author
Article
  • 94 Downloads

Abstract

In this paper we study the deformation of a body with a notch subject to an anti-plane state of stress within the context of a new class of elastic models. These models stem as approximations of constitutive response functions for an elastic body that is defined within the context of an implicit constitutive relation between the stress and the deformation gradient. Gum metal and many metallic alloys are described well by such constitutive relations. We consider the state of anti-plane stress of a body with a smoothened V-notch within the context of constitutive relations for the linearized strain in terms of a power-law for the stretch. The problem is solved numerically and the convergence and the stability of the solution is studied.

Keywords

Implicit constitutive theory Power law models Small strain elasticity 

Mathematics Subject Classification

74B20 74B15 35Q74 

Notes

Acknowledgements

Josef Málek thanks the Czech Science Foundation for support through the project 18-12719S. K.R. Rajagopal thanks the Office of Naval Research for support of this work.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Vojtěch Kulvait
    • 1
  • Josef Málek
    • 1
  • K. R. Rajagopal
    • 2
    Email author
  1. 1.Charles University, Faculty of Mathematics and PhysicsMathematical InstitutePragueCzech Republic
  2. 2.Department of Mechanical EngineeringTexas A&M UniversityCollege StationUSA

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