Damageable elastic buckling bodies with a crack

Abstract

Damageable elastic buckling beams with a crack motivate to formulate a differential equation system which can be extended to higher-dimensional problems. Elastic buckling bodies are assumed to evolve their damage and break apart from an edge crack. A nonlinear variational formulation is derived that is equivalent to a partial differential equation, subject to crack conditions and boundary conditions. Then, time discretizations are applied to the variational formulation and a first-order nonlinear ordinary differential equation which describes the evolution of damage. We pass to limits as time step sizes tend to zero, to prove that numerical trajectories are convergent to solutions. The fully discrete numerical schemes for a one-dimensional problem are proposed, and some numerical simulations are presented as well.

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Correspondence to Jeongho Ahn.

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Ahn, J. Damageable elastic buckling bodies with a crack. Z. Angew. Math. Phys. 71, 66 (2020). https://doi.org/10.1007/s00033-020-1292-y

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Keywords

  • Elastic buckling bodies
  • Crack
  • Damage functions
  • Differential equation system
  • Nonlinear variational formulation

Mathematics Subject Classification

  • 74M15
  • 34B60
  • 35L85