Buckling of a nonlinearly elastic slab lying on the surface of a liquid with allowance for phase transformation

Victor A. Eremeyev (1)

1 Institut für Mechanik

The equations of the three-dimensional nonlinear theory of elasticity [1] are used to formulate equilibrium conditions with finite strains for an arbitrary thermoelastic body undergoing a phase transformation. These conditions are then used to study the equilibrium of a circular uniform slab lying on the surface of a melt in a gravitational field. We use the model of a non-Hookian material as the governing relation for the material of the slab, this model being one possible generalization of the model of an incompressible linearly elastic body to the case of finite strains. The method of superimposing a small strain on a finite strain [1] is used to study local loss of stability of the slab due to its compression in the radial direction. The critical strains are determined numerically. A similar approach is used to study buckling of the slab in the absence of phase transformation.

Domaines: Mécanique [physics.med-ph]

Victor A. Eremeyev. Buckling of a nonlinearly elastic slab lying on the surface of a liquid with allowance for phase transformation. Journal of Applied Mechanics and Technical Physics, 1991, 32 (3), pp.433-439. ⟨hal-00826425⟩