Second-order work criterion: from material point to boundary value problems

Abstract : Although the concept of the second-order work criterion dates back to the middle of the past century, its physical meaning often continues to be debated. Recent papers have established that a certain class of instabilities, related to the occurrence of an outburst in kinetic energy, could be properly detected by the vanishing of the second-order work. This manuscript attempts to extend the second-order work formalism to boundary value problems. For this purpose, the role of the boundary stiffness tensor (relating external forces and displacement components) is put forward in the occurrence of instability by divergence. Omitting body forces, a global method is then given to compute the second-order work terms directly. The capability of this formalism is finally demonstrated in the context of engineering issues.
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François Nicot, Jean Lerbet, Félix Darve. Second-order work criterion: from material point to boundary value problems. Acta Mechanica, Springer Verlag, 2017, 228 (7), pp.2483--2498. ⟨10.1007/s00707-017-1844-1⟩. ⟨hal-01515726⟩

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