Bifurcation and Stability of Dissipative Systems
Q.S. Nguyen
āĻŽā§â ā§¨ā§Ļā§§ā§Ē ¡ CISM International Centre for Mechanical Sciences āĻāĻŋāĻ¤āĻžāĻĒ 327 ¡ Springer
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The first theme concerns the plastic buckling of structures in the spirit of Hillâs classical approach. Non-bifurcation and stability criteria are introduced and post-bifurcation analysis performed by asymptotic development method in relation with Hutchinsonâs work. Some recent results on the generalized standard model are given and their connection to Hillâs general formulation is presented. Instability phenomena of inelastic flow processes such as strain localization and necking are discussed. The second theme concerns stability and bifurcation problems in internally damaged or cracked colids. In brittle fracture or brittle damage, the evolution law of crack lengths or damage parameters is time-independent like in plasticity and leads to a similar mathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hill can be again obtained from the discussion of the rate response.
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