Bifurcation and stability of dissipative systems
Springer Verlag, 1993 - Mathematics - 291 pages
The first theme concerns the plastic buckling of structures in the spirit of Hill's classical approach. Non-bifurcation and stability criteria are introduced and post-bifurcation analysis performed by asymptotic development method in relation with Hutchinson's work. Some recent results on the generalized standard model are given and their connection to Hill's 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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Bifurcation and Stability of TimeIndependent Standard Dissipative Systems
Theory of Bifurcation and Instability in TimeIndependent Plasticity
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applied assumed assumption beam behaviour bifurcated branch bifurcation in velocities bifurcation modes bifurcation point bifurcation problem bifurcation theory boundary value problem brittle cavitation classical comparison solid complementing condition configuration considered constitutive equations constitutive law convex corresponding crack criterion critical load cross-section damage defined deformation gradient deformation path deformation process denotes discontinuities discussed displacement dissipative dissipative systems domain eigenstate elastic elastic-plastic solids elliptic energy equilibrium example expression finite formulation Fredholm operator function fundamental solution given gradient hardening Hill's homogeneous Hutchinson incremental initial interface kinematic linear localization material Mech mechanics moduli NGUYEN nonlinear obtained Phys plane strain plastic buckling positive definite post-bifurcation post-buckling potential primary bifurcation point quasi-static rate problem respectively satisfied shear band singular stability of equilibrium stress symmetric tangent modulus tensor theorem time-independent TRIANTAFYLLIDIS Tvergaard uniqueness unloading zone variational inequality vector velocity field yield surface zero