A lower bound on bifurcation buckling of viscoplastic structures
The buckling of structures of elastic-viscoplastic materials is a stability problem that does not admit a realistic bifurcation formulation in the classical manner. In the absence of imperfections and inertial effects, the standard bifurcation criterion leads only to elastic buckling since an instantaneous jump in strain rate would develop at the critical condition. However, an expression for the “short time” inelastic tangent modulus at the pre-buckling strain rate can be developed from an appropriate incremental constitutive theory and this can be used in the quasi-static bifurcation buckling condition appropriate to the structure and loading. Such a buckling value can be interpreted as a lower bound on the actual instability condition. For the case of structures with initial imperfections, the calculation of local inelastic tangent moduli at the current state should lead to close correspondence between bifurcation and instability. Under creep conditions, the procedure gives approximate creep buckling times for both perfect and initially imperfect structures. For situations where the buckling mode generates abrupt changes in the multiaxial stress state, modifications to the reference constitutive theory are required to properly represent the governing physics. In this manner, the procedure seems capable of indicating buckling values consistent with test results without relying on a “deformation” type plasticity theory.
KeywordsDirectional Hardening Isotropic Hardening Constitutive Theory Tangent Modulus Plastic Strain Rate
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