Hysteretic Beam Finite-Element Model Including Multiaxial Yield/Capacity Surface Evolution with Degradations

A multiaxial degrading hysteretic model is developed, enabling consistent multiaxial yield/capacity surface evolution with degradations, and is appropriately incorporated in a finite-element framework using hysteretic Timoshenko beam elements. Degradation phenomena are introduced in this model in the form of either symmetric or asymmetric strength degradation, stiffness degradation, pinching functions, and various combinations thereof. More specifically, a new strength degradation function is developed and enhancements in other existing functions are suggested to simulate the physically observed degradation phenomena in structural elements. The degradation functions are then employed in a multiaxial classical damage-plasticity framework to satisfy the consistency criterion of the yield/capacity surface, thereby resulting in a set of new multiaxial hysteretic evolution equations. The proposed evolution equations are specifically formulated so as they could be seamlessly incorporated into a hysteretic finite-element formulation, using appropriate displacement and hysteretic interpolation functions, to satisfy the exact equilibrium conditions and model distributed plasticity characteristics, thereby avoiding any shear locking effects. As such, the proposed hysteretic finite-element model accounts for equilibrium, distributed plasticity, degradations, and multiaxial inelasticity with capacity interactions in a single consistent and unified framework. Constant system matrices are employed that do not require updating throughout the analysis, while the degradations and inelasticity are captured through the suggested multiaxial hysteretic evolution equations. An efficient numerical solution scheme is also devised, where the finite-element model can be expressed explicitly in terms of first order ordinary differential equations (ODEs), rather than a set of complex differential-algebraic equations for quasi-static cases. The resulting system of equations can be then straightforwardly solved using any standard ODE solver, without any required linearization. Numerical illustrations and experimental verifications are provided to demonstrate the performance and utility of the suggested methodology.