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 new degradation functions are then employed in a multiaxial classical damageplasticity 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 distributed plasticity, 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 1 Amir, October 4, 2019 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. Amir, October 4, 2019 et al. (2014) have shown the capability of such uniaxial hysteretic models to fully satisfy Drucker or Ilyushin conditions of plasticity, including for short unloading-reloading paths. These and other hysteretic variants, e.g. Papakonstantinou et al. (2008), Miah et al. (2015), among others, have been extensively used in various applications to simulate the response of a diverse array of materials and structural components/devices, as summarized in Ismail et al. (2009). These models are mainly of a phenomenological nature, and the progression in this work is towards a model based on multiaxial classical plasticity and damage theories, as described in detail subsequently. In the original formulation of Baber and Wen (1981), the strength degradation is defined by a linearly increasing function of the energy ...
