A Small-Deformation Rate-Independent Continuous-Flow Model for Elasto-Plastic Frames Allowing Rapid Fatigue Predictions in Metallic Structures

Fatigue analysis in metallic frame structures can be challenging due to associated computational costs; if localized plasticity is involved, then the approach of three-dimensional (3D) continuum plasticity models for direct computation of stresses will be infeasible for the analysis of cyclic loading that would need to be modeled in medium- to high-cycle fatigue and vibratory fatigue applications. This difficulty is particularly accentuated in architected structures, for which high-resolution 3D finite element analysis (FEA) would be prohibitively expensive. In this work, we propose an alternative approach based on the use of novel elasto-plastic frame model with continuous flow (i.e. no sharp yield function) for modeling 3D frame and lattice structures. Rather than splitting the strains (as is done in classical plasticity) we split the deformation measures, extension, curvature and twist, into elastic and plastic components and postulate a rate type evolution rule for the plastic variables in terms of the stress resultants (axial force, bending moment, and torque). The combination of structural models together with the use of elasto-plastic operator split to solve the resulting boundary value problem allows for much faster determination of localized plasticity than continuum models can provide. The use of a continuous transition from elastic to rate-independent plasticity (as opposed to an abrupt change with classical plasticity models) allows us to capture localized microplasticity and determine resulting fatigue progression using a cycle-count-free, plastic work-based approach, formulated in terms of the curvatures and resultants. We demonstrate that (a) the model is able able to reproduce the response of 3D FEA with very few elements and (b) the model has the ability to rapidly predict the fatigue life under variable amplitude combined loading with relatively few frame elements.