Safety assessment of structures can be obtained employing limit design to overcome uncertainties concerning actual response due to inelastic constitutive behavior and more generally to non-linear structural response and loads’ random variability. The limit analysis is used for evaluating the safety of the structures directly starting from load level without any knowledge of the load history. In the paper, the lower bound calculation is proposed where a new strain-based approach is used that allowed describing the residual stress and displacement in terms of permanent strain. The strategy used the permanent strain as the effective parameters of the procedure so that it was possible to assess the ductility requirements for the complete load program developed till collapse or shakedown. The procedure is compared to experimental results obtained on aluminum beams in shakedown.

A phenomenological constitutive model is developed to describe the uniaxial transformation ratcheting behaviors of super–elastic shape memory alloy (SMA) by employing a cosine–type phase transformation equation with the initial martensite evolution coefficient that can capture the feature of the predictive residual martensite accumulation evolution and the nonlinear hysteresis loop on a finite element (FE) analysis framework. The effect of the applied loading level on transformation ratcheting are considered in the proposed model. The evolutions of transformation ratcheting and transformation stresses are constructed as the function of the accumulated residual martensite volume fraction. The FE implementation of the proposed model is carried out for the numerical analysis of transformation ratcheting of the SMA bar element. The integration algorithm and the expression of consistent tangent modulus are deduced in a new form for the forward and reverse transformation. The numerical results are compared with those of existing model and the experimental results to show the validity of the proposed model and its FE implementation in transformation ratcheting. Finally, a FE modeling is established for a repeated preload analysis of SMA bolted joint

The present study evaluates ratcheting response of notched and press-fitted Al 7075-T6 specimens under stress-controlled asymmetric cycles. The degree of interference fit (DIF) directly influenced progressive plastic strain magnitude and rate at notch root region. Local ratcheting at the hole-pin interference region was analyzed by means of two kinematic hardening rules of Ahmadzadeh-Varvani (A-V) and Chaboche coupled with the Neuber rule. Ratcheting strains at notch root of aluminum samples with DIF=0 (non-press-fitting samples) were measured to be highest in magnitude. For the press-fitted samples, however ratcheting strains dropped noticeably as DIF increased from 1% to 2%. Press-fitted samples plastically deformed the perimeter edge of notches and improved materials locally at the notch edge, resulting in a better resistance against ratcheting progress. Local ratcheting at different distances of 0.5, 1.3 and 3.0 mm from the notch root were evaluated for both pinned and unpinned samples through the hardening rules and compared with those of measured values. The predicted ratcheting curves by means of the A-V and Chaboche hardening rules closely agreed with experimental data and respectively positioned above and below the measured data.