Second-order bifurcation in elastic-plastic solidS

On the Algorithmic Implementation of a Material Model Accounting for the Effects of Martensitic Transformation

“…For a low stress level (-10 MPa) the difference in the amount of variant 22 and the fractions of the variants 15 and 16 is less pronounced, indicating that the material exhibits a significant elongation due to the orientation effect if the applied load has been set to a high enough value ( Figure Sa). Note also that the overall transformation kinetics depicted in Figures 4 and 5 shows the typical sigmoidal shape that has also been observed in the experiments [3,21,22], even though the dragging forces, interpretable as transformation hardening terms, evolve according to equation (20) featuring an instantaneous sharp transition at the onset of transformation.…”

“…In earlier papers [3] it has been proven that the KM kinetics does not reflect the martensite evolution sufficiently well, especially right after the onset of transformation, because it does not account for the creation of nucleation sites within a small temperature range around M, already appearing as a moderate increase in the martensite fraction as a function of temperature. Nonetheless, for the mere purpose of studying the variant selection mechanism the hardening law according to equation (20) will be a satisfactory approximation. The constant in this equation can be calibrated from the transformation kinetics of the load-free specimen found in earlier experiments (see e.g.…”

“…Obviously martensitic transformation starts at significantly higher temperatures under the influence of a given load. The dotted line in Figure 3 represents the Koistinen-Marburger fit of the data pertaining to the stress-free case, which is the one that will be used for calibrating the constant in equation (20). Note that this constant also implicitly contains the slope of the chemical driving force P~CPchem being a linear function of temperature over a wide range.…”

“…* the resulting polyhedron has to be convex anywhere in stress space. The issue of the convexity has profoundly been treated by Petryk and Thermann [20] for the case of crystal plasticity with a yield function similar to what is expected for…”

An elastoplastic framework for granular materials becoming cohesive through mechanical densification. Part II – the formulation of elastoplastic coupling at large strain

“…Since the existing large strain formulations do not appear to be easily generalizable to admit a coupling between elastic and plastic deformations, we have recurred to the early formulation by Hill and Rice (1973) (see also Hill, 1978;Petryk and Thermann 1985;Bigoni, 1996;, which (although not explicitely mentioned) has been formulated in such a generality to include coupling. Following this approach, the level of generality is so high that the following choices are not required: stress/strain measures [except that these are work-conjugate (Hill, 1968)], elastic and plastic strain decomposition, elastic law, yield function, flow and hardening rules.…”