On the combined gradient-stochastic plasticity model: Application to Mo-micropillar compression

Internal Length Gradient (ILG) Material Mechanics Across Scales and Disciplines

“…Mo-micropillars with different diameters (d) (reprinted from [135] with the permission of AIP Publishing).…”

“…at the end of the elastic region. In this case the local yield [135] with the permission of AIP Publishing).…”

“…at the end of the elastic region. In this case the local yield strength loc y  is related to the local strain at yield loc y  through the relation[135] E is, as usually, the modulus of elasticity. Moreover, the micropillars are divided in a number of slices with size  , i.e.…”

Gradient Extension of Classical Material Models: From Nuclear & Condensed Matter Scales to Earth & Cosmological Scales

“…The resulting combined gradient-stochastic models can capture the observed behavior at micro/nano scales, including size dependent serrated stress-strain graphs and intermittent plasticity phenomena. Some initial results along this direction have recently been reported by the author and his coworkers [30] by resorting to empirical Weibull distribution functions, as also reviewed in [1]. This approach can be adopted to describe existing experimental data on stress drops/strain jumps routinely observed in micro tension/compression and nanoindentation laboratory tests.…”

“…Standard deterministic ILG models cannot provide any information on measured statistical aspects of plastic deformation, such as fractal dimensions for deformation patterns; power-law exponents for dislocation avalanches [33]; and strain bursts recorded during nanoindentation [34] or micro/nanopillar compression tests [14,30]. When differential equations cannot be invented to interpret experimental data and simulations, system characterization is left to statistical analyses for establishing fractality and universal power-laws.…”