Shakedown in elastic contact problems with Coulomb friction

AbstractElastic systems with frictional interfaces subjected to periodic loading are sometimes predicted to ‘shake down’ in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elastic–plastic constitutive behaviour have prompted various authors to speculate that Melan’s theorem might apply to them – i.e., that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down.In this paper, we prove this result for ‘complete’ contact problems in the discrete formulation (i) for systems with no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions and (ii) for certain two-dimensional problems in which the friction coefficient at each node is less than a certain critical value. We also present counter-examples for all systems that do not fall into these categories, thus giving a definitive statement of the conditions under which Melan’s theorem can be used to predict whether such a system will shake down

Na–Ni–H phase formation at high pressures and high temperatures: hydrido complexes [NiH5]3– versus the perovskite NaNiH3

The Na-Ni-H system was investigated by in situ synchrotron diffraction studies of reaction mixtures NaH-Ni-H-2 at around 5, 10, and 12 GPa. The existence of ternary hydrogen-rich hydrides with compositions Na3NiH5 and NaNiH3, where Ni attains the oxidation state II, is demonstrated. Upon heating at similar to 5 GPa, face-centered cubic (fcc) Na3NiH5 forms above 430 degrees C. Upon cooling, it undergoes a rapid and reversible phase transition at 330 degrees C to an orthorhombic (Cmcm) form. Upon pressure release, Na3NiH5 further transforms into its recoverable Pnma form whose structure was elucidated from synchrotron powder diffraction data, aided by first-principles density functional theory (DFT) calculations. Na3NiH5 features previously unknown square pyramidal 18- electron complexes NiH53-. In the high temperature fcc form, metal atoms are arranged as in the Heusler structure, and ab initio molecular dynamics simulations suggest that the complexes are dynamically disordered. The Heusler-type metal partial structure is essentially maintained in the low temperature Cmcm form, in which NiH53- complexes are ordered. It is considerably rearranged in the low pressure Pnma form. Experiments at 10 GPa showed an initial formation of fcc Na3NiH5 followed by the addition of the perovskite hydride NaNiH3, in which Ni(II) attains an octahedral environment by H atoms. NaNiH3 is recoverable at ambient pressures and represents the sole product of 12 GPa experiments. DFT calculations show that the decomposition of Na3NiH5 = NaNiH3 + 2 NaH is enthalpically favored at all pressures, suggesting that Na3NiH5 is metastable and its formation is kinetically favored. Ni-H bonding in metallic NaNiH3 is considered covalent, as in electron precise Na3NiH5, but delocalized in the polyanion [NiH3](-).Funding Agencies|Swedish Research Council (VR)Swedish Research Council [2019-05551]; Swedish Government Strategic Research Area in Materials Science on Advanced Functional Materials at at Linkoping University (Faculty Grant SFO-Mat-LiU) [200900971]; Carl Tryggers Stiftelse (CTS) [16:198, 17:206]</p