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- ItemLower nanometer-scale size limit for the deformation of a metallic glass by shear transformations revealed by quantitative AFM indentation(Frankfurt am Main : Beilstein-Institut, 2015) Caron, Arnaud; Bennewitz, RolandWe combine non-contact atomic force microscopy (AFM) imaging and AFM indentation in ultra-high vacuum to quantitatively and reproducibly determine the hardness and deformation mechanisms of Pt(111) and a Pt57.5Cu14.7Ni5.3P22.5 metallic glass with unprecedented spatial resolution. Our results on plastic deformation mechanisms of crystalline Pt(111) are consistent with the discrete mechanisms established for larger scales: Plasticity is mediated by dislocation gliding and no rate dependence is observed. For the metallic glass we have discovered that plastic deformation at the nanometer scale is not discrete but continuous and localized around the indenter, and does not exhibit rate dependence. This contrasts with the observation of serrated, rate-dependent flow of metallic glasses at larger scales. Our results reveal a lower size limit for metallic glasses below which shear transformation mechanisms are not activated by indentation. In the case of metallic glass, we conclude that the energy stored in the stressed volume during nanometer-scale indentation is insufficient to account for the interfacial energy of a shear band in the glassy matrix.
- ItemDeformation characteristics of solid-state benzene as a step towards understanding planetary geology([London] : Nature Publishing Group UK, 2022) Zhang, Wenxin; Zhang, Xuan; Edwards, Bryce W.; Zhong, Lei; Gao, Huajian; Malaska, Michael J.; Hodyss, Robert; Greer, Julia R.Small organic molecules, like ethane and benzene, are ubiquitous in the atmosphere and surface of Saturn’s largest moon Titan, forming plains, dunes, canyons, and other surface features. Understanding Titan’s dynamic geology and designing future landing missions requires sufficient knowledge of the mechanical characteristics of these solid-state organic minerals, which is currently lacking. To understand the deformation and mechanical properties of a representative solid organic material at space-relevant temperatures, we freeze liquid micro-droplets of benzene to form ~10 μm-tall single-crystalline pyramids and uniaxially compress them in situ. These micromechanical experiments reveal contact pressures decaying from ~2 to ~0.5 GPa after ~1 μm-reduction in pyramid height. The deformation occurs via a series of stochastic (~5-30 nm) displacement bursts, corresponding to densification and stiffening of the compressed material during cyclic loading to progressively higher loads. Molecular dynamics simulations reveal predominantly plastic deformation and densified region formation by the re-orientation and interplanar shear of benzene rings, providing a two-step stiffening mechanism. This work demonstrates the feasibility of in-situ cryogenic nanomechanical characterization of solid organics as a pathway to gain insights into the geophysics of planetary bodies.
- ItemNoise enhanced coupling between two oscillators with long-term plasticity(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Lücken, Leonhard; Popovych, Oleksandr V.; Tass, Peter A.; Yanchuk, SerhiySpike time-dependent plasticity is a fundamental adaptation mechanism of the nervous system. It induces structural changes of synaptic connectivity by regulation of coupling strengths between individual cells depending on their spiking behavior. As a biophysical process its functioning is constantly subjected to natural fluctuations. We study theoretically the influence of noise on a microscopic level by considering only two coupled neurons. Adopting a phase description for the neurons we derive a two-dimensional system which describes the averaged dynamics of the coupling strengths. We show that a multistability of several coupling configurations is possible, where some configurations are not found in systems without noise. Intriguingly, it is possible that a strong bidirectional coupling, which is not present in the noise-free situation, can be stabilized by the noise. This means that increased noise, which is normally expected to desynchronize the neurons, can be the reason for an antagonistic response of the system, which organizes itself into a state of stronger coupling and counteracts the impact of noise. This mechanism, as well as a high potential for multistability, is also demonstrated numerically for a coupled pair of Hodgkin-Huxley neurons.
- ItemGlobal existence result for thermoviscoelastic problems with hysteresis : dedicated to the memory of M. Schatzman(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Paoli, Laetitia; Petrov, Adrien; Schatzman, M.We consider viscoelastic solids undergoing thermal expansion and exhibiting hysteresis effects due to plasticity or phase transformations. Within the framework of generalized standard solids, the problem is described in a 3D setting by the momentum equilibrium equation, the flow rule describing the dependence of the stress on the strain history, and the heat transfer equation. Under appropriate regularity assumptions on the data, a local existence result for this thermodynamically consistent system is established, by combining existence results for ordinary differential equations in Banach spaces with a fixed-point argument. Then global estimates are obtained by using both the classical energy estimate and more specific techniques for the heat equation introduced by Boccardo and Gallouet. Finally a global existence result is derived.
- ItemStochastic homogenization of rate-dependent models of monotone type in plasticity(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Heida, Martin; Nesenenko, SergiyIn this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure which can be characterised by random measures. Based on the Fitzpatrick function concept we reduce the study of the asymptotic behaviour of monotone operators associated with our models to the problem of the stochastic homogenization of convex functionals within an ergodic and stationary setting. The concept of Fitzpatricks function helps us to introduce and show the existence of the weak solutions for rate-dependent systems. The derivations of the homogenization results presented in this work are based on the stochastic two-scale convergence in Sobolev spaces. For completeness, we also present some two-scale homogenization results for convex functionals, which are related to the classical Gamma-convergence theory.
- ItemA rate-independent gradient system in damage coupled with plasticity via structured strains(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Bonetti, Elena; Rocca, Elisabetta; Rossi, Riccarda; Thomas, MaritaThis contribution deals with a class of models combining isotropic damage with plasticity. It has been inspired by a work by Freddi and Royer-Carfagni [FRC10], including the case where the inelastic part of the strain only evolves in regions where the material is damaged. The evolution both of the damage and of the plastic variable is assumed to be rate-independent. Existence of solutions is established in the abstract energetic framework elaborated by Mielke and coworkers (cf., e.g., [Mie05, Mie11b]).