The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Daniel M Sussman - One of the best experts on this subject based on the ideXlab platform.
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a force level theory of the rheology of entangled rod and chain polymer liquids i tube deformation microscopic yielding and the nonlinear Elastic Limit
Journal of Chemical Physics, 2016Co-Authors: Kenneth S Schweizer, Daniel M SussmanAbstract:We employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two Limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear Elastic Limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an external...
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a force level theory of the rheology of entangled rod and chain polymer liquids i tube deformation microscopic yielding and the nonlinear Elastic Limit
arXiv: Soft Condensed Matter, 2016Co-Authors: Kenneth S Schweizer, Daniel M SussmanAbstract:We employ a first principles, force-level approach to self-consistently construct the anharmonic tube confinement field for entangled fluids of rigid needles and for primitive-path (PP) level chains in two Limiting situations where chain stretching is assumed to either completely relax or remain unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear Elastic Limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a Gaussian analysis of transverse polymer dynamical fluctuations predicts that deformation-induced orientation leads to tube dilation. In contrast, for deformed polymers in which chain stretch does not relax we find tube compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome (a force imbalance) by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear Elastic Limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance is found to occur at a stress of order the equilibrium shear modulus and thus a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from Elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.
Andrew J. Bushby - One of the best experts on this subject based on the ideXlab platform.
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Elastic Limit and strain hardening of thin wires in torsion
Physical Review Letters, 2009Co-Authors: David J. Dunstan, R Bossis, Bruno Ehrler, Stéphane Joly, Andrew J. BushbyAbstract:A theory for the size effect in the strength of wires under torsion is reported and compared with data from thin copper wires. Critical thickness theory is solved rigorously and used to validate a useful approximation which is combined with slip-distance theory modified for a finite structure size. Experimental data with high accuracy around and above the Elastic Limit show excellent agreement with the theory. The results strongly imply that the physical principle is the constraint that size, whether grain size or structure size, puts on allowed dislocation curvature.
C. Mouhot - One of the best experts on this subject based on the ideXlab platform.
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Stability, Convergence to Self-Similarity and Elastic Limit for the Boltzmann Equation for InElastic Hard Spheres
Communications in Mathematical Physics, 2009Co-Authors: S. Mischler, C. MouhotAbstract:We consider the spatially homogeneous Boltzmann equation for inElastic hard spheres , in the framework of so-called constant normal restitution coefficients $${\alpha \in [0,1]}$$ . In the physical regime of a small inElasticity (that is $${\alpha \in [\alpha_*,1)}$$ for some constructive $${\alpha_* \in [0,1)}$$ ) we prove uniqueness of the self-similar profile for given values of the restitution coefficient $${\alpha \in [\alpha_*,1)}$$ , the mass and the momentum; therefore we deduce the uniqueness of the self-similar solution (up to a time translation). Moreover, if the initial datum lies in $${L^1_3}$$ , and under some smallness condition on $${(1-\alpha_*)}$$ depending on the mass, energy and $${L^1 _3}$$ norm of this initial datum, we prove time asymptotic convergence (with polynomial rate) of the solution towards the self-similar solution (the so-called homogeneous cooling state ). These uniqueness, stability and convergence results are expressed in the self-similar variables and then translate into corresponding results for the original Boltzmann equation. The proofs are based on the identification of a suitable Elastic Limit rescaling, and the construction of a smooth path of self-similar profiles connecting to a particular Maxwellian equilibrium in the Elastic Limit, together with tools from perturbative theory of linear operators. Some universal quantities, such as the “quasi-Elastic self-similar temperature” and the rate of convergence towards self-similarity at first order in terms of (1−α), are obtained from our study. These results provide a positive answer and a mathematical proof of the Ernst-Brito conjecture [16] in the case of inElastic hard spheres with small inElasticity.
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stability convergence to self similarity and Elastic Limit for the boltzmann equation for inElastic hard spheres
arXiv: Analysis of PDEs, 2007Co-Authors: S. Mischler, C. MouhotAbstract:We consider the spatially homogeneous Boltzmann equation for {\em inElastic hard spheres}, in the framework of so-called {\em constant normal restitution coefficients} $\alpha \in [0,1]$. In the physical regime of a small inElasticity (that is $\alpha \in [\alpha_*,1)$ for some constructive $\alpha_*>0$) we prove uniqueness of the self-similar profile for given values of the restitution coefficient $\alpha \in [\alpha_*,1)$, the mass and the momentum; therefore we deduce the uniqueness of the self-similar solution (up to a time translation). Moreover, if the initial datum lies in $L^1_3$, and under some smallness condition on $(1-\alpha_*)$ depending on the mass, energy and $L^1_3$ norm of this initial datum, we prove time asymptotic convergence (with polynomial rate) of the solution towards the self-similar solution (the so-called {\em homogeneous cooling state}). These uniqueness, stability and convergence results are expressed in the self-similar variables and then translate into corresponding results for the original Boltzmann equation. The proofs are based on the identification of a suitable Elastic Limit rescaling, and the construction of a smooth path of self-similar profiles connecting to a particular Maxwellian equilibrium in the Elastic Limit, together with tools from perturbative theory of linear operators. Some universal quantities, such as the "quasi-Elastic self-similar temperature" and the rate of convergence towards self-similarity at first order in terms of $(1-\alpha)$, are obtained from our study. These results provide a positive answer and a mathematical proof of the Ernst-Brito conjecture [16] in the case of inElastic hard spheres with small inElasticity.
Kenneth S Schweizer - One of the best experts on this subject based on the ideXlab platform.
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a force level theory of the rheology of entangled rod and chain polymer liquids i tube deformation microscopic yielding and the nonlinear Elastic Limit
Journal of Chemical Physics, 2016Co-Authors: Kenneth S Schweizer, Daniel M SussmanAbstract:We employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two Limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear Elastic Limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an external...
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a force level theory of the rheology of entangled rod and chain polymer liquids i tube deformation microscopic yielding and the nonlinear Elastic Limit
arXiv: Soft Condensed Matter, 2016Co-Authors: Kenneth S Schweizer, Daniel M SussmanAbstract:We employ a first principles, force-level approach to self-consistently construct the anharmonic tube confinement field for entangled fluids of rigid needles and for primitive-path (PP) level chains in two Limiting situations where chain stretching is assumed to either completely relax or remain unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear Elastic Limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a Gaussian analysis of transverse polymer dynamical fluctuations predicts that deformation-induced orientation leads to tube dilation. In contrast, for deformed polymers in which chain stretch does not relax we find tube compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome (a force imbalance) by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear Elastic Limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance is found to occur at a stress of order the equilibrium shear modulus and thus a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from Elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.
Zvi Rosenberg - One of the best experts on this subject based on the ideXlab platform.
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On the relation between the Hugoniot Elastic Limit and the yield strength of brittle materials
Journal of Applied Physics, 1993Co-Authors: Zvi RosenbergAbstract:We derive a new relation between the Hugoniot Elastic Limit (HEL) of brittle materials and their compressive strength (Yc). This relation is based on Griffith’s yield criterion [Proceedings of the 1st Conference on Applied Mechanics, Delft, Holland (1924), p. 55] for brittle behavior in contrast with the traditional relation, which is based on the criteria of Tresca or von Mises. Our newly derived relation results in a larger ratio between the HEL and Yc, in agreement with all the experimental observations on polycrystalline ceramics.