Mechanics of marginal solids: Length, strain, and time scales

Network materials, foams, and emulsions are ubiquitous in our daily life. We have a good intuition about how they respond as we handle them, but our theoretical understanding is poor. One of their most interesting features is that they are unusually fragile and appear to switch between solid and liquid state seamlessly. In fact, foams and emulsions undergo a non-equilibrium phase transition as their packing fraction increases - this is the jamming transition. Networks show a similar transition as their connectivity increases, where the material switches from sloppy to rigid.The fact that these materials undergo a phase transition, opens up the theoretical toolset of statistical mechanics. An important part of current research is therefore dedicated to finding diverging length and time scales and investigating the critical behavior of the systems in detail. Because the systems in question are highly disordered, analytical modeling is challenging. At the same time there are significant experimental obstacles to approaching the critical point closely. For this reason, the development of simulation software plays an important role - all data presented in this thesis is generated through simulations. As the subtitle of this dissertation suggests, our findings concern length, strain, and time scales which can be found in the linear response to external forces.Engineering Thermodynamic

Moduli and modes in the Mikado model

We determine how low frequency vibrational modes control the elastic shear modulus of Mikado networks, a minimal mechanical model for semi-flexible fiber networks. From prior work it is known that when the fiber bending modulus is sufficiently small, (i) the shear modulus of 2D Mikado networks scales as a power law in the fiber line density, G ∼ ρα+1, and (ii) the networks also possess an anomalous abundance of soft (low-frequency) vibrational modes with a characteristic frequency ωκ ∼ ρβ/2. While it has been suggested that α and β are identical, the preponderance of evidence indicates that α is larger than theoretical predictions for β. We resolve this inconsistency by measuring the vibrational density of states in Mikado networks for the first time. Supported by these results, we then demonstrate analytically that α = β + 1. In so doing, we uncover new insights into the coupling between soft modes and shear, as well as the origin of the crossover from bending- to stretching-dominated response. This journal is Engineering ThermodynamicsMulti Phase System

Normal stresses, contraction, and stiffening in sheared elastic networks

When elastic solids are sheared, a nonlinear effect named after Poynting gives rise to normal stresses or changes in volume. We provide a novel relation between the Poynting effect and the microscopic Grüneisen parameter, which quantifies how stretching shifts vibrational modes. By applying this relation to random spring networks, a minimal model for, e.g., biopolymer gels and solid foams, we find that networks contract or develop tension because they vibrate faster when stretched. The amplitude of the Poynting effect is sensitive to the network's linear elastic moduli, which can be tuned via its preparation protocol and connectivity. Finally, we show that the Poynting effect can be used to predict the finite strain scale where the material stiffens under shear.Engineering Thermodynamic

Viscous forces and bulk viscoelasticity near jamming

When weakly jammed packings of soft, viscous, non-Brownian spheres are probed mechanically, they respond with a complex admixture of elastic and viscous effects. While many of these effects are understood for specific, approximate models of the particles' interactions, there are a number of proposed force laws in the literature, especially for viscous interactions. We numerically measure the complex shear modulus G* of jammed packings for various viscous force laws that damp relative velocities between pairs of contacting particles or between a particle and the continuous fluid phase. We find a surprising sensitive dependence of G* on the viscous force law: the system may or may not display dynamic critical scaling, and the exponents describing how G* scales with frequency can change. We show that this sensitivity is closely linked to manner in which viscous damping couples to floppy-like, non-affine motion, which is prominent near jamming.Engineering Thermodynamic

Nonlocal elasticity near jamming in frictionless soft spheres

We use simulations of frictionless soft sphere packings to identify novel constitutive relations for linear elasticity near the jamming transition. By forcing packings at varying wavelengths, we directly access their transverse and longitudinal compliances. These are found to be wavelength dependent, in violation of conventional (local) linear elasticity. Crossovers in the compliances select characteristic length scales, which signify the appearance of nonlocal effects. Two of these length scales diverge as the pressure vanishes, indicating that critical effects near jamming control the breakdown of local elasticity. We expect these nonlocal constitutive relations to be applicable to a wide range of weakly jammed solids, including emulsions, foams, and granulates.Engineering Thermodynamic

A minimal-length approach unifies rigidity in underconstrained materials

We present an approach to understand geometric-incompatibility–induced rigidity in underconstrained materials, including subisostatic 2D spring networks and 2D and 3D vertex models for dense biological tissues. We show that in all these models a geometric criterion, represented by a minimal length ℓ¯min, determines the onset of prestresses and rigidity. This allows us to predict not only the correct scalings for the elastic material properties, but also the precise magnitudes for bulk modulus and shear modulus discontinuities at the rigidity transition as well as the magnitude of the Poynting effect. We also predict from first principles that the ratio of the excess shear modulus to the shear stress should be inversely proportional to the critical strain with a prefactor of 3. We propose that this factor of 3 is a general hallmark of geometrically induced rigidity in underconstrained materials and could be used to distinguish this effect from nonlinear mechanics of single components in experiments. Finally, our results may lay important foundations for ways to estimate ℓ¯min from measurements of local geometric structure and thus help develop methods to characterize large-scale mechanical properties from imaging data.Accepted Author ManuscriptEngineering Thermodynamic

Post-anaesthesia pulmonary complications after use of muscle relaxants (POPULAR): a multicentre, prospective observational study

Background Results from retrospective studies suggest that use of neuromuscular blocking agents during general anaesthesia might be linked to postoperative pulmonary complications. We therefore aimed to assess whether the use of neuromuscular blocking agents is associated with postoperative pulmonary complications.Methods We did a multicentre, prospective observational cohort study. Patients were recruited from 211 hospitals in 28 European countries. We included patients (aged >= 18 years) who received general anaesthesia for any in-hospital procedure except cardiac surgery. Patient characteristics, surgical and anaesthetic details, and chart review at discharge were prospectively collected over 2 weeks. Additionally, each patient underwent postoperative physical examination within 3 days of surgery to check for adverse pulmonary events. The study outcome was the incidence of postoperative pulmonary complications from the end of surgery up to postoperative day 28. Logistic regression analyses were adjusted for surgical factors and patients' preoperative physical status, providing adjusted odds ratios (ORadj) and adjusted absolute risk reduction (ARR(adj)). This study is registered with ClinicalTrials. gov, number NCT01865513.Findings Between June 16, 2014, and April 29, 2015, data from 22 803 patients were collected. The use of neuromuscular blocking agents was associated with an increased incidence of postoperative pulmonary complications in patients who had undergone general anaesthesia (1658 [7.6%] of 21 694); ORadj 1.86, 95% CI 1.53-2.26; ARR(adj) -4.4%, 95% CI -5.5 to -3.2). Only 2.3% of high-risk surgical patients and those with adverse respiratory profiles were anaesthetised without neuromuscular blocking agents. The use of neuromuscular monitoring (ORadj 1.31, 95% CI 1.15-1.49; ARR(adj) -2.6%, 95% CI -3.9 to -1.4) and the administration of reversal agents (1.23, 1.07-1.41; -1.9%, -3.2 to -0.7) were not associated with a decreased risk of postoperative pulmonary complications. Neither the choice of sugammadex instead of neostigmine for reversal (ORadj 1.03, 95% CI 0.85-1 center dot 25; ARR(adj) -0.3%, 95% CI -2.4 to 1.5) nor extubation at a train-of-four ratio of 0.9 or more (1.03, 0.82-1.31; -0.4%, -3.5 to 2.2) was associated with better pulmonary outcomes.Interpretation We showed that the use of neuromuscular blocking drugs in general anaesthesia is associated with an increased risk of postoperative pulmonary complications. Anaesthetists must balance the potential benefits of neuromuscular blockade against the increased risk of postoperative pulmonary complications