From patterns in turbulence to the buckling of shells – the role of unstable invariant solutions in nonlinear mechanics
Emergent Complexity in Physical Systems Laboratory, EPFL Lausanne
Date/Time: May 6, Thursday, 12:15-13:15
The transition to turbulence of fluid flows is ubiquitous, arising in our every-day experience when we ride a bicycle or take off in an airplane. Despite this ubiquity, the laminar-turbulent transition in wall-bounded flows is one of the least understood phenomena in fluid mechanics. During transition, the flow may self-organize into patterns with regular spatial and temporal structure, whose origins remain unexplained. A canonical flow exhibiting a large variety of complex spatio-temporal flow patterns is thermal convection in a fluid layer between two parallel plates kept at different temperature and inclined against gravity. We study the dynamics of the so-called inclined layer convection (ILC) system, using a fully nonlinear dynamical systems approach based on a state space analysis of the governing equations. Exploiting the computational power of our highly parallelized numerical continuation tools (www.channelflow.ch), we construct a large set of invariant solutions of ILC and discuss their bifurcation structure. We show that unstable equilibria, travelling waves, periodic orbits and heteroclinic orbits form dynamical networks that support moderately complex chaotic dynamics.
The introduced nonlinear dynamical systems methods centered around invariant solutions are not only revolutionizing our understanding of fluid turbulence but they may also help explain complex behaviour in other intrinsically nonlinear mechanical systems. We will specifically argue that unstable elastic equilibria control when thin-walled cylindrical shells such as rocket walls or soda cans buckle and collapse. This may open avenues towards predicting the notoriously imperfect-sensitive load-carrying capacity of shell structures without prior knowledge of the shell’s defects.
On the coalescence of structural mechanics models with data for condition monitoring
Chair of Structural Mechanics, ETH Zurich
Date/Time: April 8, Thursday, 12:15-13:15
Abstract: The monitoring of the condition of structural systems operating under diverse dynamic loads involves the tasks of simulation (forward engineering), identification (inverse engineering) and maintenance/control actions. The efficient and successful implementation of these tasks is however non-trivial, due to the ever-changing nature of these systems, the variability in their interactive environment, and the polymorphic uncertainties involved. Structural Health Monitoring (SHM) attempts to tackle these challenges by exploiting information stemming from sensor networks. SHM comprises a hierarchy across levels of increasing complexity aiming to i) detect damage, ii) localize and iii) quantify damage, and iv) finally offer a prognosis over the system’s residual life.
When considering higher levels in this hierarchy, including damage assessment and even performance prognosis, purely data-driven methods are found to be lacking. For higher-level SHM tasks, or for furnishing a digital twin of a monitored structure, it is necessary to integrate the knowledge stemming from physics-based representations, relying on the underlying mechanics. This talk discusses implementation of such a hybrid approach to SHM for tackling the aforementioned challenges. Among other topics, we will discuss the potential and limitations of purely data-driven schemes, and the benefits stemming from infusion of data with reduced order structural mechanics models, in support of diagnostics and prognostics for engineered systems.
Particles and snowflakes falling through turbulence
Experimental Fluid Dynamics, ETH Zurich
Date/Time: February 11, Thursday, 12:15-13:15
Abstract: Multiphase flows in which an inertial dispersed phase interacts with a turbulent fluid flow are ubiquitous in environmental, industrial and biomedical settings. Even stripped down to its minimal components, the problem remains complex because of the wide range of scales involved and the multiple physical parameters at play. In this talk, I will first focus on the seemingly simple case of dilute microscopic spherical particles falling through homogeneous air turbulence. A unique experimental facility is leveraged, in which hundreds of jets are individually controlled to produce the largest volume of zero-mean-flow homogeneous turbulence ever created. Using high-resolution laser imaging, I will show how inertial particles group in larger clusters than previously thought, experiencing anomalously large accelerations and a multi-fold increase in fall speed compared to their still-air terminal velocity. At concentrations found in dust storms, the particles also cause a substantial increase in turbulence intensity, at odds with most numerical simulations. The relevance of such observations is demonstrated by outdoor field measurements, in which snowflakes are illuminated and tracked over vertical planes about 30 m^2 using high-speed cameras. The snow particles display strikingly similar behaviors as seen in the laboratory, including self-similar clustering, anomalous accelerations, and turbulence-enhanced fall speed. These findings demonstrate that the fundamental phenomenology of particle-laden turbulence can be leveraged towards the predictive understanding of snow precipitation. They also demonstrate how environmental flows can be used to investigate dispersed multiphase flow physics at Reynolds numbers not accessible in laboratory experiments or numerical simulations.
Mechanical behavior of fluid-induced earthquakes
Laboratory of Experimental Rock Mechanics, EPFL Lausanne
Date/Time: December 10, Thursday, 12:15-13:15
Abstract: Fluids play an important role in fault zone and in earthquakes generation. Fluid pressure reduces the normal effective stress, lowering the frictional strength of the fault, potentially triggering earthquake ruptures. Fluid injection induced earthquakes (FIE) are direct evidence of the effect of fluid pressure on the fault strength. In addition, natural earthquake sequences are often associated with high fluid pressures at seismogenic depths. Although simple in theory, the mechanisms that govern the nucleation, propagation and recurrence of FIEs are poorly constrained, and our ability to assess the seismic hazard that is associated with natural and induced events remains limited. Here we study the role of pore fluid pressure on fault mechanical behavior during the entire seismic cycle. i.e., strain rates from ~10-9/s (fault creep) to ~103/s (co-seismic slip). We reproduced at the scale of the laboratory miniature injection experiments. The velocity of the rupture propagation front, fault slip, dynamic stress drop and acoustic emission were recorded with a state of-the-art monitoring system. We demonstrated that the nature of seismicity is mostly governed by the initial stress level (i.e pore fluid pressure) along the faults and that the dynamic fault weakening depends on both fluid rheology and thermodynamic.
Phase-field modeling of brittle fracture: an overview and a new paradigm to address multiple solutions
Computational Mechanics Group, ETH Zurich
Date/Time: November 12, Thursday, 12:15-13:15
Abstract: The phase-field modeling approach to fracture has recently attracted a lot of attention due to its remarkable capability to naturally handle fracture phenomena with arbitrarily complex crack topologies in three dimensions. On one side, the approach can be obtained through the regularization of the variational approach to fracture introduced by Francfort and Marigo in 1998, which is conceptually related to Griffith’s view of fracture; on the other side, it can be constructed as a gradient damage model with some specific properties. The functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual computation is typically one out of several local minimizers. Evidence of multiple solutions induced by small perturbations of numerical or physical parameters was occasionally recorded but not explicitly investigated in the literature.
In the first part of this talk, the speaker gives a brief overview of the phase-field approach to fracture and of recent related research carried out in her group. In the second part of the talk, the focus is placed on the issue of multiple solutions. Here a paradigm shift is advocated, away from the search for one particular solution towards the simultaneous description of all possible solutions (local minimizers), along with the probabilities of their occurrence. We propose the stochastic relaxation of the variational brittle fracture problem through random perturbations of the functional and introduce the concept of stochastic solution represented by random fields. In the numerical experiments, we use a simple Monte Carlo approach to compute approximations to such stochastic solutions. The final result of the computation is not a single crack pattern, but rather several possible crack patterns and their probabilities. The stochastic solution framework using evolving random fields allows additionally the interesting possibility of conditioning the probabilities of further crack paths on intermediate crack patterns.