We study the elasto-plastic behaviour of materials made of individual (discrete) objects, such as a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual objects is taken into account through statistical quantities, such as the elastic strain of the structure, the yield strain and the yield function. The past history of the sample plays no explicit role, except through its effect on these statistical quantities. They suffice to relate the discrete scale with the collective, global scale. At this global scale, the material behaves as a continuous medium; it is described with tensors such as elastic strain, stress and velocity gradient. We write the differential equations which predict their elastic and plastic behaviour in both the general case and the case of simple shear. An overshoot in the shear strain or shear stress is interpreted as a rotation of the deformed structure, which is a purely tensorial effect that exists only if the yield strain is at least of order 0.3. We suggest practical applications, including: when to choose a scalar formalism rather than a tensorial one; how to relax trapped stresses; and how to model materials with a low, or a high, yield strain.
Stress Relaxation Driven by Elementary Plastic Events in Non-Ageing Liquid Foams
Lund University（隆德大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Paul Scherrer Institut（保罗谢尔研究所）；Université Côte d’Azur（蔚蓝海岸大学）；Technical University of Denmark（丹麦技术大学）；ENS de Lyon（里昂高等师范学校）；Institut Universitaire de France (IUF)（法国高等研究院）
We study the deflection and fluctuations of a clamped elastic fiber embedded in 2D foam under quasistatic flow. At all times, the fiber conformation results from the elasto-capillary interactions with the foam. We independently measure the action of capillary and pressure forces on the fiber, and show that the fiber deformation is adequately described assuming a uniform continuous normal force acting on it. When bending energy exceeds a threshold value, the fiber relaxes to a less deflected shape, generating a cascade of plastic rearrangements within the foam, and the process repeats periodica…
我们制定和应用一个连续模型，结合弹性，屈服应力，塑性和粘性阻力。它是由Debregeas等人[G. Debregeas，H. Tabuteau和J. - M. di Meglio，Phys. Rev. Lett. 87，178305（2001）]和Wang等人[Y. Wang，K. Krishan和M. Dennin，Phys.Rev.E73，031401（2006）]，并且成功地展示了它们的主要特征，即指数衰减的速度分布和应变局部化。瞬态效应也被确定。
The mechanical response of syntactic foams comprising hollow thermoplastic microspheres (HTMs) embedded in a polyurethane matrix were experimentally examined under uniaxial compressive strain. Phenomenological strain energy models were subsequently developed to capture both the axial stress-strain and transverse strain response of the foams. HTM syntactic foams were found to exhibit increased small-strain stiffness with reduced density, revealing a highly tuneable and extremely lightweight syntactic foam blend for applications. The foams were also found to become strongly compressible at large…
Multiscale stress dynamics in sheared liquid foams revealed by tomo-rheoscopy
Lund University（隆德大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；ENS de Lyon, Université de Lyon（里昂高等师范学校，里昂大学）；Paul Scherrer Institut（保罗谢尔研究所）；Université Côte d’Azur（蔚蓝海岸大学）；Institut Universitaire de France (IUF)（法国大学学院）；Technical University of Denmark（丹麦技术大学）
The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods to extract the size and orientation of these shear transformations in simulations of a two-dimensional (2D) athermal model glass under simple shear. We find that the shear angles are broadly distributed around the macroscopic shear direction, with a more or less Gaussian distribution with a standard deviation of around 20 $\bullet$ about the direction of ma…
Three-dimensional foam flow resolved by fast X-ray tomographic microscopy
CNRS（法国国家科学研究中心）；Institut de Physique de Rennes（雷恩物理研究所）；Institute for Biomedical Engineering, University and ETH Zurich（苏黎世联邦理工学院生物医学工程研究所）；ETH Zurich（苏黎世联邦理工学院）；Swiss Light Source, Paul Scherrer Institute（瑞士光子源，保罗谢尔研究所）；Laboratoire de Physique, ENS Lyon（里昂高等师范学校物理实验室）
Plastic rearrangements play a crucial role in the characterization of soft-glassy materials, such as emulsions and foams. Based on numerical simulations of soft-glassy systems, we study the dynamics of plastic rearrangements at the hydrodynamic scales where thermal fluctuations can be neglected. Plastic rearrangements require an energy input, which can be either provided by external sources, or made available through time evolution in the coarsening dynamics, in which the total interfacial area decreases as a consequence of the slow evolution of the dispersed phase from smaller to large drople…
We study numerically the yielding transition of a two dimensional model glass subjected to athermal quasi-static cyclic shear deformation, with the aim of investigating the effect on the yielding behaviour of the degree of annealing, which in turn depends on the preparation protocol. We find two distinct regimes of annealing separated by a threshold energy. Poorly annealed glasses progressively evolve towards the threshold energy as the strain amplitude is increased towards the yielding value. Well annealed glasses with initial energies below the threshold energy exhibit stable behaviour, with…
All solids yield under sufficiently high mechanical loads. Below yield, the mechanical responses of all disordered solids are nearly alike, but above yield every different disordered solid responds in its own way. Brittle systems can shatter without warning, like ordinary window glass, or exhibit strain localization prior to fracture, like metallic or polymeric glasses. Ductile systems, e.g. foams like shaving cream or emulsions like mayonnaise, can flow indefinitely with no strain localization. While there are empirical strategies for tuning the degree of strain localization, there is no fram…
We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass-former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in th…
