Cooperative effects driving the multi-periodic dynamics of cyclically sheared amorphous solids

Abstract

Plasticity in amorphous materials, such as glasses, colloids, or granular materials, is mediated by local rearrangements called "soft spots". Experiments and simulations have shown that soft spots are two-state entities interacting via quadrupolar displacement fields generated when they switch states. When the system is subjected to cyclic strain driving, the soft spots can return to their original state after one or more forcing cycles. In this case, the system has periodic dynamics and will always repeat the same microscopic states. Here we focus on multi-periodic dynamics, i.e. dynamics that has periodicity larger than the periodicity of the drive, and use a graph-theoretical approach to analyze the dynamics obtained from numerical simulations. In this approach, mechanically stable configurations that transform purely elastically into each other over a range of applied strains, are represented by vertices, and plastic events leading from one stable configuration to the other, are represented by directed edges. An algorithm based on the graph topology and the displacement fields of the soft spots reveals that multi-periodic behavior results from the states of some soft spots repeating after more than one period and provides information regarding the mechanisms that allow for such dynamics. To better understand the physical mechanisms behind multi-periodicity, we use a model of interacting hysterons. Each hysteron is a simplified two-state element representing hysteretic soft-spot dynamics. We identify several mechanisms for multi-periodicity in this model, some involving direct interactions between multi-periodic hysterons and another resulting from cooperative dynamics involving several hysterons. These cooperative events are naturally more common when more hysterons are present, thus explaining why multi-periodicity is more prevalent at large drive amplitudes.

References in corpus (35)

• Dynamics of Viscoplastic Deformation in Amorphous Solids
• Rheology of Soft Glassy Materials
• Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
• Amorphous Systems in Athermal, Quasistatic Shear
• Vibrational modes identify soft spots in a sheared disordered packing
• Memory formation in matter
• The yielding transition in amorphous solids under oscillatory shear deformation
• Oscillatory athermal quasi-static deformation of a model glass
• A molecular-dynamics study of ductile and brittle fracture in model non-crystalline solids
• Onset of Irreversibility and Chaos in Amorphous Solids Under Periodic Shear
• Mechanical and microscopic properties of the reversible plastic regime in a 2D jammed material
• Macroscopic yielding in jammed solids is accompanied by a non-equilibrium first-order transition in particle trajectories
• Nonequilibrium Thermodynamics of Amorphous Materials II: Effective-Temperature Theory
• Locality and Non-locality in Elasto-plastic Responses of Amorphous Solids
• Yielding and microstructure in a 2D jammed material under shear deformation
• Networks and Hierarchies: How Amorphous Materials Learn to Remember
• Reversible plasticity in amorphous materials
• Complex pathways and memory in compressed corrugated sheets
• Reversible plastic events during oscillatory deformation of amorphous solids
• Memory from coupled instabilities in unfolded crumpled sheets
• Strength of Mechanical Memories is Maximal at the Yield Point of a Soft Glass
• Particle-scale reversibility in athermal particulate media below jamming
• Global Memory from Local Hysteresis in an Amorphous Solid
• Multiple memory formation in glassy landscapes
• Multiperiodic orbits from interacting soft spots in cyclically-sheared amorphous solids
• Period proliferation in periodic states in cyclically sheared jammed solids
• Topology of the energy landscape of sheared amorphous solids and the irreversibility transition
• Relationships among structure, memory, and flow in sheared disordered materials
• State transition graph of the Preisach model and the role of return point memory
• Dynamical heterogeneity in periodically deformed polymer glasses
• The structure of state transition graphs in hysteresis models with return point memory: I. General Theory
• Cyclic annealing as an iterated random map
• Subharmonics and Aperiodicity in Hysteresis Loops
• Minimal descriptions of cyclic memories
• The Effective Temperature in Elasto-Plasticity of Amorphous Solids

Cited by in corpus (15)

• Emergent Disorder and Mechanical Memory in Periodic Metamaterials
• Soft Metamaterials: Adaptation and Intelligence
• Perspective on Reversible to Irreversible Transitions in Periodic Driven Many Body Systems and Future Directions For Classical and Quantum Systems
• Mechanical memories in solids, from disorder to design
• Mechanical annealing and memories in a disordered solid
• Generalizing multiple memories from a single drive: The hysteron latch
• Competition between energy and dynamics in memory formation
• Geometric control and memory in networks of hysteretic elements
• Transition Graphs of Interacting Hysterons: Structure, Design, Organization and Statistics
• Microstructural and rheological training and memory of nanocolloidal soft glasses under cyclic shear
• Relaxation dynamics in amorphous alloys under asymmetric cyclic shear deformation
• Far-from-equilibrium complex landscapes
• Yielding and memory in a driven mean-field model of glasses
• A catastrophic approach to designing interacting hysterons
• Transients and multiperiodic responses: a hierarchy of material bits