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Linking the macroscopic flow properties and nanoscopic structure is a fundamental challenge to understanding, predicting, and designing disordered soft materials. Under small stresses, these materials are soft solids, while larger loads can lead to yielding and the acquisition of plastic strain, which adds complexity to the task. In this work, we connect the transient structure and rheological memory of a colloidal gel under cyclic shearing across a range of amplitudes via a generalized memory function using rheo-X-ray photon correlation spectroscopy (rheo-XPCS). Our rheo-XPCS data show that the nanometer scale aggregate-level structure recorrelates whenever the change in recoverable strain over some interval is zero. The macroscopic recoverable strain is therefore a measure of the nano-scale structural memory. We further show that yielding in disordered colloidal materials is strongly heterogeneous and that memories of prior deformation can exist even after the material has been subjected to flow. 

Many soft materials yield under mechanical loading, but how this transition from solid-like behavior to liquid-like behavior occurs can vary significantly. Understanding the physics of yielding is of great interest for the behavior of biological, environmental, and industrial materials, including those used as inks in additive manufacturing and muds and soils. For some materials, the yielding transition is gradual, while others yield abruptly. We refer to these behaviors as being ductile and brittle. The key rheological signatures of brittle yielding include a stress overshoot in steady-shear-startup tests and a steep increase in the loss modulus during oscillatory amplitude sweeps. In this work, we show how this spectrum of yielding behaviors may be accounted for in a continuum model for yield stress materials by introducing a parameter we call the brittility factor. Physically, an increased brittility decreases the contribution of recoverable deformation to plastic deformation, which impacts the rate at which yielding occurs. The model predictions are successfully compared to results of different rheological protocols from a number of real yield stress fluids with different microstructures, indicating the general applicability of the phenomenon of brittility. Our study shows that the brittility of soft materials plays a critical role in determining the rate of the yielding transition and provides a simple tool for understanding its effects under various loading conditions. 

Empirical rules play a crucial role in industrial and experimental settings for efficiently determining the rheological properties of materials, thereby saving both time and resources. An example is the Cox–Merz rule, which equates the steady-shear viscosity with the magnitude of the complex viscosity obtained in oscillatory tests. This empirical rule provides access to the steady-shear viscosity that is useful for processing conditions without the instabilities associated with experiments at high shear rates. However, the Cox–Merz rule is empirical and has been shown to work in some cases and fail in others. The underlying connection between the different material functions remains phenomenological and the lack of a comprehensive understanding of the rheological physics allows for ambiguity to persist in the interpretation of material responses. In this work, we revisit the Cox–Merz rule using recovery rheology, which decomposes the strain into recoverable and unrecoverable components. When viewed through the lens of recovery rheology, it is clearly seen that the steady-shear viscosity comes from purely unrecoverable acquisition of strain, while the complex viscosity is defined in terms of contributions from both recoverable and unrecoverable components. With recovery tests in mind, we elucidate why the Cox–Merz rule works only in a limited set of conditions and present an approach that could allow for universal comparisons to be made. This work further highlights the significance of recovery rheology by showing how it is possible to extend beyond phenomenological approaches through clear rheophysical metrics obtained by decomposing the material response into recoverable and unrecoverable components. 

Understanding the yielding of complex fluids is an important rheological challenge that affects our ability to engineer and process materials for a wide variety of applications. Common theoretical understandings of yield stress fluids follow the Oldroyd–Prager formalism in which the material behavior below the yield stress is treated as solidlike, and above the yield stress as liquidlike, with an instantaneous transition between the two states. This formalism was built on a quasi-static approach to the yield stress, while most applications, ranging from material processing to end user applications, involve a transient approach to yielding over a finite timescale. Using stress-controlled oscillatory shear experiments, we show that yield stress fluids flow below their yield stresses. This is quantified through measuring the strain shift, which is the value about which the strain oscillates during a stress-controlled test and is a function of only the unrecoverable strain. Measurements of the strain shift are, therefore, measurements of flow having taken place. These experimental results are compared to the Herschel–Bulkley form of the Saramito model, which utilizes the Oldroyd–Prager formalism, and the recently published Kamani–Donley–Rogers (KDR) model, in which one constitutive equation represents the entire range of material responses. Scaling relationships are derived, which allow us to show why yield stress fluids will flow across all stresses, above and below their yield stress. Finally, derivations are presented that show strain shift can be used to determine average metrics previously attainable only through recovery rheology, and these are experimentally verified. 

The ability to concisely describe the dynamical behavior of soft materials through closed-form constitutive relations holds the key to accelerated and informed design of materials and processes. The conventional approach is to construct constitutive relations through simplifying assumptions and approximating the time- and rate-dependent stress response of a complex fluid to an imposed deformation. While traditional frameworks have been foundational to our current understanding of soft materials, they often face a twofold existential limitation: i) Constructed on ideal and generalized assumptions, precise recovery of material-specific details is usually serendipitous, if possible, and ii) inherent biases that are involved by making those assumptions commonly come at the cost of new physical insight. This work introduces an approach by leveraging recent advances in scientific machine learning methodologies to discover the governing constitutive equation from experimental data for complex fluids. Our rheology-informed neural network framework is found capable of learning the hidden rheology of a complex fluid through a limited number of experiments. This is followed by construction of an unbiased material-specific constitutive relation that accurately describes a wide range of bulk dynamical behavior of the material. While extremely efficient in closed-form model discovery for a real-world complex system, the model also provides insight into the underpinning physics of the material. 

Graphene oxide (GO) has attracted attention in materials science and engineering due to its large aspect ratio and dispersibility in polar solvent including water. It has recently been applied to direct-ink-writing (DIW) printing to realize the fabrication of three-dimensional structures, suggesting a wide variety of potential applications. Without post-processing, DIW printing requires yield stress fluids to fully build three-dimensional objects. The key properties of these inks are the yield stress and the viscoelastic properties during yielding. DIW ink rheology has therefore received significant interest in materials science, as well as mechanical and chemical engineering. Despite this interest, the yielding process has not been clearly elucidated and understanding yielding remains an outstanding problem. In this study, we discuss the yielding behavior of GO colloids via oscillatory rheology by decomposing the total strain into the recoverable and unrecoverable parts through iterative experimental techniques. The recoverable and unrecoverable responses represent viscoelastic solid and plastic properties, respectively, and they are used to determine the averaged storage and dissipation of energies. By mapping these contributions, we more clearly elucidate the yielding behavior of the GO colloids and suggest guidelines for energy efficiency. Beyond the specific lessons learned regarding the DIW-relevant rheology of GO colloids, our study contributes to an evolving development of material-centric and energy-focused methods for understanding the out-of-equilibrium rheological physics associated with the yielding of soft materials. 

The rapid development of additive manufacturing, also known as three-dimensional (3D) printing, is driving innovations in both industry and academia. Direct ink writing (DIW), an extrusion-based 3D printing technology, can build 3D structures through the deposition of custom-made inks and produce devices with complex architectures, excellent mechanical properties, and enhanced functionalities. A paste-like ink is the key to successful printing. However, as new ink compositions have emerged, the rheological requirements of inks have not been well connected to printability, or the ability of a printed object to maintain its shape and support the weight of subsequent layers. In this review, we provide an overview of the rheological properties of successful DIW inks and propose a classification system based on ink composition. Factors influencing the rheology of different types of ink are discussed, and we propose a framework for describing ink printability using measures of rheology and print resolution. Furthermore, evolving techniques, including computational studies, high-throughput rheological measurements, machine learning, and materiomics, are discussed to illustrate the future directions of feedstock development for DIW. The goals of this review are to assess our current understanding of the relationship between rheological properties and printability, to point out specific challenges and opportunities for development, to provide guidelines to those interested in multi-material DIW, and to pave the way for more efficient, intelligent approaches for DIW ink development.