Clinically, palpation is one of the important diagnostic methods to assess tumor malignancy. In laboratory research, it is well accepted that the bulk stiffness of the tumor and the surrounding tissue is closely correlated with the malignant state of the tumor. Here, we postulate that, in addition to tumor stiffness, tumor viscoelasticity - the fact that tumor tissue takes time to bounce back after compression, can also be used to evaluate the tumor malignancy state. In this work, we characterized the viscoelastic properties of tumor spheroids using a recently developed microfluidic compression device by quantifying their relaxation dynamics upon load removal. Tumor spheroids were made using breast tumor cells spanning various malignancy levels; non-tumorigenic epithelial (MCF10A), moderately malignant tumor (MCF7) and triple negative metastatic tumor (MDA-MB-231) cell line. Spheroids embedded within a 3D extracellular matrix were periodically compressed, and their strain responses were recorded using microscopic imaging. Our results revealed that the measured strain relaxation dynamics can be successfully described by a modified power law model, demonstrated that non-tumorigenic tumor spheroids were more elastic, exhibited shorter relaxation time and less plasticity than those of tumorigenic spheroids. This work highlights that viscoelastic properties in addition to bulk stiffness of the tumor spheroids can serve as a complementary mechanical biomarker of tumor malignancy and demonstrate the validity of a modified power law model for the mechanical characterization of a living tissue.

Lubricated contacts in soft materials are important in various engineering systems and natural settings. Three major lubrication regimes are boundary (BL), mixed (ML), and elastohydrodynamic (EHL) lubrication, where the contact region is dry, partially wetted, or fully wetted, respectively. The transition between these regimes is insufficiently understood, especially for soft contacts, which impedes desired control of lubricated sliding friction. Here, we report on the role of solid wettability and adhesion on these transitions. Wettability of glycerol on polydimethylsiloxane (PDMS) surfaces and adhesion between a glass indenter and PDMS were varied by exposure of the PDMS to an ultraviolet light-ozone cleaner. By combining friction tests and visualization, we demonstrate that the transition from ML to BL regime is dominated by the wettability of the lubricant; increasing wettability of glycerol makes removal of liquid from the contact region more difficult. Transition from EHL to ML is related to a series of events with increasing normal load, which are thinning of the lubricant layer, sudden jump to contact between the glass indenter and solid substrate across a gap of tens of nanometers, and attendant mechanical instabilities such as wrinkling and stick-slip. These results provide a deeper understanding of transitions in lubricated frictional behavior of soft materials which govern the maximum and minimum friction achievable.

In lubrication applications, a common scenario involves a hard solid in contact with a soft viscoelastic substrate. However, most of the existing literature focuses on the case of an elastic substrate. In this paper, we introduce a numerical method that overcomes the challenges of converging iterative techniques and is specifically designed to handle viscoelastic substrates described by a Prony series. Our approach is fully automated, stable, and efficient, requiring only the solution of a linear matrix equation at each time step. We apply this method to investigate the transient squeezing of a thin liquid film between a rigid spherical indenter and a soft viscoelastic substrate. We explore intriguing differences between the EHL (Elasto-hydrodynamic lubrication) problem and three viscoelastic substrates with single and multiple relaxation times to understand how temporally evolving stiffness affects the pressure, surface displacement, and liquid film thickness. One of the key differences between the EHL and the VEHL (Visco-elasto-hydrodynamic lubrication) problem comes to light upon looking at the entrapped volume which can be held nearly constant when using a viscoelastic substrate whereas elastic substrates show exponential decay.

Clinically, the feel, touch, and shape of a solid tumor are important diagnostic methods for determining the malignant state of the disease. However, there are limited tools for quantifying the mechanics and the malignancy of the tumor in a physiologically realistic setting. Here, we developed a microfluidic rheometer - termed the microrheometer - that enables simultaneous measurements of breast tumor spheroid mechanics and their invasiveness into a 3D extracellular matrix (ECM). The microrheometer consists of a pneumatic pressure control unit for applying controlled static or cyclic compression to tumor spheroids, and a sample chamber for containing spheroid embedded ECM. The innovation here lies in the integration of a polyacrylamide membrane force sensor within the sample chamber, enabling a direct force measurement in a physiologically relevant setting. We found that both breast tumor stiffness and the viscoelastic properties of the tumor are closely correlated with tumor invasiveness. The microrheometer allowed us to measure tumor mechanics in a short time (less than a minute) and has the potential to be used clinically in the future. We note that the microrheometer here can be easily extended to studies of mechanics of single cell, nucleus, as well as other cell/tissue types.

In stick-slip fracture, a crack stays still or only propagates a small amount until it reaches a critical energy release rate. Then, it suddenly grows rapidly, causing the energy release rate to drop and the crack to stop again. This behavior is common in many polymers, including glassy polymers and soft materials like adhesives. However, the theoretical understanding of this phenomenon is fragmented and incomplete. Here we propose a unified theory based on a rate-dependent cohesive model to explain these phenomena. Using this model, we demonstrate that an elastic backing layer in a zero-degree peel test can experience different types of stick-slip instability depending on the peeling rate. At slow peeling rates, the crack grows slowly until it reaches a maximum velocity, corresponding to a fixed maximum force, after which the growth becomes unstable. However, above a certain critical peeling rate, there is no slow crack growth: the crack enters the stick-slip regime once the critical energy release rate is reached for a reduced value of the applied force. Although our mathematical modeling is developed in a specific geometry that makes the computations easier, this behavior can be argued to be a more general feature of most materials and geometries presenting stick-slip fracture.

In this work, we have found that a prenotched double-network (DN) hydrogel, when subjected to tensile loading in a pure-shear geometry, exhibits intriguing stick-slip crack dynamics. These dynamics synchronize with the oscillation of the damage (yielding) zone at the crack tip. Through manipulation of the loading rate and the predamage level of the brittle network in DN gels, we have clarified that this phenomenon stems from the significant amount of energy dissipation required to form the damage zone at the crack tip, as well as a kinetic contrast between the rapid crack extension through the yielding zone (slip process) and the slow formation of a new yielding zone controlled by the external loading rate (stick process).

Recent experiments reveal that adhesive interactions can play a key role in causing surface instability in soft lubrication. Instances of instability include fluid entrapment in isolated pockets upon a soft sphere's normal contact with a hard substrate and surface wrinkling of a soft substrate as a hard sphere slides across it. These phenomena underscore a substantial distinction between hard and soft lubrication. They are of paramount importance from a fundamental standpoint, providing an entirely new explanation for the transition mechanism from elasto-hydrodynamics to the mixed lubrication regimes. Here, we introduce a new theory to elucidate these observations. Our theory modifies the Reynolds elasto-hydrodynamics equation by incorporating adhesive interaction across the fluid layer, investigating the interplay between adhesion, fluid flow and elastic instability. Our analysis proposes the addition of a new dimensionless parameter in lubrication theory, that compares the stiffness of the adhesive interaction to that of the substrate. When this parameter exceeds unity, the soft solid surface exhibits instability to small perturbations in its shape. In mathematical terms, the Reynolds equation undergoes a transition from a nonlinear diffusion equation to a nonlinear wave equation at this critical point. Post-transition, the diffusivity of the nonlinear diffusion equation turns negative, rendering the problem ill-posed. We investigate the transition using the method of characteristics and present an exact analytic solution. This solution offers insights into the occurrence of a vanishing liquid film thickness at specific locations, resulting in dry contact—initiating transition to mixed lubrication.

The Pure Shear (PS) crack specimen is widely employed to assess the fracture toughness of soft elastic materials. It serves as a valuable tool for investigating the behavior of crack growth in a steady-state manner following crack initiation. One of its advantages lies in the fact that the energy release rate ( J ) remains approximately constant for sufficiently long cracks, independent of crack length. Additionally, the PS specimen facilitates the easy evaluation of J for long cracks by means of a tension test conducted on an uncracked sample. However, the lack of a published expression for short cracks currently restricts the usefulness of this specimen. To overcome this limitation, we conducted a series of finite element (FE) simulations utilizing three different constitutive models, namely the neo-Hookean (NH), Arruda-Boyce (AB), and Mooney-Rivlin (MR) models. Our finite element analysis (FEA) encompassed practical crack lengths and strain levels. The results revealed that under a fixed applied displacement, the energy release rate ( J ) monotonically increases with the crack length for short cracks, reaches a steady-state value when the crack length exceeds the height of the specimen, and subsequently decreases as the crack approaches the end of the specimen. Drawing from these findings, we propose a simple closed-form expression for J that can be applied to most hyper-elastic models and is suitable for all practical crack lengths, particularly short cracks.

Tough soft materials such as multiple network elastomers (MNE) or filled elastomers are typically stretchable and include significant energy dissipation mechanisms that prevent or delay crack growth. Yet most studies and fracture models focus on steady-state propagation and damage is assumed to be decoupled from the local stress and strain fields near the crack tip. We report an in situ spatial-temporally resolved 3D measurement of molecular damage in mechanophore-labeled MNE just before a crack propagates. This technique, complemented by digital image correlation, allows us to compare the spatial distribution of both damage and deformation in single network (SN) elastomers and in MNE. Compared to SN, MNE have a wide-spread damage in front of the crack and, surprisingly, delocalize strain concentration. A continuum model, where damage distribution is fully coupled to the crack tip fields, is proposed to explain these results. Additional measurements of time-dependent molecular damage during fixed grips relaxation in the presence of a crack reveal that the less localized damage distribution delays fracture initiation. The observations and exploratory modeling reveal the dynamic fracture mechanism of MNE, providing guidance for rational design of high-performance tough elastomers.

A computational model is used to study contact sliding of soft single pillar pairs.

Energy dissipation around a propagating crack is the primary mechanism for the enhanced fracture toughness in viscoelastic solids. Such dissipation is spatially non-uniform and is highly coupled to the crack propagation process due to the history-dependent nature of viscoelasticity. We present an experimental approach to map the dissipation field during crack propagation in soft viscoelastic solid. Specifically, we track randomly distributed tracer particles to measure the evolving deformation field. The measured deformation field is then put into a nonlinear constitutive model to determine the dissipation field. Our methodology was used to investigate the deformation and dissipation fields around a propagating crack in a Polyampholyte (PA) hydrogel. The deformation field measurements allowed us to assess whether the commonly assumed translational invariance in viscoelastic fracture theories holds true in practical experiments. Furthermore, by combining the obtained deformation fields with a nonlinear viscoelastic model, we captured the complete history of the dissipation field during crack propagation. We found that dissipation occurred even at material points that are a few millimeters away from the crack tip. The mapped dissipation field also enabled the separate determination of the intrinsic and dissipative components of fracture toughness for the viscoelastic hydrogel.

Optical image of the interface formed when two slightly misaligned pillar arrays are pressed into contact. Sliding is accommodated by motion of this pattern.

Many important problems in elasto-hydrodynamic lubrication arise when one of the contacting bodies is elastically soft. An example is the squeezing of a thin liquid film between a rigid sphere/ cylinder and a soft elastic substrate, in which the sphere may not be sliding and be subjected only to normal loads (stationary contact), or it can be sheared at the same time and undergo steady or non-steady sliding. These problems are notoriously difficult to solve for soft solids under large loads and thin lubricant films. For this reason, indentation and sliding problems have usually been analyzed separately, and solutions for transient sliding problems are few. Here we develop a numerical method that avoids difficult-to-converge iterative methods and is able to solve both normal indentation and/or transient sliding lubrication problems. The scheme is fully automatic, stable, and efficient and requires only a linear matrix equation to be solved at every time step. We present solutions of two transient sliding problems: in the first of which, a rigid sphere undergoes transient normal lubricated contact followed by transient sliding on an elastic half space. In the second, a rigid cylinder undergoes transient lubricated sliding on an elastic foundation.

We report on the delamination of thin (≈μm) hydrogel films grafted to silicon substrates under the action of swelling stresses. Poly(dimetylacrylamide) (PDMA) films are synthesized by simultaneously cross-linking and grafting preformed polymer chains onto the silicon substrate using a thiol-ene reaction. The grafting density at the film/substrate interface is tuned by varying the surface density of reactive thiol-silane groups on the silicon substrate. Delamination of the films from well controlled line defects with low adhesion is monitored under a humid water vapor flow ensuring full saturation of the polymer network. A propagating delamination of the film is observed under the action of differential swelling stresses at the debonding front. A threshold thickness for the onset of this delamination is evidenced which is increasing with grafting density while the debonding velocity is also observed to decrease with an increase in grafting density. These observations are discussed within the framework of a nonlinear fracture mechanics model which assumes that the driving force for crack propagation is the difference between the swelling state of the bonded and delaminated parts of the film. Using this model, the threshold energy for crack initiation was determined from the measured threshold thickness and discussed in relation to the surface density of reactive thiol groups on the substrate.

The fracture of materials can take place below the critical failure condition via the slow accumulation of internal damage followed by fast crack propagation. While failure due to subcritical fracture accounts for most of the structural failures in use, it is theoretically challenging to bridge the gap between molecular damage and fracture mechanics, not to mention predicting the occurrence of sudden fracture, due to the lack of current nondestructive detection methods with suitable resolution. Here, we investigate the fracture of elastomers by using simultaneously space- and time-resolved multispeckle diffusing wave spectroscopy (MSDWS) and molecular damage mapping by mechanophore. We identify a fracture precursor that accelerates the strain-rate field over a large area (cm2 scale), at considerably long times (up to thousands of seconds) before macroscopic fracture occurs. By combining deformation or damage mapping and finiteelement simulations of the crack-tip strain field, we unambiguously attribute the macroscopic response in elastic deformation to highly localized molecular damage that occurs over a sample area of about 0.01 mm2. By unveiling this mechanism of interaction between the microscopic molecular damage and the minute but long-ranged elastic deformation field, we are able to develop MSDWS as a flexible, wellcontrolled tool to characterize and predict microscopic damage well before it becomes critical. Tested using ordinary imaging and simple image processing, MSDWS predictions are proven applicable for unlabeled and even opaque samples under different fracture conditions.

It is well established that a thin silica-like surface layer is formed when a cross-linked PDMS structure is subjected to ultraviolet/ozone treatment. Due to surface geometry, especially near the corners, this silica-like surface layer has non-uniform thickness, which can impact many mechanical properties, including adhesion and fracture strength. Here we use a simple analytic model based on diffusion of reactive species to predict the thickness of the oxidized surface layer near the corners. We demonstrate that these corner solutions can be patched together to determine the thickness of the oxidized layer in complex geometries.

We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on surface. Nonlinear theories allow us to systematically study porous solids in a wide range of applications, such as drug delivery, biomaterial design, fundamental study of biomechanics and mechanobiology, and the design of sensors and actuators. As we aim to understand the physical phenomena at a smaller length scale, towards comprehending fundamental biological processes and miniaturization of devices, surface effect becomes more pertinent. Although existing methodologies provide the necessary tools to study coupled bulk effects for deformation and diffusion; however, very little is known about fully coupled bulk and surface poroelasticity at finite strain. Here we develop a thermodynamically consistent formulation for surface and bulk poroelasticity, specialized for soft hydrated solids, along with a corresponding finite element implementation that includes a three-field weak form. Our approach captures the interplay between competing multiphysical processes of finite deformation and species diffusion, accounting for surface kinematics and surface transport, and provides invaluable insight when surface effects are important.

A challenge in the constitutive modeling of time dependent, non-linear solids is the identification of potentially large numbers of material parameters. Here we present an efficient method to determine these parameters using a machine learning algorithm based on Singular Value Decomposition (SVD) and an adaptive neural network (NN). SVD compresses training data and provides outputs for the NN. The trained network rapidly computes the material responses for a large set of material parameters. These responses are then compared with experimental data to determine the optimal parameters. We test our algorithm by performing uniaxial cyclic and relaxation tests on three hydrogels with very different time dependent behaviors: a chemically and physically crosslinked polyampholyte (c-PA) gel; a pure physically crosslinked PA (p-PA) gel, and a Poly(vinylalcohol) (PVA) hydrogel with both chemical and physical crosslinks.

Lubricated contacts in soft materials are common in various engineering and natural settings, such as tires, haptic applications, contact lenses, and the fabrication of soft electronic devices. Two major regimes are elasto-hydrodynamic lubrication (EHL), in which solid surfaces are fully separated by a fluid film, and mixed lubrication (ML), in which there is partial solid-to-solid contact. The transition between these regimes governs the minimum sliding friction achievable and is thus very important. Generally, the transition from EHL to ML regimes is believed to occur when the thickness of the lubricant layer is comparable with the amplitude of surface roughness. Here, it is reported that in lubricated sliding experiments on smooth, soft, poly(dimethylsiloxane) substrates, the transition can occur when the thickness of the liquid layer is much larger than the height of the asperities. Direct visualization of the "contact" region shows that the transition corresponds to the formation of wave-like surface wrinkles at the leading contact edge and associated instabilities at the trailing contact edge, which are believed to trigger the transition to the mixed regime. These results change the understanding of what governs the important EHL-ML transition in the lubricated sliding of soft solids.

Relaxation experiments are performed on single edge notch tension (SENT) and T shape specimens consisting of different variations of polyampholyte (PA) hydrogels. These specimens share a common feature of containing regions of high and low stress/strain. This feature enables us to probe the load transfer mechanisms between permanent and dynamic networks of different strengths. This load transfer mechanism is connected to viscoelastic behavior. PA gels are nonlinear viscoelastic, with timedependent behavior controlled by the breaking and reforming of ionic bonds in the dynamic network. In contrast to the prediction of linear viscoelastic theory, the displacement and strain fields during stress relaxation are not fixed but change with time in a complex way depending on the strength of the dynamic bonds and the observation time window. These experimental results are explained by a nonlinear viscoelastic model. Additional physical insights are gained by appealing to the nonlinear rheology of dynamic bonds or stickers. Our result shows that load transfer between networks can be controlled by modifying the strength of dynamic bonds. (c) 2022 Elsevier Ltd. All rights reserved.