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Tal Cohen

Publications and source records attributed to Tal Cohen.

34 records · Page 2Linked to original sources
arXiv2021

Nonlinear Inclusion Theory with Application to the Growth and Morphogenesis of a Confined Body

One of the most celebrated contributions to the study of the mechanical behavior of materials is due to J.D. Eshelby, who in the late 50s revolutionized our understanding of the elastic stress and strain fields due to an ellipsoidal inclusion/inhomogeneity that undergoes a transformation of shape and size. While Eshelby's work laid the foundation for significant advancements in various fields, including fracture mechanics, theory of phase transitions, and homogenization methods, its extension into the range of large deformations, and to situations in which the material can actively reorganize in response to the finite transformation strain, is in a nascent state. Beyond the theoretical difficulties imposed by highly nonlinear material response, a major hindrance has been the absence of experimental observations that can elucidate the intricacies that arise in this regime. To address this limitation, our experimental observations reveal the key morphogenesis steps of Vibrio cholerae biofilms embedded in hydrogels, as they grow by four orders of magnitude from their initial size. Using the biofilm growth as a case study, our theoretical model considers various growth scenarios and employs two different and complimentary methods -- a minimal analytical model and finite element computations -- to obtain approximate equilibrium solutions. A particular emphasis is put on determining the natural growth path of an inclusion that optimizes its shape in response to the confinement, and the onset of damage in the matrix, which together explain the observed behavior of biofilms. Beyond bacterial biofilms, this work sheds light on the role of mechanics in determining the morphogenesis pathways of confined growing bodies and thus applies to a broad range of phenomena that are ubiquitous in both natural and engineered material systems.

cond-mat.soft↗
arXiv2021

Stick-slip phenomena and Schallamach waves captured using reversible cohesive elements

Reversibility is of paramount importance in the correct representation of surface peeling in various physical settings, ranging from motility in nature, to gripping devices in robotic applications, and even to sliding of tectonic plates. Modeling the detachment-reattachment sequence, known as stick-slip, imposes several challenges in a continuum framework. Here we exploit customized reversible cohesive elements in a hybrid finite element model that can handle occurrence of snap-through instabilities. The simulations capture various peeling phenomena that emerge in experimental observations, where layers are pulled from a flat, rigid substrate in the direction parallel to the surface. For long layers, periodicity in reattachment is shown to develop and is linked to the concept of Schallamach waves. Further, the connection between surface properties and stick-slip behavior is investigated: we find that stick-slip is linked to the propensity of the interface to localize deformation and damage. Beyond elucidating the various peeling behaviors and the detachment modes, the computational framework developed here provides a straightforward approach for investigation of complex delamination processes, which can guide development of future applications across different scales and in various settings.

cond-mat.soft↗
arXiv2021

Observation of ultra-slow shock waves in a tunable magnetic lattice

The combination of fast propagation speeds and highly localized nature has hindered the direct observation of the evolution of shock waves at the molecular scale. To address this limitation, an experimental system is designed by tuning a one-dimensional magnetic lattice to evolve benign wave forms into shock waves at observable spatial and temporal scales, thus serving as a 'magnifying glass' to illuminate shock processes. An accompanying analysis confirms that the formation of strong shocks is fully captured. The exhibited lack of a steady state induced by indefinite expansion of a disordered transition zone points to the absence of local thermodynamic equilibrium, and resurfaces lingering questions on the validity of continuum assumptions in presence of strong shocks.

cond-mat.soft↗
arXiv2020

Probing local nonlinear viscoelastic properties in soft materials

Minimally invasive experimental methods that can measure local rate dependent mechanical properties are essential in understanding the behaviour of soft and biological materials in a wide range of applications. Needle based measurement techniques such as Cavitation Rheology and Volume Controlled Cavity Expansion (VCCE), allow for minimally invasive local mechanical testing, but have been limited to measuring the elastic material properties. Here, we propose several enhancements to the VCCE technique to adapt it for characterization of viscoelastic response at low to medium stretch rates ($10^{-2}$ - $1$ s${}^{-1}$). The proposed technique performs several cycles of expansion-relaxation at controlled stretch rates in a cavity expansion setting and then employs a large deformation viscoelastic model to capture the measured material response. Application of the technique to soft PDMS rubber reveals significant rate dependent material response with high precision and repeatability, while isolating equilibrated states that are used to directly infer the quasistatic elastic modulus. The technique is further established by demonstrating its ability to capture changes in the rate dependent material response of a tuneable PDMS system. The measured viscoelastic properties are used to explain earlier reports of rate insensitive material response by needle based methods: it is demonstrated that the conventional use of constant volumetric rate cavity expansion can induce high stretch rates that lead to viscoelastic stiffening and an illusion of rate insensitive material response. We thus conclude with a cautionary note on possible overestimation of the quasistatic elastic modulus in previous studies and suggest that the stretch rate controlled expansion protocol, proposed in this work, is essential for accurate estimation of both quasistatic and dynamic material parameters.

cond-mat.soft↗
arXiv2020

Controlled Propagation and Jamming of a Delamination Front

We study the birth and propagation of a delamination front in the peeling of a soft, weakly adhesive layer. In a controlled-displacement setting, the layer partially detaches via a subcritical instability and the motion continues until arrested, by jamming of the two lobes. Using numerical solutions and scaling analysis, we quantitatively describe the equilibrium shapes and obtain constitutive sensitivities of jamming process to material and interface properties. We conclude with a way to delay or avoid jamming altogether by tunable interface properties.

cond-mat.soft↗
arXiv2020

Morphogenesis and proportionate growth: A finite element investigation of surface growth with coupled diffusion

Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic laws that orchestrate their function are accounted for, a minimal theoretical model may exhibit similar growth behaviors. The ubiquity of surface growth, a mechanism by which material is added or removed on the boundaries of the body, has motivated the development of theoretical models, which can capture the diffusion-coupled kinetics that govern it. However, due to their complexity, application of these models has been limited to simplified geometries. In this paper, we tackle these complexities by developing a finite element framework to study the diffusion-coupled growth and morphogenesis of finite bodies formed on uniform and flat substrates. We find that in this simplified growth setting, the evolving body exhibits a sequence of distinct growth stages that are reminiscent of natural systems, and appear spontaneously without any externally imposed regulation or coordination. The computational framework developed in this work can serve as the basis for future models that are able to account for growth in arbitrary geometrical settings, and can shed light on the basic physical laws that orchestrate growth and morphogenesis in the natural world.

cond-mat.soft↗
arXiv2020

Effect of Elasticity on Phase Separation in Heterogeneous Systems

A recent study has demonstrated that phase separation in binary liquid mixtures is arrested in the presence of elastic networks and can lead to a nearly uniformly-sized distribution of the dilute-phase droplets. At longer timescales, these droplets exhibit a directional preference to migrate along elastic property gradients to form a front of dissolving droplets [K. A. Rosowski, T. Sai, E. Vidal-Henriquez, D. Zwicker, R. W. Style, E. R. Dufresne, Elastic ripening and inhibition of liquid-liquid phase separation, Nature Physics (2020) 1-4]. In this work, we develop a complete theoretical understanding of this phenomenon in nonlinear elastic solids by employing an energy-based approach that captures the process at both short and long timescales to determine the constitutive sensitivities and the dynamics of the resulting front propagation. We quantify the thermodynamic driving forces to identify diffusion-limited and dissolution-limited regimes in front propagation. We show that changes in elastic properties have a nonlinear effect on the process. This strong influence can have implications in a variety of material systems including food, metals, and aquatic sediments, and further substantiates the hypothesis that biological systems exploit such mechanisms to regulate important function.

cond-mat.soft↗
arXiv2019

Extreme cavity expansion in soft solids: damage without fracture

Cavitation is a common damage mechanism in soft solids. Here, we study this using a phase-separation technique in stretched, elastic solids to controllably nucleate and grow small cavities by several orders of magnitude. The ability to make stable cavities of different sizes, as well as the huge range of accessible strains, allows us to systematically study the early stages of cavity expansion. Cavities grow in a scale-free manner, accompanied by irreversible bond breakage that is distributed around the growing cavity, rather than being localized to a crack tip. Furthermore, cavities appear to grow at constant driving pressure. This has strong analogies with the plasticity that occurs surrounding a growing void in ductile metals. In particular we find that, although elastomers are normally considered as brittle materials, small-scale cavity expansion is more like a ductile process. Our results have broad implications for understanding and controlling failure in soft solids.

cond-mat.soft↗
arXiv2019

Shear shock evolution in incompressible soft solids

Nonlinear evolution of shear waves into shocks in incompressible elastic materials is investigated using the framework of large deformation elastodynamics, for a family of loadings and commonly used hyperelastic material models. Closed form expressions for the shock formation distance are derived and used to construct non-dimensional phase maps that determine regimes in which a shock can be realized. These maps reveal the sensitivity of shock evolution to the amplitude, shape, and ramp time of the loading, and to the elastic material parameters. In light of a recent study (Espindola et al., 2017), which hypothesizes that shear shock formation could play a signicant role in Traumatic Brain Injury (TBI), application to brain tissue is considered and it is shown that the size matters in TBI research. Namely, for realistic loadings, smaller brains are less susceptible to formation of shear shocks. Furthermore, given the observed sensitivity to the imparted waveform and the constitutive properties, it is suggested that the non-dimensional maps can guide the design of protective structures by determining the combination of loading parameters, material dimensions, and elastic properties that can avoid shock formation.

cond-mat.soft↗
arXiv2019

Dynamic enlargement of a hole in a sheet: crater formation and propagation of cylindrical shock waves

Predicting the shape of a crater formed by high velocity impact is of interest in several fields. It can aid in design of more efficient protective structures, in forensic analysis of bullet holes, and in understanding the effects of meteorite impact in both space systems and in extreme geological events. In this paper we present, for the first time, a complete theoretical solution of the dynamic plane-stress problem. We consider the steady-state expansion of a cylindrical hole in a strain hardening elastoplastic sheet and find that a self-similar field emerges if the `specific cavitation energy' is constant. It is shown that at the quasistatic limit this solution reduces to available classical solutions, while at high expansion velocities shock waves can appear. Investigation of the constitutive sensitivities of the expansion field is conducted and compared with available results for the spherical field which is commonly applied to predict resistance to high velocity penetration. It is shown that shock waves appear at significantly lower expansion velocities, in the plane-stress deformation pattern, for which material compressibility is found to have a negligible effect. This insensitivity can be taken advantage of in the future for design of light weight protective layers by incorporating porosity.

physics.app-ph↗
arXiv2019

Capturing Strain Stiffening Using Volume Controlled Cavity Expansion

Strain-stiffening is a well-documented behavior in soft biological materials such as liver and brain tissue. Measuring and characterizing this nonlinear response, which is commonly considered as a mechanism for damage prevention, is of great interest to engineers for design of better biomimetic materials, and to physicians for diagnostic purposes. However, probing the elastic response of soft or biological materials at large deformation in their natural habitat, is an arduous task. Here, we present the Volume Controlled Cavity Expansion (VCCE) technique as an in-vivo measurement method that offers the ability of characterizing the stiffening response of materials in addition to identifying their shear modulus. By employing minimal constitutive representations involving only two constants (Mooney-Rivlin, Gent, and Ogden) we show that for the conventional PDMS samples, this technique and an accompanying data analysis method capture the shear modulus, as well as providing reliable measures of the stiffening behavior of the samples.

cond-mat.soft↗
arXiv2019

The Intimate Relationship between Cavitation and Fracture

Nearly three decades ago, the field of mechanics was cautioned of the obscure nature of cavitation processes in soft materials [Gent, A.N., 1990. Cavitation in rubber: a cautionary tale. Rubber Chemistry and Technology, 63(3)]. Since then, the debate on the mechanisms that drive this failure process is ongoing. Using a high precision volume controlled cavity expansion procedure, this paper reveals the intimate relationship between cavitation and fracture. Combining a Griffith inspired formulation for crack propagation, and a Gent inspired formulation for cavity expansion, we show that despite the apparent complexity of the fracture patterns, the pressure-volume response follows a predictable path. In contrast to available studies, both the model and our experiments are able to track the entire process including the unstable branch, by controlling the volume of the cavity. Moreover, this minimal theoretical framework is able to explain the ambiguity in previous experiments by revealing the presence of metastable states that can lead to first order transitions at onset of fracture. The agreement between the simple theory and all of the experimental results conducted in PDMS samples with shear moduli in the range of 25-246 [kPa], confirms that cavitation and fracture work together in driving the expansion process. Through this study we also determine the fracture energy of PDMS and show its significant dependence on strain stiffening.

cond-mat.soft↗
arXiv2018

Kinetics of surface growth with coupled diffusion and the emergence of a universal growth path

Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a single cell, and is increasingly applied in engineering processes for fabrication and self-assembly. A significant complexity in describing the kinetics of such processes arises due to their inherent coupled interaction with the diffusing constituents that are needed to sustain the growth, and the influence of local stresses on the growth rates. Moreover, changes in concentration of solvent within the bulk of the body, generated by diffusion, can affect volumetric changes, thus leading to an additional interacting growth mechanism. In this paper we present a general theoretical framework that captures these complexities to describe the kinetics of surface growth while accounting for coupled diffusion. Then, by combination of analytical and numerical tools, applied to a simple growth geometry, we show that the evolution of such growth processes rapidly tends towards a universal path that is independent of initial conditions. This path, on which surface growth mechanisms and diffusion act harmoniously, can be extended to analytically portray the evolution of a body from inception up to a treadmilling state, in which addition and removal of material are balanced.

cond-mat.soft↗
arXiv2016

Steady accretion of an elastic body on a hard spherical surface and the notion of a four-dimensional reference space

Taking the cue from experiments on actin growth on spherical beads, we formulate and solve a model problem describing the accretion of an incompressible elastic solid on a rigid sphere due to attachment of diffusing free particles. One of the peculiar characteristics of this problem is that accretion takes place on the interior surface that separates the body from its support rather than on its exterior surface, and hence is responsible for stress accumulation. Simultaneously, ablation takes place at the outer surface where material is removed from the body. As the body grows, mechanical effects associated with the build-up of stress and strain energy slow down accretion and promote ablation. Eventually, the system reaches a point where internal accretion is balanced by external ablation. The present study is concerned with this stationary regime called "treadmilling". The principal ingredients of our model are: a nonstandard choice of the reference configuration, which allows us to cope with the continually evolving material structure; and a driving force and a kinetic law for accretion/ablation that involves the difference in chemical potential, strain energy and the radial stress. By combining these ingredients we arrive at an algebraic system which governs the stationary treadmilling state. We establish the conditions under which this system has a solution and we show that this solution is unique. Moreover, by an asymptotic analysis we show that for small beads the thickness of the solid is proportional to the radius of the support and is strongly affected by the stiffness of the solid, whereas for large beads the stiffness of the solid is essentially irrelevant, the thickness being proportional to a characteristic length that depends on the parameters that govern diffusion and accretion kinetics.

math-ph↗
arXiv2014

Linearized Theory of Traffic Flow

The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena. Specifically, the scenarios examined involve a smooth velocity field in stop-and-go traffic, a discontinuous velocity field with shock waves in a traffic light problem, and discontinuous displacement fields in a problem where a single platoon of vehicles splits into two, and later merges back into one.

physics.soc-ph↗