We use the normal mode formalism to study the shear rheology of the vertex model for epithelial tissue mechanics in the overdamped linear response regime. We consider systems with external (e.g., cell-substrate) and internal (e.g., cell-cell) dissipation mechanisms, and derive expressions for stresses on cells due to mechanical and dissipative forces. The semi-analytical method developed here is, however, general and can be directly applied to study the linear response of a broad class of soft matter systems with internal and external dissipation. It involves normal mode decomposition to calculate linear loss and storage moduli of the system. Specifically, displacements along each normal mode produce stresses due to elastic deformation and internal dissipation, which are in force balance with loads due to external dissipation. Each normal mode responds with a characteristic relaxation timescale, and its rheological behavior can be described as a combination of a standard linear solid element due to elastic stresses and a Jeffreys model element due to the internal dissipative stresses. The total response of the system is then fully determined by connecting in parallel all the viscoelastic elements corresponding to individual normal modes. This allows full characterization of the potentially complex linear rheological response of the system at all driving frequencies and identification of collective excitations. We show that internal and external dissipation mechanisms lead to qualitatively different rheological behaviors due to the presence or absence of Jeffreys elements, which is particularly pronounced at high driving frequencies. Our findings, therefore, underscore the importance of microscopic dissipation mechanisms in understanding the rheological behavior of soft materials and tissues, in particular.
Epithelial tissues act as barriers and, therefore, must repair themselves, respond to environmental changes and grow without compromising their integrity. Consequently, they exhibit complex viscoelastic rheological behavior where constituent cells actively tune their mechanical properties to change the overall response of the tissue, e.g., from solid-like to fluid-like. Mesoscopic mechanical properties of epithelia are commonly modeled with the vertex model. While previous studies have predominantly focused on the rheological properties of the vertex model at long time scales, we systematicall…
In this paper, we propose a numerical model to describe the adhesive normal contact between a "rigid" spherical indenter and a viscoelastic rough substrate. The model accounts for dissipative process under the assumption that viscoelastic losses are localized at the (micro)-contact lines. Numerical predictions are then compared with experimental measurements, which show a strong adhesion hysteresis mostly due to viscous energy dissipation occurring during pull-off. This hysteresis is satisfactorily described by the contact model which allows to distinguish the energy loss due to material dissi…
Based on a Hamiltonian that incorporates the elastic coupling between a tracer and active particles, we derive a generalized Langevin model for the non-equilibrium mechanical response of active viscoelastic biomatter. Our model accounts for the power-law viscoelastic response of the embedding polymeric network as well as for the non-equilibrium energy transfer between active and tracer particles. Our analytical expressions for the frequency-dependent response function and the positional autocorrelation function agree nicely with experimental data for red blood cells and actomyosin networks wit…
A living non-Newtonian matter like the cell cortex and tissues are driven out-of-equilibrium at multiple spatial and temporal scales. The stochastic dynamics of a particle embedded in such a medium are non-Markovian, given by a generalized Langevin equation. Due to the non-Markovian nature of the dynamics, the heat dissipation and the entropy production rate cannot be computed using the standard methods for Markovian processes. In this work, to calculate heat dissipation, we use an effective Markov description of the non-Markovian dynamics, which includes the degrees-of-freedom of the medium. …
We study the frictional behavior of both elastic and viscoelastic thin coatings bonded to a seemingly rigid substrate and sliding against a rough profile in the presence of Coulomb friction at the interface. The aim is to explore the effect of the coupling between the normal and tangential displacement fields arising from the finiteness of the material thickness and to quantify the contribution this can have on energy losses. We found that, due to normal-tangential coupling, asymmetric contacts and consequently additional friction are observed even for purely elastic layers, indeed associated …
We consider the dynamics of a charged inertial active Ornstein-Uhlenbeck particle in a viscoelastic suspension under the action of an uniform magnetic field. With the help of both numerical simulation and analytical framework, we exactly investigate the viscoelastic response of the particle to the magnetic field by means of particle trajectories, mean displacement, and mean square displacement (MSD) calculations. The simulated particle trajectories and MSD calculations reveal that the steady state response of a confined harmonic particle to the magnetic field show interesting features due to t…
We investigate freely expanding viscoelastic sheets. The sheets are produced by the impact of drops on a quartz plate covered with a thin layer of liquid nitrogen that suppresses shear viscous dissipation as a result of the cold Leidenfrost effect. The time evolution of the sheet is simultaneously recorded from top and side views using high-speed cameras. The investigated viscoelastic fluids are Maxwell fluids, which are characterized by low elastic moduli, and relaxation times that vary over almost two orders of magnitude, thus giving access to a large spectrum of viscoelastic and elastocapil…
The influence of compressibility on the coefficient of restitution in the normal impact of a rigid sphere onto a linear-viscoelastic compressible standard solid under quasi-static conditions is studied using a numerical solution procedure for the contact-impact problem based on the Method of Dimensionality Reduction. We find that the influence of compressible material behavior is most significant in parameter combinations with high energy dissipation in the bulk material during the impact. Thereby the restitution coefficient is usually underestimated, if the material is assumed to be incompres…
The functionality of adhesives relies on their response under the application of a load. Yet, it has remained a challenge to quantitatively relate the macroscopic dynamics of peeling to the dissipative processes inside the adhesive layer. Here we investigate the peeling of a reversible adhesive made of a polymer gel, measuring the relationship between the peeling force, the peeling velocity, and the geometry of the interface at small-scale. Experiments are compared to a theory based on the linear viscoelastic response of the adhesive, augmented with an elastocapillary regularization approach. …
Viscoelasticity reshapes the frequency response of a rotating magnetic particle
Zhejiang University of Science and Technology（浙江科技学院）；Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州国际创新学院）；School of Mechanical Engineering and Automation, Beihang University（北京航空航天大学机械与电气工程学院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院）
We investigate freely expanding sheets formed by ultrasoft gel beads, and liquid and viscoelastic drops, produced by the impact of the bead or drop on a silicon wafer covered with a thin layer of liquid nitrogen that suppresses viscous dissipation thanks to an inverse Leidenfrost effect. Our experiments show a unified behaviour for the impact dynamics that holds for solids, liquids, and viscoelastic fluids and that we rationalize by properly taking into account elastocapillary effects. In this framework, the classical impact dynamics of solids and liquids as far as viscous dissipation is negli…
