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Tuning cell rearrangements is essential in collective cell movement that underlies cancer progression, wound repair, and embryonic development. A key question is how tissue material properties and morphology emerge from cellular factors…
In this paper we introduce a new mathematical model for the active contraction of cardiac muscle, featuring different thermo-electric and nonlinear conductivity properties. The passive hyperelastic response of the tissue is described by an…
We investigate a continuum mechanical model for an adherent cell on two dimensional adhesive micropatterned substrates. The cell is modeled as an isotropic and homogeneous elastic material subject to uniform internal contractile stresses.…
Active gels are a class of biologically-relevant material containing embedded agents that spontaneously generate forces acting on a sparse filament network. In vitro experiments of protein filaments and molecular motors have revealed a…
Yield stress fluids display a rich rheological phenomenology. Beyond the defining existence of a yield stress in the steady state flow curve, this includes in many materials rather flat viscoelastic spectra over many decades of frequency in…
Surface stresses have recently emerged as a key player in the mechanics of highly compliant solids. The classic theories of contact mechanics describe adhesion with a compliant substrate as a competition between surface energies driving…
We introduce a mathematical model, based on networks, for the elasticity and plasticity of materials. We define the tension tensor for a periodic graph in a Euclidean space, and we show that the tension tensor expresses elasticity under…
We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…
Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are in turn transmitted to distant cells. We calculate the mechanical work that each cell performs in order to deform the matrix,…
This article is a description of elasticity theory for readers with mathematical background. The first sections are an abridgment of parts of the book by Marsden and Hughes, including a compact identification of the equations of motion as…
We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal…
It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can…
Traditionally, the deformation of continuum is divided into elastic, plastic, and flow. For a large deformation with cracking, they are combined together. So, for complicated deformation, a formulation to express the evolution of…
Active solids such as cell collectives, colloidal clusters, and active metamaterials exhibit diverse collective phenomena, ranging from rigid body motion to shape-changing mechanisms. The nonlinear dynamics of such active materials remains…
We study the flow of an electrically charged fluid through an elastic and porous medium. A three continuum model consisting of an elastic solid, a viscous fluid, and a mobile charge continuum is used. The relevant laws of physics are…
We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion and the $6-$fold orientational order…
Elasto-plastic models are among the most successful ways to study the critical properties of the plastic yielding transition of amorphous solids. Typically these models are studied under a condition of constant transition rates from one…
This paper first reviews the shoving model for the non-Arrhenius viscosity of viscous liquids. According to this model the main contribution to the activation energy of a flow event is the energy needed for molecules to shove aside the…
During development and under normal physiological conditions, biological tissues are continuously subjected to substantial mechanical stresses. In response to large deformations cells in a tissue must undergo multicellular rearrangements in…
Filamentous bio-materials such as fibrin or collagen networks exhibit an enormous stiffening of their elastic moduli upon large deformations. This pronounced nonlinear behavior stems from a significant separation between the stiffnesses…