We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of large solid-like deformations, in any dimension, of the type that might otherwise require the finite element method. The generality of the method stems from its ability to easily compute kinematic quantities essential to solid mechanics, that are elusive outside of Lagrangian frame. This introductory work focuses on large-strain, hyperelastic materials. After a brief review of hyperelasticity, a discretization of the method is presented and some non-trivial elastic deformations are simulated, both static and dynamic. The method's accuracy is directly verified against known analytical solutions.
We use numerical simulations to show how a fully flexible filament binding to a deformable cylindrical surface may acquire a macroscopic persistence length and a helical conformation. This is a result of the nontrivial elastic response to deformations of elastic sheets. We find that the filament's helical pitch is completely determined by the mechanical properties of the surface, and can be tuned by varying the filament binding energy. We propose simple scaling arguments to understand the physical mechanism behind this phenomenon and present a phase diagram indicating under what conditions one…
Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the body. In contrast to bulk growth in the interior, the description of surface growth requires the addition of new continuum particles to the body. This is challenging for standard continuum formulations for solids that are meant for situations with a fixed amount of material. Recent approaches to handle this have used time-evolving reference configurations. In t…
Actomyosin actively generates contractile forces that provide the plasma membrane with the deformation stresses essential to carry out biological processes. Although the contractile property of purified actomyosin has been extensively studied, to understand the physical contribution of the actiomyosin contractile force on a deformable membrane is still a challenging problem and of great interest in the field of biophysics. Here, we reconstituted a model system with a cell-sized deformable interface that exhibits anomalous curvature dependent wrinkling caused by actomyosin cortex underneath the…
We present a simple method for accessing the elastic properties of microscopic deformable particles. This method is based on measuring the pressure-induced deformation of soft particles as they are forced through a tapered glass microcapillary. It allows us to determine both the compressive and the shear modulus of a deformable object in one single experiment. Measurements on a model system of poly-acrylamide microgel particles exhibit excellent agreement with measurements on bulk gels of identical composition. Our approach is applicable over a wide range of mechanical properties and should th…
Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex, or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number interfacial hydrodynamics, chemistry, and geometry, and govern important biological processes such as cellular traffic, division, migration, or tissue morphogenesis. To address the modelling challenges posed by this class of problems, in which interfacial phenomena tightly interact with the shape and dynamics of the surface, we develop a general continuum mechanics an…
The steady flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens model for blood) in a two-dimensional channel, partly bound by a deformable, finite thickness neo-Hookean solid, is computed. The limiting Weissenberg number beyond which computations fail to converge is found to increase with increasing dimensionless solid elasticity parameter Γ, following the trend Owens > FENE- P > Oldroyd-B. The highly shear thinning nature of Owens model leads to the elastic solid always collapsing into the channel, for the wide range of values of Γ considered here. In the case of the FENE-P and Ol…
We analyze a suspension of deformable particles in a pressure-driven flow. The suspension is composed of neutrally buoyant initially spherical particles and a Newtonian carrier fluid, and the flow is solved by means of direct numerical simulations, using a fully Eulerian method based on a one-continuum formulation. The solid phase is modeled with an incompressible viscous hyperelastic constitutive relation, and the flow is characterized by three main dimensionless parameters, namely the solid volume fraction, the Reynolds and capillary numbers. The dependency of the effective viscosity on thes…
Phase-Field Fracture Simulation of Highly Deformable Thin Structures via a Discrete Differential Geometry Framework
Northwestern Polytechnical University（西北工业大学）；Newcastle University（纽卡斯尔大学）；Shenzhen Research Institute of Northwestern Polytechnical University（西北工业大学深圳研究院）；University of Liverpool（利物浦大学）；Sun Yat-sen University（中山大学）；Harvard University（哈佛大学）
Young's law fails on soft solid and liquid substrates where there are substantial deformations near the contact line. On liquid substrates, this is captured by Neumann's classic analysis, which provides a geometrical construction for minimising the interfacial free energy. On soft solids, the total free energy includes an additional contribution from elasticity. A linear-elastic model incorporating an out-of-plane restoring force due to solid surface tension was recently shown to accurately predict the equilibrium shape of a thin elastic film due to a large sessile droplet. Here, we extend thi…
We present a comparative modelling study of fluid-structure interactions in microchannels. Through a mathematical analysis based on plate theory and the lubrication approximation for low-Reynolds-number flow, we derive models for the flow rate-pressure drop relation for long shallow microchannels with both thin and thick deformable top walls. These relations are tested against full three-dimensional two-way-coupled fluid-structure interaction simulations. Three types of microchannels, representing different elasticity regimes and having been experimentally characterized previously, are chosen …
Numerical and experimental framework for bending elasticity of highly flexible slender structures
School of Integrated Design Engineering, Graduate School of Science and Technology, Keio University（庆应义塾大学理工学研究科综合设计工程学院）；Graduate School of Engineering Science, Osaka University（大阪大学工学研究科）；Department of Mechanical Engineering, Faculty of Science and Technology, Keio University（庆应义塾大学理工学部机械工学科）
Compressing a porous material will decrease the volume of the pore space, driving fluid out. Similarly, injecting fluid into a porous material can expand the pore space, distorting the solid skeleton. This poromechanical coupling has applications ranging from tissue mechanics to hydrogeology. The classical theory of linear poroelasticity captures this coupling by combining Darcy's law with Terzaghi's effective stress and linear elasticity in a linearized kinematic framework. Linear poroelasticity is a good model for very small deformations, but it becomes increasingly inappropriate for moderat…
