Localized Structures in Indented Shells: A Numerical Investigation

We present results from a numerical investigation of the localization of deformation in thin elastomeric spherical shells loaded by differently shaped indenters. Beyond a critical indentation, the deformation of the shell ceases to be axisymmetric and sharp structures of localized curvature form, referred to as “s-cones,” for “shell-cones.” We perform a series of numerical experiments to systematically explore the parameter space. We find that the localization process is independent of the radius of the shell. The ratio of the radius of the shell to its thickness, however, is an important parameter in the localization process. Throughout, we find that the maximum principal strains remain below 6%, even at the s-cones. As a result, using either a linear elastic (LE) or hyperelastic constitutive description yields nearly indistinguishable results. Friction between the indenter and the shell is also shown to play an important role in localization. Tuning this frictional contact can suppress localization and increase the load-bearing capacity of the shell under indentation.National Science Foundation (U.S.) (1122374)National Science Foundation (U.S.) (CMMI-1351449

Localization of deformation in thin shells under indentation

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 72-77).We perform a hybrid experimental and numerical study of the localization of deformation in thin spherical elastic shells under indentation. Past a critical indentation, the deformation of the shell ceases to be axisymmetric and sharp points of localized curvature form. In plates, these sharp points are known as d-cones. By way of analogy, regions of localization in shells are referred to as s-cones, for 'shell-cones'. We quantify how the formation and evolution of s-cones is affected by the indenter's curvature. Juxtaposing results from precision model experiments and Finite Element simulations enables the exploration of the frictional nature of the shell-indenter contact. The numerics also allow for a characterization of the relative properties of strain energy focusing, at the different loci of localization. The predictive power of the numerics is taken advantage of to further explore parameter space and perform numerical experiments that are not easily conducted physically. This combined experimental and computational approach allows us to gain invaluable physical insight towards rationalizing this geometrically nonlinear process.by Alice M. Nasto.S.M

Strain-stiffening in random packings of entangled granular chains

Random packings of granular chains are presented as a model polymer system to investigate the contribution of entanglements to strain-stiffening in the absence of Brownian motion. The chain packings are sheared in triaxial compression experiments. For short chain lengths, these packings yield when the shear stress exceeds a the scale of the confining pressure, similar to packings of spherical particles. In contrast, packings of chains which are long enough to form loops exhibit strain-stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography measurements reveal that the strain-stiffening packings contain system-spanning clusters of entangled chains.Comment: 4 pages, 4 figures. submitted to Physical Review Letter

Hairy interfaces

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 97-102).Textured surfaces are known to play an important role in water-repellency and uptake for a number of creatures. While the influence of chemistry and surface roughness on the wettability of surfaces has been studied extensively, little is known about the role of larger-scale objects such as hairs. This thesis is directed towards rationalizing the benefits gained from hairy textures through a combined experimental and theoretical approach. First, we are motivated by semi-aquatic mammals, who rely on fur for insulation underwater. This thesis investigates the mechanism of dynamic air entrainment for hairy surfaces plunged in liquid. Hairy surfaces that are fabricated by casting PDMS elastomer in laser cut molds are plunged into a fluid bath. Modeling the hairy texture as a network of capillary tubes, the imbibition speed of liquid into the hairs is obtained through a balance of hydrostatic pressure and viscous stress. In this scenario, the bending of the hairs, capillary forces, and inertial effects are negligible. The maximum diving depth that can be achieved before the hairs are wetted to the roots is predicted from a comparison of the diving speed and imbibition speed. Second, motivated by nectar-drinking animals with hairy tongues, we investigate the reverse scenario, where a hairy surface is withdrawn from a bath of fluid, emerging with viscous liquid entrained in the hairy texture. The drainage of the liquid trapped between the texture is modeled using a Darcy-Brinkmann like approach. The amount of fluid that is entrained depends on the viscosity of the fluid, the density of the hairs, and the withdrawal speed. Both theory and experiments show that there is an optimal hair density to maximize fluid uptake. Finally, we investigate drop impact on hairy surfaces. By varying the speed of the drop, the spacing of the hairs, and the viscosity of the liquid, we observe a variety of behaviors. In some cases, the liquid drop can remain on top of the hair after impact, similar to a Cassie-Baxter state. If the drop penetrates the hairy surface, the hairs can resist its spreading. Using this scenario as a reference case, we rationalize the role of the hairs in mitigating the inertia of the impacting drop through a balance of inertial, viscous, and surface tension effects.by Alice Nasto.Ph. D

Localized Structures in Indented Shells: A Numerical Investigation

We present results from a numerical investigation of the localization of deformation in thin elastomeric spherical shells loaded by differently shaped indenters. Beyond a critical indentation, the deformation of the shell ceases to be axisymmetric and sharp structures of localized curvature form, referred to as “s-cones,” for “shell-cones.” We perform a series of numerical experiments to systematically explore the parameter space. We find that the localization process is independent of the radius of the shell. The ratio of the radius of the shell to its thickness, however, is an important parameter in the localization process. Throughout, we find that the maximum principal strains remain below 6%, even at the s-cones. As a result, using either a linear elastic (LE) or hyperelastic constitutive description yields nearly indistinguishable results. Friction between the indenter and the shell is also shown to play an important role in localization. Tuning this frictional contact can suppress localization and increase the load-bearing capacity of the shell under indentation

Drop impact on hairy surfaces

We investigate the impact of liquid drops on millimeter-scale hairy surfaces. By varying the speed of the drop, the spacing of the hairs, and the viscosity of the liquid, we observe a variety of behaviors. In some cases, the liquid drop can remain on top of the hair after impact, similar to a Cassie-Baxter superhydrophobic state. If the drop penetrates the hairy surface, the hairs can resist droplet spreading. Using this scenario as a reference case, we rationalize the role of the hairs in dissipating the kinetic energy of the impacting drop through a balance of inertia, viscosity, and surface tension. The various observed behaviors are classified according to scenarios in which kinetic energy is insufficient or in excess of this reference scenario, an argument that allows us to build and rationalize a phase diagram

Viscous entrainment on hairy surfaces

Nectar-drinking bats and honeybees have tongues covered with hairlike structures, enhancing their ability to take up viscous nectar by dipping. Using a combination of model experiments and theory, we explore the physical mechanisms that govern viscous entrainment in a hairy texture. Hairy surfaces are fabricated using laser cut molds and casting samples with polydimethylsiloxane (PDMS) elastomer. We model the liquid trapped within the texture using a Darcy-Brinkmann-like approach and derive the drainage flow solution. The amount of fluid that is entrained is dependent on the viscosity of the fluid, the density of the hairs, and the withdrawal speed. Both experiments and theory reveal an optimal hair density to maximize fluid uptake.United States. Army Research Office (Grant W911NF-15-1-0166

Drop impact on hairy surfaces

We investigate the impact of liquid drops on millimeter-scale hairy surfaces. By varying the speed of the drop, the spacing of the hairs, and the viscosity of the liquid, we observe a variety of behaviors. In some cases, the liquid drop can remain on top of the hair after impact, similar to a Cassie-Baxter superhydrophobic state. If the drop penetrates the hairy surface, the hairs can resist droplet spreading. Using this scenario as a reference case, we rationalize the role of the hairs in dissipating the kinetic energy of the impacting drop through a balance of inertia, viscosity, and surface tension. The various observed behaviors are classified according to scenarios in which kinetic energy is insufficient or in excess of this reference scenario, an argument that allows us to build and rationalize a phase diagram

Localization of deformation in thin shells under indentation

We perform a hybrid experimental and numerical study of the localization of deformation in thin spherical elastic shells under indentation. Past a critical indentation, the deformation of the shell ceases to be axisymmetric and sharp points of localized curvature form. In plates, these sharp points are known as d-cones. By way of analogy, we refer to regions of localization in shells as s-cones, for ‘shell-cones’. We quantify how the formation and evolution of s-cones is affected by the indenter's curvature. Juxtaposing results from precision model experiments and finite element simulations enables us to explore the frictional nature of the shell–indenter contact and characterize the relative properties of strain energy focusing, at different loci of localization. Our combined experimental and computational approach allows us to gain invaluable physical insight towards rationalizing this geometrically nonlinear process