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Special issue on non-linear mechanics of biological structures
International Journal of Non-Linear Mechanics 46 (2011) 555–556
Contents lists available at ScienceDirect
International Journal of Non-Linear Mechanics journal homepage: www.elsevier.com/locate/nlm
Editorial
Special issue on non-linear mechanics of biological structures
This special issue dedicated to the non-linear mechanics of biological structures is an opportunity to feature in this journal a fascinating inquiry into the way naturally occurring mechanical structures and interactions govern or are governed by biological function. As the reader will be able to appreciate, many biological systems—from fish to spiders to pumpkins—have developed functions to optimize the use of resources or to play on subtle mechanical effects that are inherently non-linear. The focus of this issue on the interplay between biological function and mechanical structure not only allows us to answer fundamental questions in the life sciences, but also creates an opportunity to showcase the beauty and importance of mechanics. A century of unquestioning acceptance of linear theories in mechanics has lulled us into expecting response which is not typical. It appears likely that nonlinear effects will be discovered in increasing number and may eventually have a greater practical importance than is now foreseen. C. Truesdell, ‘‘An Idiot’s Fugitive Essays on Science: Methods, Criticism, Training, Circumstances’’, Springer-Verlag, 1984, pp. 18–19 Several papers in this issue are concerned with or inspired by biological locomotion; in aquatic environments, at the air–water interface, or in subsea wetted soils. The contributions in this volume demonstrate that the field of biological locomotion continues to be a vibrant field of research with great diversity and scientific outcomes. An underlying theme is that constraints on the musculature and evolutionary pressure toward reduced energy consumption during locomotion can be expected to induce structural changes in biological mechanisms that take optimal advantage of passive elements. In the study of human, bipedal locomotion, the paradigm of passive dynamic walking, in which gait-like dynamics are observed in anthropomorphic rigidbody mechanisms down slight inclines in the absence of actuation other than gravity, has inspired fundamental work in multibody systems, non-linear dynamics, biomechanics, robotics, and bioassistive device technology. Whether similar advantage follows by substituting passive, resistive, structural elements for fully prescribed and actuated joint kinematics in underwater locomotion is the focus of the paper by Wilson and Eldredge. These authors investigate the swimming efficiency in a viscous fluid environment, which results from jellyfish-inspired reciprocating shape change to an articulated rigid-body mechanism. The analysis demonstrates improvements in swimming performance when actuators are replaced by elastic springs and shows that optimal choices for the mechanical 0020-7462/$ - see front matter & 2011 Published by Elsevier Ltd. doi:10.1016/j.ijnonlinmec.2011.04.001
characteristics of the passive elements may be arrived at by considering local fluid–structure interactions associated with vortex shedding. Whereas actual jellyfish locomotion is recognized to rely on a more complex interplay between actuation and passive relaxation, the work serves as an inspiration for higherfidelity models of jellyfish structure and dynamics. Propulsive performance of an underwater swimmer is also the focus of the study by Eloy and Schouveiler. These authors consider the thrust and energy consumption that result from a prescribed undulatory swimming motion of a flexible plate. They identify optimal swimming gaits in terms of the wavelength of undulation and the frequency of oscillation and associate these with different regimes in leading-edge suction and body inertia. In particular, numerical observations of the characteristic Strouhal number suggest that undulating motion in swimming and flying animals is ‘‘tuned for high hydrodynamical efficiency.’’ The geometry studied by Eloy and Schouveiler resembles that of the family of rays, due to their flattened body shape and undulatory fin motions. As observed by the authors, these fish swim in the immediate vicinity of the sea floor, suggesting that an analysis of their locomotive performance would need to include the influence of the wall. The study of swimming-like motion in confined geometries is the focus of the work by Crowdy. Using an exact solution for a restricted motion of a solid cylinder near a no-slip wall, this author derives a non-linear dynamical system whose system state describes the swimming velocity and angular velocity of a wall-bounded, circular, low-Reynolds-number swimmer. As mentioned by the author, interactions between a swimming mechanism and confining boundaries may lead to spatio-temporally complex behaviors reminiscent of those observed for certain species of algae. In the paper by Alben, the interactions between point vortices and a flexible wall are analyzed in terms of the resultant wall deformations and the resultant speed of the point vortex as a function of the vortex distance from the wall. The author motivates his analysis by the importance of vortex–body interactions in biological flows, for example, the propulsive advantage that may result from swimming in the wake of vortices. Indeed, in the work by Oskouei et al., the emphasis is on interactions between neighboring von Karman vortex streets in the mid-wake region from a school of swimming fish. The authors demonstrate non-trivial exchange of fluid between neighboring wakes as the relative distances decrease, suggestive of potentially complex cooperative effects between members of the school. Distinctly different paradigms for locomotion are presented in the papers by Jung et al. on burrowing strategies of razor clams and by Prakash and Bush on water-walking insects and spiders.
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Editorial / International Journal of Non-Linear Mechanics 46 (2011) 555–556
In the former study, reciprocal kinematic shape changes are shown to result in net displacement through frictional interactions with the surrounding soil. Jung et al. find that burrowing efficiency is particularly sensitive to body aspect ratio. The propulsive efficiency of water-striding creatures is shown experimentally by Prakash and Bush to be closely related to the orientation and elasticity of hairy cuticles on the creature’s legs. This is suggested as a novel paradigm for bio-inspired design of ‘‘unidirectional superhydrophobic surfaces.’’ Rather than a precursor to locomotion, whale flukeprints are the characteristic oval-shaped persistent surface patches that result from swimming or diving motion of whales. Commonly used to detect and trace whales, Levy et al. demonstrate that these ‘‘whale footprints’’ are primarily associated with vortex ring shedding from the whale’s tail (fluke) and the interactions of these rings with the ocean surface rather than with the presence of any naturally occurring surfactants. The work reported here relies on in-the-field observations, hydrodynamics, and lab tests with an experimental fluke. Still in the aquatic domain, the work by Ewoldt et al. concerns the non-linear rheological properties of hagfish slime, a fibrous gel-like substance used by the animal as a defensive measure against predators. The work reported here is the first experimental study of the material properties of the slime, observing a remarkable combination of strain-softening of the overall elastic modulus and strain-hardening of the local tangent elastic modulus at large strain. A microstructural network model is proposed by the authors to explain the observed constitutive behavior and as more general approach to the study of gel-like biological materials. Material properties and the interplay between structure and gravity are the sources of the shape changes seen in giant pumpkins during peak growth studied by Hu et al. In this truly unique contribution, the authors, inspired by in-the-field observations, as well as physical experiments on whole pumpkins, propose a structural model that couples plant growth with tensile yield stress. When implemented in a computational simulation, the model demonstrates that this coupling provides a mechanism for relaxing local internal stress concentrations, thereby supporting continued growth and the absence of crack formation.
As hypothesized by Aristoff et al. in their contribution to this special issue, biological structures may exist whose purpose it is to deform in the presence of liquid water so as to limit further evaporation. In their paper, the authors analyze the deformations of flexible sheets separated by a narrow initially gas-filled gap, as a liquid volume is imbibed and eventually trapped between the sheets. The predictions of their study include estimates on the bounds of biological structures that would rely on such elastocapillary imbibition for manipulating water. They further suggest innovative biomimetic approaches to device design. Finally, a phenomenon associated with dental caries, biologically induced mineral precipitation may also be used to engineering advantage, for example, for bioremediation of areas contaminated by heavy metals. By accounting for effects associated with bio-induced chemistry, fluid mechanics, thermodynamics, and electrodiffusion, Zhang and Klapper analyze the spatio-temporal dynamics of calcium carbonate precipitation in the presence of a ureolytic biofilm. Numerical simulations performed by the authors show that the presence of electrodiffusion results in the occurrence of a net electric field across the mixture, which in turn serves to enhance precipitation. The application of mechanics to the study of micro-organisms is still in its infancy and this last contribution clearly demonstrates the importance of a quantitative approach to microbiology. As exemplified by these brief summaries of the content of this special issue, the coupling between mechanics and biology offers a wealth of challenging modeling, analysis, simulation, and bioinspired design problems that will advance further inquiry into the individual subject areas while promoting cross-disciplinary efforts and the sharing of insight and information. It is our hope that this special issue can serve as an inspiration and a useful reference.
Harry Dankowicz, Anette Hosoi, Alain Goriely E-mail addresses: [email protected] (H. Dankowicz), [email protected] (A. Hosoi), [email protected] (A. Goriely)
Contents lists available at ScienceDirect
International Journal of Non-Linear Mechanics journal homepage: www.elsevier.com/locate/nlm
Editorial
Special issue on non-linear mechanics of biological structures
This special issue dedicated to the non-linear mechanics of biological structures is an opportunity to feature in this journal a fascinating inquiry into the way naturally occurring mechanical structures and interactions govern or are governed by biological function. As the reader will be able to appreciate, many biological systems—from fish to spiders to pumpkins—have developed functions to optimize the use of resources or to play on subtle mechanical effects that are inherently non-linear. The focus of this issue on the interplay between biological function and mechanical structure not only allows us to answer fundamental questions in the life sciences, but also creates an opportunity to showcase the beauty and importance of mechanics. A century of unquestioning acceptance of linear theories in mechanics has lulled us into expecting response which is not typical. It appears likely that nonlinear effects will be discovered in increasing number and may eventually have a greater practical importance than is now foreseen. C. Truesdell, ‘‘An Idiot’s Fugitive Essays on Science: Methods, Criticism, Training, Circumstances’’, Springer-Verlag, 1984, pp. 18–19 Several papers in this issue are concerned with or inspired by biological locomotion; in aquatic environments, at the air–water interface, or in subsea wetted soils. The contributions in this volume demonstrate that the field of biological locomotion continues to be a vibrant field of research with great diversity and scientific outcomes. An underlying theme is that constraints on the musculature and evolutionary pressure toward reduced energy consumption during locomotion can be expected to induce structural changes in biological mechanisms that take optimal advantage of passive elements. In the study of human, bipedal locomotion, the paradigm of passive dynamic walking, in which gait-like dynamics are observed in anthropomorphic rigidbody mechanisms down slight inclines in the absence of actuation other than gravity, has inspired fundamental work in multibody systems, non-linear dynamics, biomechanics, robotics, and bioassistive device technology. Whether similar advantage follows by substituting passive, resistive, structural elements for fully prescribed and actuated joint kinematics in underwater locomotion is the focus of the paper by Wilson and Eldredge. These authors investigate the swimming efficiency in a viscous fluid environment, which results from jellyfish-inspired reciprocating shape change to an articulated rigid-body mechanism. The analysis demonstrates improvements in swimming performance when actuators are replaced by elastic springs and shows that optimal choices for the mechanical 0020-7462/$ - see front matter & 2011 Published by Elsevier Ltd. doi:10.1016/j.ijnonlinmec.2011.04.001
characteristics of the passive elements may be arrived at by considering local fluid–structure interactions associated with vortex shedding. Whereas actual jellyfish locomotion is recognized to rely on a more complex interplay between actuation and passive relaxation, the work serves as an inspiration for higherfidelity models of jellyfish structure and dynamics. Propulsive performance of an underwater swimmer is also the focus of the study by Eloy and Schouveiler. These authors consider the thrust and energy consumption that result from a prescribed undulatory swimming motion of a flexible plate. They identify optimal swimming gaits in terms of the wavelength of undulation and the frequency of oscillation and associate these with different regimes in leading-edge suction and body inertia. In particular, numerical observations of the characteristic Strouhal number suggest that undulating motion in swimming and flying animals is ‘‘tuned for high hydrodynamical efficiency.’’ The geometry studied by Eloy and Schouveiler resembles that of the family of rays, due to their flattened body shape and undulatory fin motions. As observed by the authors, these fish swim in the immediate vicinity of the sea floor, suggesting that an analysis of their locomotive performance would need to include the influence of the wall. The study of swimming-like motion in confined geometries is the focus of the work by Crowdy. Using an exact solution for a restricted motion of a solid cylinder near a no-slip wall, this author derives a non-linear dynamical system whose system state describes the swimming velocity and angular velocity of a wall-bounded, circular, low-Reynolds-number swimmer. As mentioned by the author, interactions between a swimming mechanism and confining boundaries may lead to spatio-temporally complex behaviors reminiscent of those observed for certain species of algae. In the paper by Alben, the interactions between point vortices and a flexible wall are analyzed in terms of the resultant wall deformations and the resultant speed of the point vortex as a function of the vortex distance from the wall. The author motivates his analysis by the importance of vortex–body interactions in biological flows, for example, the propulsive advantage that may result from swimming in the wake of vortices. Indeed, in the work by Oskouei et al., the emphasis is on interactions between neighboring von Karman vortex streets in the mid-wake region from a school of swimming fish. The authors demonstrate non-trivial exchange of fluid between neighboring wakes as the relative distances decrease, suggestive of potentially complex cooperative effects between members of the school. Distinctly different paradigms for locomotion are presented in the papers by Jung et al. on burrowing strategies of razor clams and by Prakash and Bush on water-walking insects and spiders.
556
Editorial / International Journal of Non-Linear Mechanics 46 (2011) 555–556
In the former study, reciprocal kinematic shape changes are shown to result in net displacement through frictional interactions with the surrounding soil. Jung et al. find that burrowing efficiency is particularly sensitive to body aspect ratio. The propulsive efficiency of water-striding creatures is shown experimentally by Prakash and Bush to be closely related to the orientation and elasticity of hairy cuticles on the creature’s legs. This is suggested as a novel paradigm for bio-inspired design of ‘‘unidirectional superhydrophobic surfaces.’’ Rather than a precursor to locomotion, whale flukeprints are the characteristic oval-shaped persistent surface patches that result from swimming or diving motion of whales. Commonly used to detect and trace whales, Levy et al. demonstrate that these ‘‘whale footprints’’ are primarily associated with vortex ring shedding from the whale’s tail (fluke) and the interactions of these rings with the ocean surface rather than with the presence of any naturally occurring surfactants. The work reported here relies on in-the-field observations, hydrodynamics, and lab tests with an experimental fluke. Still in the aquatic domain, the work by Ewoldt et al. concerns the non-linear rheological properties of hagfish slime, a fibrous gel-like substance used by the animal as a defensive measure against predators. The work reported here is the first experimental study of the material properties of the slime, observing a remarkable combination of strain-softening of the overall elastic modulus and strain-hardening of the local tangent elastic modulus at large strain. A microstructural network model is proposed by the authors to explain the observed constitutive behavior and as more general approach to the study of gel-like biological materials. Material properties and the interplay between structure and gravity are the sources of the shape changes seen in giant pumpkins during peak growth studied by Hu et al. In this truly unique contribution, the authors, inspired by in-the-field observations, as well as physical experiments on whole pumpkins, propose a structural model that couples plant growth with tensile yield stress. When implemented in a computational simulation, the model demonstrates that this coupling provides a mechanism for relaxing local internal stress concentrations, thereby supporting continued growth and the absence of crack formation.
As hypothesized by Aristoff et al. in their contribution to this special issue, biological structures may exist whose purpose it is to deform in the presence of liquid water so as to limit further evaporation. In their paper, the authors analyze the deformations of flexible sheets separated by a narrow initially gas-filled gap, as a liquid volume is imbibed and eventually trapped between the sheets. The predictions of their study include estimates on the bounds of biological structures that would rely on such elastocapillary imbibition for manipulating water. They further suggest innovative biomimetic approaches to device design. Finally, a phenomenon associated with dental caries, biologically induced mineral precipitation may also be used to engineering advantage, for example, for bioremediation of areas contaminated by heavy metals. By accounting for effects associated with bio-induced chemistry, fluid mechanics, thermodynamics, and electrodiffusion, Zhang and Klapper analyze the spatio-temporal dynamics of calcium carbonate precipitation in the presence of a ureolytic biofilm. Numerical simulations performed by the authors show that the presence of electrodiffusion results in the occurrence of a net electric field across the mixture, which in turn serves to enhance precipitation. The application of mechanics to the study of micro-organisms is still in its infancy and this last contribution clearly demonstrates the importance of a quantitative approach to microbiology. As exemplified by these brief summaries of the content of this special issue, the coupling between mechanics and biology offers a wealth of challenging modeling, analysis, simulation, and bioinspired design problems that will advance further inquiry into the individual subject areas while promoting cross-disciplinary efforts and the sharing of insight and information. It is our hope that this special issue can serve as an inspiration and a useful reference.
Harry Dankowicz, Anette Hosoi, Alain Goriely E-mail addresses: [email protected] (H. Dankowicz), [email protected] (A. Hosoi), [email protected] (A. Goriely)