The softness distribution index: towards the creation of guidelines for the modeling of soft-bodied robots

Modeling soft robots is not an easy task owing to their highly nonlinear mechanical behavior. So far, several researchers have tackled the problem using different approaches, each having advantages and drawbacks in terms of accuracy, ease of implementation, and computational burden. The soft robotics community is currently working to develop a unified framework for modeling. Our contribution in this direction consists of a novel dimensionless quantity that we call the softness distribution index (SDI). The SDI for a given soft body is computed based on the distribution of its structural properties. We show that the index can serve as a tool in the choice of a modeling technique among multiple approaches suggested in literature. At the moment, the investigation is limited to bodies performing planar bending. The aim of this work is twofold: (i) to highlight the importance of the distribution of the geometrical and material properties of a soft robotic link/body throughout its structure; and (ii) to demonstrate that a classification based on this distribution provides guidelines for the modeling.

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Internal constraints and arrested relaxation in main-chain nematic elastomers

Nature Communications ◽

10.1038/s41467-021-21036-3 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Takuya Ohzono ◽

Kaoru Katoh ◽

Hiroyuki Minamikawa ◽

Mohand O. Saed ◽

Eugene M. Terentjev

Keyword(s):

Mechanical Properties ◽

Main Chain ◽

Polymer Networks ◽

Nematic Order ◽

Nematic Elastomers ◽

Nematic Director ◽

Highly Nonlinear ◽

Nonlinear Mechanical ◽

Liquid Crystal Elastomers ◽

Memory Applications

AbstractNematic liquid crystal elastomers (N-LCE) exhibit intriguing mechanical properties, such as reversible actuation and soft elasticity, which manifests as a wide plateau of low nearly-constant stress upon stretching. N-LCE also have a characteristically slow stress relaxation, which sometimes prevents their shape recovery. To understand how the inherent nematic order retards and arrests the equilibration, here we examine hysteretic stress-strain characteristics in a series of specifically designed main-chain N-LCE, investigating both macroscopic mechanical properties and the microscopic nematic director distribution under applied strains. The hysteretic features are attributed to the dynamics of thermodynamically unfavoured hairpins, the sharp folds on anisotropic polymer strands, the creation and transition of which are restricted by the nematic order. These findings provide a new avenue for tuning the hysteretic nature of N-LCE at both macro- and microscopic levels via different designs of polymer networks, toward materials with highly nonlinear mechanical properties and shape-memory applications.

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Material properties and effect of preconditioning of human sclera, optic nerve, and optic nerve sheath

Biomechanics and Modeling in Mechanobiology ◽

10.1007/s10237-021-01448-2 ◽

2021 ◽

Author(s):

Joseph Park ◽

Andrew Shin ◽

Somaye Jafari ◽

Joseph L. Demer

Keyword(s):

Optic Nerve ◽

Mechanical Behavior ◽

Material Properties ◽

Biomechanical Properties ◽

Ocular Tissues ◽

Tangent Moduli ◽

Nonlinear Mechanical ◽

Human Eyes ◽

Range Of Variation ◽

Great Stress

AbstractThe optic nerve (ON) is a recently recognized tractional load on the eye during larger horizontal eye rotations. In order to understand the mechanical behavior of the eye during adduction, it is necessary to characterize material properties of the sclera, ON, and in particular its sheath. We performed tensile loading of specimens taken from fresh postmortem human eyes to characterize the range of variation in their biomechanical properties and determine the effect of preconditioning. We fitted reduced polynomial hyperelastic models to represent the nonlinear tensile behavior of the anterior, equatorial, posterior, and peripapillary sclera, as well as the ON and its sheath. For comparison, we analyzed tangent moduli in low and high strain regions to represent stiffness. Scleral stiffness generally decreased from anterior to posterior ocular regions. The ON had the lowest tangent modulus, but was surrounded by a much stiffer sheath. The low-strain hyperelastic behaviors of adjacent anatomical regions of the ON, ON sheath, and posterior sclera were similar as appropriate to avoid discontinuities at their boundaries. Regional stiffnesses within individual eyes were moderately correlated, implying that mechanical properties in one region of an eye do not reliably reflect properties of another region of that eye, and that potentially pathological combinations could occur in an eye if regional properties are discrepant. Preconditioning modestly stiffened ocular tissues, except peripapillary sclera that softened. The nonlinear mechanical behavior of posterior ocular tissues permits their stresses to match closely at low strains, although progressively increasing strain causes particularly great stress in the peripapillary region.

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A Unified and Efficient Approach to Power Flow Analysis

Energies ◽

10.3390/en12122425 ◽

2019 ◽

Vol 12 (12) ◽

pp. 2425

Author(s):

HyungSeon Oh

Keyword(s):

Power Flow ◽

Optimal Power Flow ◽

System Analysis ◽

Flow Analysis ◽

Model Systems ◽

Flow State ◽

Unified Framework ◽

Convergence Region ◽

Power Flow Analysis ◽

Highly Nonlinear

Highly nonlinear and nonconvex power flow analysis plays a key role in the monitoring, control, and operation of power systems. There is no analytic solution to power flow problems, and therefore, finding a numerical solution is oftentimes an aim of modern computation in power system analysis. An iterative Newton-Raphson method is widely in use. While most times this method finds a solution in a reasonable time, it often involves numerical robustness issues, such as a limited convergence region and an ill-conditioned system. Sometimes, the truncation error may not be small enough to ignore, which can make the iterative process significantly expansive. We propose a new unified framework, based on the Kronecker product, that does not involve any truncation, and which is bilinear to make it possible to incorporate statistical analysis. The proposed method is tested for power flow, state estimation, probabilistic power flow, and optimal power flow studies on various IEEE model systems.

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A Theoretical Investigation of the Effect of the Stochasticity in the Material Properties on the Chatter Detection During Turning

Volume 8: 29th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2017-67900 ◽

2017 ◽

Cited By ~ 6

Author(s):

Henrik T. Sykora ◽

Daniel Bachrathy ◽

Gabor Stepan

Keyword(s):

White Noise ◽

Time Evolution ◽

Material Properties ◽

Discretization Method ◽

Chatter Detection ◽

Turning Process ◽

Stochastic Parameters ◽

Stability Chart ◽

The Moment ◽

Moment Stability

In this work the effect of the inhomogeneous material properties are investigated in regenerative turning processes by introducing white noise in the cutting coefficient. The model is a one degree of freedom linear delayed oscillator with stochastic parameters. A full discretization method is used to calculate the time evolution of the second moment to determine the moment stability of the turning process. The resultant stability chart is compared with the deterministic turning model.

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Bridging proper orthogonal decomposition methods and augmented Newton–Krylov algorithms: An adaptive model order reduction for highly nonlinear mechanical problems

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2010.10.009 ◽

2011 ◽

Vol 200 (5-8) ◽

pp. 850-866 ◽

Cited By ~ 80

Author(s):

P. Kerfriden ◽

P. Gosselet ◽

S. Adhikari ◽

S.P.A. Bordas

Keyword(s):

Proper Orthogonal Decomposition ◽

Model Order Reduction ◽

Order Reduction ◽

Decomposition Methods ◽

Orthogonal Decomposition ◽

Adaptive Model ◽

Model Order ◽

Highly Nonlinear ◽

Nonlinear Mechanical ◽

Proper Orthogonal

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Growing and Evolving Soft Robots

Artificial Life ◽

10.1162/artl_a_00101 ◽

2014 ◽

Vol 20 (1) ◽

pp. 143-162 ◽

Cited By ~ 36

Author(s):

John Rieffel ◽

Davis Knox ◽

Schuyler Smith ◽

Barry Trimmer

Keyword(s):

Material Properties ◽

Body Shape ◽

Design Development ◽

Seed Structure ◽

Soft Body ◽

Soft Robots ◽

Body Shapes ◽

And Control ◽

High Degree ◽

Degree Of Coupling

Completely soft and flexible robots offer to revolutionize fields ranging from search and rescue to endoscopic surgery. One of the outstanding challenges in this burgeoning field is the chicken-and-egg problem of body-brain design: Development of locomotion requires the preexistence of a locomotion-capable body, and development of a location-capable body requires the preexistence of a locomotive gait. This problem is compounded by the high degree of coupling between the material properties of a soft body (such as stiffness or damping coefficients) and the effectiveness of a gait. This article synthesizes four years of research into soft robotics, in particular describing three approaches to the co-discovery of soft robot morphology and control. In the first, muscle placement and firing patterns are coevolved for a fixed body shape with fixed material properties. In the second, the material properties of a simulated soft body coevolve alongside locomotive gaits, with body shape and muscle placement fixed. In the third, a developmental encoding is used to scalably grow elaborate soft body shapes from a small seed structure. Considerations of the simulation time and the challenges of physically implementing soft robots in the real world are discussed.

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Cell contraction induces long-ranged stress stiffening in the extracellular matrix

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1722619115 ◽

2018 ◽

Vol 115 (16) ◽

pp. 4075-4080 ◽

Cited By ~ 86

Author(s):

Yu Long Han ◽

Pierre Ronceray ◽

Guoqiang Xu ◽

Andrea Malandrino ◽

Roger D. Kamm ◽

...

Keyword(s):

Extracellular Matrix ◽

Optical Tweezers ◽

Model Systems ◽

Animal Cells ◽

Surrounding Matrix ◽

Highly Nonlinear ◽

Nonlinear Stress ◽

Nonlinear Mechanical ◽

The Matrix ◽

3D Matrix

Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here, we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing nonlinear stress inference microscopy (NSIM), a technique to infer stress fields in a 3D matrix from nonlinear microrheology measurements with optical tweezers. Using NSIM and simulations, we reveal large long-ranged cell-generated stresses capable of buckling filaments in the matrix. These stresses give rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which can provide a mechanism for mechanical communication between cells.

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The Influence of the Material Properties on the Ultimate Behaviour of Aluminium H-shaped Beams

The Open Construction and Building Technology Journal ◽

10.2174/1874836802115010176 ◽

2021 ◽

Vol 15 (1) ◽

pp. 176-188

Author(s):

Rosario Montuori ◽

Elide Nastri ◽

Vincenzo Piluso ◽

Alessandro Pisapia

Keyword(s):

Material Properties ◽

Slenderness Ratio ◽

Bending Moment ◽

Constitutive Law ◽

Rotation Capacity ◽

Moment Gradient ◽

Dimensional Parameters ◽

The Moment ◽

Plastic Rotation Capacity ◽

Ultimate Resistance

Background: In this paper, the influence of the Ramberg-Osgood exponent on the ultimate behaviour of the H-shaped (or I-shaped) aluminium beams subjected to non-uniform bending moment is investigated. Methods: In particular, the results of a wide parametric analysis recently carried out by the authors are herein exploited to point out the influence of the material properties. The flange slenderness, the flange-to-web slenderness ratio, and the non-dimensional shear length, accounting for the moment gradient, are the main non-dimensional parameters governing the ultimate resistance and the rotation capacity of H-shaped aluminium beams. Results: The influence of these parameters was investigated considering four different materials covering both low yielding-high hardening alloys and high yielding-low hardening alloys, which are characterised by significant differences in the values of the Ramberg-Osgood exponent of the stress-strain constitutive law of the material. Conclusion: Finally, empirical formulations for predicting the non-dimensional ultimate flexural strength and the plastic rotation capacity of H-section aluminium beams under moment gradient have been provided as a function of the Ramberg-Osgood exponent and all the above non-dimensional parameters.

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Stiffness Comparisons Between Adventitia, Media and Full Thickness Specimens From Human Atherosclerotic Carotid Arteries

ASME 2009 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2009-206401 ◽

2009 ◽

Author(s):

Allen H. Hoffman ◽

Zhongzhao Teng ◽

Calvin Mui ◽

Jie Zheng ◽

Pamela K. Woodard ◽

...

Keyword(s):

Material Properties ◽

Computational Models ◽

Carotid Arteries ◽

Layered Composite ◽

Material Behavior ◽

Full Thickness ◽

Paired Samples ◽

Highly Nonlinear ◽

Deductive Method ◽

The Media

Arteries display highly nonlinear, anisotropic material behavior and can be considered to be a layered composite of fiber oriented materials composed of three layers: intima, media and adventitia. The intima does not affect the material properties of the artery. Thus, the mechanical properties of an artery result from the combined interaction of the media and adventitia with each layer displaying different material properties. It has been widely accepted that atherosclerosis changes the material properties of the arterial wall. However, little experimental data exists relating the properties of the media and adventitia of atherosclerotic vessels to the overall properties of the artery. Knowledge of the properties of human atherosclerotic tissues is essential for an improved understanding the effects of atherosclerosis and also for creating more accurate computational models for predicting the effects of the disease [1]. A prior study of bovine carotid arteries determined the properties of the adventitia and media using a deductive method [2]. This paper focuses on directly measuring and comparing the stiffness of paired samples of adventitia, media and full thickness specimens from human atherosclerotic carotid arteries.

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ON EFFICIENCY GAINS FROM MULTIPLE INCOMPLETE SUBSAMPLES

Econometric Theory ◽

10.1017/s0266466619000239 ◽

2019 ◽

Vol 36 (3) ◽

pp. 488-525

Author(s):

Saraswata Chaudhuri

Keyword(s):

Survey Methods ◽

Cost Effective ◽

Target Population ◽

Efficient Estimation ◽

Efficiency Gains ◽

Unified Framework ◽

Full Generality ◽

Dimensional Parameter ◽

Finite Dimensional ◽

The Moment

Cost-effective survey methods such as multi(R)-phase sampling typically generate samples that are collections of monotonic subsamples, i.e., the variables observed for the units in subsample r are also observed for the units in subsample r + 1 for r = 1,…,R – 1. These subsamples represent subpopulations that can be systematically different if the selection of a unit in each phase of sampling depends on the observed variables for that unit from past phases. Our article is about optimally combining all the subsamples for the efficient estimation of a finite dimensional parameter defined by moment restrictions on a generic target population that is an arbitrary union of these subpopulations. Only the R-th subsample is assumed to contain all the variables that are arguments of the moment function. Semiparametric efficiency bounds for estimation are obtained under a unified framework, allowing for full generality of the selection on observables in the sampling design. Contribution of each subsample toward efficient estimation is analyzed; and this turns out to differ fundamentally from that in setups where the same collection of subsamples is instead generated unplanned by unknown sampling. Uniquely, our setup enables all the subsamples to contribute to the efficient estimation for all the target populations, which we show is not possible in other setups. Efficient estimation is standard. Simulation evidence of substantive efficiency gains from using all the subsamples is provided for all the targets.

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