Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler

Gidoni, Paolo; DeSimone, Antonio

doi:10.1007/s11012-016-0408-0

Cited by 19 publications

(21 citation statements)

References 19 publications

(25 reference statements)

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“…Figure 3: Representation of the sets C ⊂ X * , with in red the sectionĈ sh (above), and C sh ⊂ Z * (below) for Example 3.3, in the two main qualitative scenarios (cf. [29]). The compatible direction of motion, indicated for the edges of the stasis domains, can be obtained at a glance from the pictures above, applying Remark 2.8.…”

Section: Interpretation As Sweeping Processmentioning

confidence: 99%

“…a circular orbit in the space of shape control parameters). Indeed, in case of anisotropic friction a suitable periodic shape-change may be able to move the crawler also in the direction of higher opposing friction, as shown in [5,27,29]. Nevertheless, also in this case anisotropic friction can facilitate motility in the chosen direction, as intuitively imaginable.…”

Section: Introductionmentioning

confidence: 98%

“…We then use our formulation of the problem to represent the motility properties of the crawler through its stasis domain. This description, introduced in [29], allows to analyse the locomotion capabilities without any assumption on the shape-change strategy adopted. The main models with time-independent are discussed in Section 3.…”

Section: Introductionmentioning

confidence: 99%

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Rate-independent soft crawlers

Gidoni

2018

The Quarterly Journal of Mechanics and Applied Mathematics

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This paper applies the theory of rate-independent systems to model the locomotion of bio-mimetic soft crawlers. We prove the well-posedness of the approach and illustrate how the various strategies adopted by crawlers to achieve locomotion, such as friction anisotropy, complex shape changes and control on the friction coefficients, can be effectively described in terms of stasis domains.Compared to other rate-independent systems, locomotion models do not present any Dirichlet boundary condition, so that all rigid translations are admissible displacements, resulting in a non-coercivity of the energy term. We prove that existence and uniqueness of solution are guaranteed under suitable assumptions on the dissipation potential. Such results are then extended to the case of time-dependent dissipation.arXiv:1710.08340v2 [math.FA] 30 Dec 2017 p. gidoni: Rate-independent soft crawlers Physically, this equation is a force balance: configurational forces (e.g. tension in an elastic body) are described as the spatial gradient of the internal energy E, while frictional forces are obtained as the subdifferential of a dissipation potential R, assumed to be positively homogeneous of degree one, in order to guarantee rate-independence.The variational structure of the problem has favoured the development of an advanced and extensive mathematical theory of rate-independent systems, assisting and inspired by applications in physics of solids and continuum mechanics, modelling phenomena such as elastoplasticity, fracture, damage, phase transitions.Along with these, systems with dry friction has immediately emerged as one of the most fitting applications of the theory, already from the first major achievements in the 70s, with the introduction of Moreau's Sweeping processes [49]. As today, dry friction still contributes to the development of the theory. We mention the recent results adopting multiscale approaches to study the effective friction in the case of fast-oscillating bodies [32] and of hairy surfaces [28]; or the illustration of the properties of non-convex rate independent systems using using simple, representative dry friction toy models [2].

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Section: Interpretation As Sweeping Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Rate-independent soft crawlers

Gidoni

2018

The Quarterly Journal of Mechanics and Applied Mathematics

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“…The first goal of this paper is to study the implications of (1), (2) on the finite-strain Cosserat algorithm, assuming radial loading and holonomic-type plasticity [16,17,18]. Secondly, as main result, a two-step preconditioning strategy of the L-BFGS algorithm is proposed that consists of a predictor step followed by a corrector iteration for solving the timediscrete problem.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of a solution method for finite-strain holonomic plasticity of Cosserat materials

Blesgen

Amendola

2019

Meccanica

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This article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent) Cosserat plasticity problem for materials, possibly with microstructure. Two improvements are made in contrast to earlier approaches: First, the micro-rotations are parameterized with the help of an Euler-Rodrigues formula related to quaternions. Secondly, as main result, a novel two-pass preconditioning scheme for searching the energyminimizing solutions based on the limited memory Broyden-Fletcher-Goldstein-Shanno quasi-Newton method is proposed that consists of a predictor step and a corrector-iteration. After outlining the necessary adaptations to the model, numerical simulations compare the performance and efficiency of the new and the old algorithm. The proposed numerical model can be effectively employed for studying the mechanical response of complicated materials featuring large size effects.

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“…toys, where this interplay can easily be studied, are the so-called descending woodpecker, the toy ramp walkers, and the rocking toy animals, see Figure 1.2. We refer to [9,6,8,7] for models on locomotion for micro-machines or animals and to [21] for the slip-stick dynamics of polymers on inhomogeneous surfaces. Application to time-dependent hysteresis in piezo-ceramic actuators are given in [2,1].…”

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Averaging of time-periodic dissipation potentials in rate-independent processes

Heida¹,

Mielke²

2017

Discrete &Amp; Continuous Dynamical Systems - S

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We study the existence and well-posedness of rate-independent systems (or hysteresis operators) with a dissipation potential that oscillates in time with period ε. In particular, for the case of quadratic energies in a Hilbert space, we study the averaging limit ε → 0 and show that the eective dissipation potential is given by the minimum of all friction thresholds in one period, more precisely as the intersection of all the characteristic domains. We show that the rates of the process do not converge weakly, hence our analysis uses the notion of energetic solutions and relies on a detailed estimates to obtain a suitable equi-continuity of the solutions in the limit ε → 0. 1. Introduction. In most applications of hysteresis or rate-independent systems the hysteresis operator or the dissipation potential is time-independent while the system is driven by a time-dependent external loading, see [24, 4, 11, 17]. However, there are also systems where the internal dissipative mechanism depends on time in a prescribed manner, see [19, 12, 2] and the references below for mathematical treatments of this case. Moreover, there are mechanical devices where friction is modulated time-periodically by using a rotating unbalance, as in a vibratory plate compactor used in construction areas, see Figure 1.1. In this paper we are interested in cases where the dissipation process is oscillating periodically on a much faster time scale than the driving of the system by an external loading. Similar, time-dependent friction mechanisms occur during walking or crawling of animals or mechanical devices. Typically, there is a periodic gait, where the contact pressure of the dierent extremities oscillates periodically, and only those legs are moved for which the normal pressure is minimal. Simple mechanical 2010 Mathematics Subject Classication. Primary: 34C55, 47J20, 49J40, 74N30. Key words and phrases. Rate-independent systems, play operator with time-dependent thresholds, energetic solutions, locomotion, sweeping process. M.H. was nanced by Deutsche Forschungsgemeinschaft (DFG) through Grant CRC 1114 Scaling Cascades in Complex Systems, Project C05 Eective models for interfaces with many scales. A.M. was partially supported by ERC through AdG 267802 AnaMultiScale. Summing this inequality over k = 1,. .. , N we see that many terms cancel by the telescoping eect. Moreover, taking the limit N → ∞, we use t N = t and t 0 = 0 and can employ Lemma 3.2 to obtain the desired estimate (4.26). Hence the proof of Proposition 4.6 is complete.

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Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler

Cited by 19 publications

References 19 publications

Rate-independent soft crawlers

Rate-independent soft crawlers

Mathematical analysis of a solution method for finite-strain holonomic plasticity of Cosserat materials

Averaging of time-periodic dissipation potentials in rate-independent processes

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