On morphoelastic rods

Tiero, Alessandro; Tomassetti, Giuseppe

doi:10.1177/1081286514546178

Cited by 8 publications

(8 citation statements)

References 48 publications

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“…Future works can consider the effects of other physical quantities (i.e. capillary adhesion, intrinsic curvature and gravity) or the coupling of growth with internal stress (Tiero and Tomassetti, 2014) on the morphology and the critical parameters.…”

Section: Discussionmentioning

confidence: 99%

Snap buckling of a confined thin elastic sheet

Napoli

Turzi

2015

Proc. R. Soc. A.

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A growing or compressed thin elastic sheet adhered to a rigid substrate can exhibit a buckling instability, forming an inward hump. Our study shows that the strip morphology depends on the delicate balance between the compression energy and the bending energy. We find that this instability is a first-order phase transition between the adhered solution and the buckled solution whose main control parameter is related to the sheet stretchability. In the nearly unstretchable regime, we provide an analytic expression for the critical threshold. Compressibility is the key assumption which allows us to resolve the apparent paradox of an unbounded pressure exerted on the external wall by a confined flexible loop.

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Section: Discussionmentioning

confidence: 99%

Snap buckling of a confined thin elastic sheet

Napoli

Turzi

2015

Proc. R. Soc. A.

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“…As we shall see below, this extra energetic term substantially affects the evolution of growth. This point is also discussed in the paper [32], which contains other examples on how the cost of accretion may be relevant to the kinetics of growth.…”

Section: The Kinetics Of Accretionmentioning

confidence: 97%

“…Returning to equations ( 14) and (15) we observe that on the growth surface r = r 0 incompressibility implies λ r = λ θ = 1. However this does not mean that the body is unstressed at r = r 0 as is seen from (32).…”

mentioning

confidence: 99%

Steady accretion of an elastic body on a hard spherical surface and the notion of a four-dimensional reference space

Tomassetti

Cohen

Abeyaratne

2016

Journal of the Mechanics and Physics of Solids

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Taking the cue from experiments on actin growth on spherical beads, we formulate and solve a model problem describing the accretion of an incompressible elastic solid on a rigid sphere due to attachment of diffusing free particles. One of the peculiar characteristics of this problem is that accretion takes place on the interior surface that separates the body from its support rather than on its exterior surface, and hence is responsible for stress accumulation. Simultaneously, ablation takes place at the outer surface where material is removed from the body. As the body grows, mechanical effects associated with the build-up of stress and strain energy slow down accretion and promote ablation. Eventually, the system reaches a point where internal accretion is balanced by external ablation. The present study is concerned with this stationary regime called "treadmilling".The principal ingredients of our model are: a nonstandard choice of the reference configuration, which allows us to cope with the continually evolving material structure; and a driving force and a kinetic law for accretion/ablation that involves the difference in chemical potential, strain energy and the radial stress. By combining these ingredients we arrive at an algebraic system which governs the stationary treadmilling state. We establish the conditions under which this system has a solution and we show that this solution is unique. Moreover, by an asymptotic analysis we show that for small beads the thickness of the solid is proportional to the radius of the support and is strongly affected by the stiffness of the solid, whereas for large beads the stiffness of the solid is essentially irrelevant, the thickness being proportional to a characteristic length that depends on the parameters that govern diffusion and accretion kinetics.

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“…While the entropy inequality can provide useful guidelines in closed systems, it often does not provide valuable information in open systems that may contain entropy sinks. Early thermodynamic considerations identified the Mandel stress and the Eshelby stress as key quantities in formulating growth laws [43,46]. They also identify two types of growth processes [6]: first, passive growth processes during which the dissipation inequality is satisfied even in the absence of entropy sinks.…”

Section: Thermodynamicsmentioning

confidence: 99%

“…Early thermodynamic considerations identified the Mandel stress and the Eshelby stress as key quantities in formulating growth laws [43,46]. They also identify two types of growth processes [6]: first, passive growth processes during which the dissipation inequality is satisfied even in the absence of entropy sinks.…”

Section: Thermodynamicsmentioning

confidence: 99%

Growth and remodelling of living tissues: perspectives, challenges and opportunities

Ambrosi

Amar²,

Cyron

et al. 2019

J. R. Soc. Interface.

177

120

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One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.

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On morphoelastic rods

Cited by 8 publications

References 48 publications

Snap buckling of a confined thin elastic sheet

Snap buckling of a confined thin elastic sheet

Steady accretion of an elastic body on a hard spherical surface and the notion of a four-dimensional reference space

Growth and remodelling of living tissues: perspectives, challenges and opportunities

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