Bending instabilities of soft biological tissues

Destrade, Michel; Annaidh, Aisling Ní; Coman, Ciprian D.

doi:10.1016/j.ijsolstr.2009.08.017

Cited by 92 publications

(94 citation statements)

References 30 publications

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“…Recalling the boundary condition AE s ðr o Þ ¼ 0, it is possible to define a functional dependence between the traction and the displacement amplitudes as r 2 AE s ¼ Z s U s , where Z s is the conditional impedance matrix, with Z s ðr o Þ ¼ 0 [28]. Therefore, it is possible to use Z s in Eq.…”

mentioning

confidence: 99%

Buckling Instability in Growing Tumor Spheroids

Ciarletta

2013

Phys. Rev. Lett.

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A growing tumor is subjected to intrinsic physical forces, arising from the cellular turnover in a spatially constrained environment. This work demonstrates that such residual solid stresses can provoke a buckling instability in heterogeneous tumor spheroids. The growth rate ratio between the outer shell of proliferative cells and the inner necrotic core is the control parameter of this instability. The buckled morphology is found to depend both on the elastic and the geometric properties of the tumor components, suggesting a key role of residual stresses for promoting tumor invasiveness.

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mentioning

confidence: 99%

Buckling Instability in Growing Tumor Spheroids

Ciarletta

2013

Phys. Rev. Lett.

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“…Optimal here is used in the sense that an efficient numerical procedure can be implemented in order to solve the incremental problem [32,34,24]. The hermitian property, also implies that the matrix iÎG is symmetric, whereÎ is defined as the block matrix with 0-blocks on the diagonal and identity blocks elsewhere.…”

Section: Solution Using the Stroh Formalismmentioning

confidence: 99%

Mathematical Modeling of Morphogenesis in Living Materials

Balbi

Ciarletta

2016

Lecture Notes in Mathematics

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From a mathematical viewpoint, the study of morphogenesis focuses on the description of all geometric and structural changes which locally orchestrate the underlying biological processes directing the formation of a macroscopic shape in living matter. In this chapter, we introduce a continuous chemo-mechanical approach of morphogenesis, deriving the balance principles and evolution laws for both volumetric and interfacial processes. The proposed theory is applied to the study of pattern formation for either a fluid-like and a solid-like biological system model, using both theoretical methods and simulation tools.

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“…Three different models of the Ogden family (Ogden, 1972(Ogden, , 1997, frequently used to approximate the constitutive behaviour of elastomeric solids (Bucchi & Hearn, 2013a, 2013bDestrade, Annaidh, & Ciprian, 2009;Fu & Xie, 2012;Volokh, 2011), are considered:…”

Section: Ogden Classmentioning

confidence: 99%

The role of constitutive relation in the stability of hyper-elastic spherical membranes subjected to dynamic inflation

Rodríguez-Martínez

Fernández-Sáez

Zaera

2015

International Journal of Engineering Science

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a b s t r a c tIn this work the mechanical response of hyper-elastic spherical membranes subjected to dynamic inflation is revisited. Specifically, a comprehensive analysis on the role that the constitutive behaviour of the material has on the mechanical stability of the membrane has been developed. Six different strain-energy functions, frequently used to approximate the constitutive behaviour of elastomeric solids, have been considered: three of the Mooney-Rivlin class and three of the Ogden class. For all the constitutive models used, the material parameters have been obtained from Bucchi and Hearn (2013a, 2013b), where the same set of experimental results was used to calibrate the models. We show that essential features of the dynamic response of the spherical shell are closely related to the strain-energy function selected to describe the constitutive behaviour of the membrane. As reported by Hearn (2013a, 2013b), this issue is frequently overlooked within the literature since too often only one strain-energy function is used to address this type of dynamic problems.

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Bending instabilities of soft biological tissues

Cited by 92 publications

References 30 publications

Buckling Instability in Growing Tumor Spheroids

Buckling Instability in Growing Tumor Spheroids

Mathematical Modeling of Morphogenesis in Living Materials

The role of constitutive relation in the stability of hyper-elastic spherical membranes subjected to dynamic inflation

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