Concurrent factors determine toughening in the hydraulic fracture of poroelastic composites

Lucantonio, Alessandro; Noselli, Giovanni

doi:10.1007/s11012-017-0621-5

Cited by 8 publications

(6 citation statements)

References 14 publications

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“…The hydrogel is itself a composite (polymer chains saturated with water) with complex mechanical properties. In this work, as in many others, e.g., [7,8,17,18], we model it as a linear poroelastic material. To that end, let u ε : Ω g ε → R 3 denote the solid deformation in the gel part and let p ε : Ω g ε → R denote the pore pressure.…”

Section: Setting Of the Problem And Main Resultsmentioning

confidence: 99%

Homogenization of a Poroelasticity Model for Fibre-Reinforced Hydrogels

Edén¹,

Mahato²

2020

Preprint

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In this paper, the analysis and homogenization of a poroelastic model for the hydro-mechanical response of fibre-reinforced hydrogels is considered. Here, the medium in question is considered to be a highly heterogeneous two-component media composed of a connected fibre-scaffold with periodically distributed inclusions of hydrogel. While the fibres are assumed to be elastic, the hydromechanical response of hydrogel is modeled via Biot's poroelasticity.We show that the resulting mathematical problem admits a unique weak solution and investigate the limit behavior (in the sense of two-scale convergence) of the solutions with respect to a scale parameter, ε, characterizing the heterogeneity of the medium. While doing ε → 0, we arrive at an effective model where the micro variations of the pore pressure give rise to a micro stress correction at the macro scale.

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Section: Setting Of the Problem And Main Resultsmentioning

confidence: 99%

Homogenization of a Poroelasticity Model for Fibre-Reinforced Hydrogels

Edén¹,

Mahato²

2020

Preprint

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“…Hydraulic fracture examples are very common in mechanobiology, too, since fluid-driven fractures are intimately connected to cells and tissues. They influence numerous cellular functions [7,8,9], even from the very early stages of life [10]. Nowadays, the numerical simulation of fluid driven fractures continues to pose challenges and, depending upon the involved physical mechanisms, the complexity of the corresponding models may vary significantly [11].…”

Section: Introductionmentioning

confidence: 99%

A novel hydraulic fractures growth formulation

Fantoni,

Salvadori

2020

Preprint

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Propagation of a fluid-driven crack in an impermeable linear elastic medium under axis-symmetric conditions is investigated in the present work. The fluid exerting the pressure inside the crack is an incompressible Newtonian one and its front is allowed to lag behind the propagating fracture tip. The tip cavity is considered as filled by fluid vapors under constant pressure having a negligible value with respect to the far field confining stress. A novel algorithm is here presented, which is capable of tracking the evolution of both the fluid and the fracture fronts. Particularly, the fracture tracking is grounded on a recent viscous regularization of the quasi-static crack propagation problem as a standard dissipative system. It allows a simple and effective approximation of the fracture front velocity by imposing Griffith's criterion at every propagation step. Furthermore, for each new fracture configuration, a non linear system of integro-differential equations has to be solved. It arises from the non local elastic relationship existing between the crack opening and the fluid pressure, together with the non linear lubrication equation governing the flow of the fluid inside the fracture.

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“…Finally, all the proposed growth-based models lack an evolution structure, since they do not include the balance of solvent mass, and thus only allow to study the equilibrium shapes of swelling plates (Gemmer and Venkataramani, 2013). Transient swelling processes are fundamental, for instance, in the toughening of homogeneous (Noselli et al, 2016) and composite gels (Lucantonio et al, 2015a;Lucantonio and Noselli, 2016).…”

Section: Introductionmentioning

confidence: 99%

Large-strain poroelastic plate theory for polymer gels with applications to swelling-induced morphing of composite plates

Lucantonio

Tomassetti

DeSimone

2017

Composites Part B: Engineering

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We derive a large-strain plate model that allows to describe transient, coupled processes involving elasticity and solvent migration, by performing a dimensional reduction of a three-dimensional poroelastic theory. We apply the model to polymer gel plates, for which a specific kinematic constraint and constitutive relations hold. Finally, we assess the accuracy of the plate model with respect to the parent three-dimensional model through two numerical benchmarks, solved by means of the finite element method. Our results show that the theory offers an efficient computational framework for the study of swelling-induced morphing of composite gel plates.

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Concurrent factors determine toughening in the hydraulic fracture of poroelastic composites

Cited by 8 publications

References 14 publications

Homogenization of a Poroelasticity Model for Fibre-Reinforced Hydrogels

Homogenization of a Poroelasticity Model for Fibre-Reinforced Hydrogels

A novel hydraulic fractures growth formulation

Large-strain poroelastic plate theory for polymer gels with applications to swelling-induced morphing of composite plates

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