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Jacques M. Huyghe
Bernal Institute, University of Limerick, Limerick, Ireland

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Review
Published: 19 February 2021 in Biophysical Reviews
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The strain-generated potential (SGP) is a well-established mechanism in cartilaginous tissues whereby mechanical forces generate electrical potentials. In articular cartilage (AC) and the intervertebral disc (IVD), studies on the SGP have focused on fluid- and ionic-driven effects, namely Donnan, diffusion and streaming potentials. However, recent evidence has indicated a direct coupling between strain and electrical potential. Piezoelectricity is one such mechanism whereby deformation of most biological structures, like collagen, can directly generate an electrical potential. In this review, the SGP in AC and the IVD will be revisited in light of piezoelectricity and mechanotransduction. While the evidence base for physiologically significant piezoelectric responses in tissue is lacking, difficulties in quantifying the physiological response and imperfect measurement techniques may have underestimated the property. Hindering our understanding of the SGP further, numerical models to-date have negated ferroelectric effects in the SGP and have utilised classic Donnan theory that, as evidence argues, may be oversimplified. Moreover, changes in the SGP with degeneration due to an altered extracellular matrix (ECM) indicate that the significance of ionic-driven mechanisms may diminish relative to the piezoelectric response. The SGP, and these mechanisms behind it, are finally discussed in relation to the cell response.

ACS Style

Philip Poillot; Christine L. Le Maitre; Jacques M. Huyghe. The strain-generated electrical potential in cartilaginous tissues: a role for piezoelectricity. Biophysical Reviews 2021, 13, 91 -100.

AMA Style

Philip Poillot, Christine L. Le Maitre, Jacques M. Huyghe. The strain-generated electrical potential in cartilaginous tissues: a role for piezoelectricity. Biophysical Reviews. 2021; 13 (1):91-100.

Chicago/Turabian Style

Philip Poillot; Christine L. Le Maitre; Jacques M. Huyghe. 2021. "The strain-generated electrical potential in cartilaginous tissues: a role for piezoelectricity." Biophysical Reviews 13, no. 1: 91-100.

Book chapter
Published: 17 December 2020 in Poromechanics II
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ACS Style

J.M. Huyghe; R. van Loon; F.T.R. Baaijens; P.M. van Kemenade; T.H. Smit. We all are porous media. Poromechanics II 2020, 17 -27.

AMA Style

J.M. Huyghe, R. van Loon, F.T.R. Baaijens, P.M. van Kemenade, T.H. Smit. We all are porous media. Poromechanics II. 2020; ():17-27.

Chicago/Turabian Style

J.M. Huyghe; R. van Loon; F.T.R. Baaijens; P.M. van Kemenade; T.H. Smit. 2020. "We all are porous media." Poromechanics II , no. : 17-27.

Journal article
Published: 24 November 2020 in Materials & Design
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Mechanotransduction is the initiation of an electrochemical signal as a result of mechanical stimuli. It is found predominately in biological tissue and its mechanisms are well documented. In the gel like tissues of the body, such as articular cartilage and intervertebral discs, mechanotransduction regulates matrix building and degrading processes as well as keeping the tissues adequately hydrated, both with the aim of minimizing degradation. The electrochemical responses to mechanical loading at constant volume of an inanimate hydrogel could assist in the understanding of these processes. There is considerable evidence that the modulus of hydrated tissues and hydrogels depend explicitly on ionic concentration. By modeling the mechano-electrochemical relationship of a hydrogel, the coupling of the elastic and electrochemical energies can be quantified. In turn, the mechanisms that govern this phenomenon can be better understood. This study modifies the Flory-Rehner theory of gels, using material-specific experimental data as input. The results show up to a 11% difference in equilibrium swelling magnitude compared to the Flory-Rehner model. Furthermore, under isochoric deformation, an increase in electrical potential is shown with increasing shear strain, something which is not possible with conventional Flory-Rehner and Donnan theory. This aligns the continuum model presented here more closely with both experiment and microscopic theories. The mechanosensing capabilities as well as varying swelling responses in different solution concentrations highlight the models potential applications in both biological and technological settings.

ACS Style

Eanna Fennell; Jacques M. Huyghe. A three-dimensional mechano-electrochemical material model of mechanosensing hydrogels. Materials & Design 2020, 198, 109340 .

AMA Style

Eanna Fennell, Jacques M. Huyghe. A three-dimensional mechano-electrochemical material model of mechanosensing hydrogels. Materials & Design. 2020; 198 ():109340.

Chicago/Turabian Style

Eanna Fennell; Jacques M. Huyghe. 2020. "A three-dimensional mechano-electrochemical material model of mechanosensing hydrogels." Materials & Design 198, no. : 109340.

Website
Published: 10 September 2020 in Computer Methods in Biomechanics & Biomedical Engineering – 2
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The swelling and shrinking behaviour of soft biological tissues is described by a four components mixture theory. In this theory four components are distinguished: a charged solid, a fluid, cations and anions. By using balance equations, constitutive equations and equations of state, a set of coupled differential equations is derived. Because of the distinction between cations and anions, we are able to describe electrical phenomena like streaming potentials. A one-dimensional finite element implementation of this model is made by using a Galerkin method, an implicit time discretization and the Newton-Raphson iteration procedure. This implementation is used to simulate confined swelling and compression experiments. It appears that physically realistic values for the stiffness, permeability and diffusion coefficients are adequate to fit the experiments. We do not need a chemical expansion stress.

ACS Style

A.J.H. Frijns; Jacques Huyghe; J.D. Janssen. Four Components Mixture Theory Applied to Soft Biological Tissue. Computer Methods in Biomechanics & Biomedical Engineering – 2 2020, 519 -526.

AMA Style

A.J.H. Frijns, Jacques Huyghe, J.D. Janssen. Four Components Mixture Theory Applied to Soft Biological Tissue. Computer Methods in Biomechanics & Biomedical Engineering – 2. 2020; ():519-526.

Chicago/Turabian Style

A.J.H. Frijns; Jacques Huyghe; J.D. Janssen. 2020. "Four Components Mixture Theory Applied to Soft Biological Tissue." Computer Methods in Biomechanics & Biomedical Engineering – 2 , no. : 519-526.

Website
Published: 10 September 2020 in Computer Methods in Biomechanics & Biomedical Engineering – 2
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Mixture models are used extensively for the description of the mechanical behaviour of biological tissues. Because of their increasing complexity there is a need for new methods to validate the models and to determine the material parameters in the constitutive equations of the individual components and their interaction. In the paper a mixed numerical experimental method to determine the material parameters in biphasic mixtures is summarized and a recursive estimation algorithm is derived to estimate parameters for biphasic mixtures. In a simulation it is shown that an inverse analysis to determine 4 material parameters can be done in a CPU-time of the order of one single direct analysis. Moreover, some results of experiments with a synthetic model material are discussed. The latter were used to validate a tri-phasic material model and have shown that the theory according to Snijders [7] is not complete.

ACS Style

C.W. Oomens; Jacques Huyghe; J.D. Janssen. Mixture Models: Validation and Parameter Estimation. Computer Methods in Biomechanics & Biomedical Engineering – 2 2020, 511 -518.

AMA Style

C.W. Oomens, Jacques Huyghe, J.D. Janssen. Mixture Models: Validation and Parameter Estimation. Computer Methods in Biomechanics & Biomedical Engineering – 2. 2020; ():511-518.

Chicago/Turabian Style

C.W. Oomens; Jacques Huyghe; J.D. Janssen. 2020. "Mixture Models: Validation and Parameter Estimation." Computer Methods in Biomechanics & Biomedical Engineering – 2 , no. : 511-518.

Journal article
Published: 09 July 2020 in International Journal of Engineering Science
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Hydrogels have a wide range of applications from medical devices to tissue engineering to industrial health products. The numerical modeling of these porous structures can provide insight into their in-situ performance. However, an accurate constitutive model to replicate the stress-strain behavior of the swelling process is essential in ensuring the efficacy of the simulation. This study presents a strain dependent constitutive model for describing the finite deformation of superabsorbent polymers undergoing solvent induced swelling. Like many elastic materials, stretch-induced softening and hardening of these polymers occurs at large deformations. In order to incorporate the deformation dependent modulus into the new model, the shear modulus of sodium polyacrylate gels were measured using a rheometer as a function of swelling. Through numerical simulations on spherical gels, the effect of both cross-link density and the dependent modulus is investigated against a control model. As experimental quantification of the initial porosity is difficult and often not consistent between samples, Monte-Carlo simulations are implemented to experimentally verify the new model. Furthermore, this model is applied to experimental uniaxial tension data of incompressible rubber to allow comparison to other strain hardening constitutive models.

ACS Style

Eanna Fennell; Szymon Leszczynski; Juliane Kamphus; Jacques M. Huyghe. A strain induced softening and hardening constitutive model for superabsorbent polymers undergoing finite deformation. International Journal of Engineering Science 2020, 154, 103346 .

AMA Style

Eanna Fennell, Szymon Leszczynski, Juliane Kamphus, Jacques M. Huyghe. A strain induced softening and hardening constitutive model for superabsorbent polymers undergoing finite deformation. International Journal of Engineering Science. 2020; 154 ():103346.

Chicago/Turabian Style

Eanna Fennell; Szymon Leszczynski; Juliane Kamphus; Jacques M. Huyghe. 2020. "A strain induced softening and hardening constitutive model for superabsorbent polymers undergoing finite deformation." International Journal of Engineering Science 154, no. : 103346.

Original paper
Published: 21 May 2020 in Computational Mechanics
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Swelling involving (extremely) large deformations simulations have wide range of applications in biomedicine, tissue engineering and hygienic product design. Typically, standard FEM is used in which deformations and chemical potential are chosen to be the prime variables. On the other hand, mixed hybrid finite element method (MHFEM) featuring an additional independent variable field flux possesses local mass conservation property. Such a property has shown its success in Darcy’s type equations with heterogeneous permeability. In this work, we perform a full-round comparison between MHFEM and FEM in solving swelling problems involving large deformations. Specifically, based on the permeability distributions, the problems fall into three categories: constant permeability, strain-dependent permeability and permeability with a discontinuous interface. For each category, we compare the two methods in aspects like solution convergence robustness, deformation, chemical potential and flux field accuracy and computational cost. We conclude that MHFEM outperforms standard FEM in terms of solution convergence robustness and the accuracy of all three fields when a swelling problem involves discontinuous interface in permeability.

ACS Style

Cong Yu; Kamyar Malakpoor; Jacques M. Huyghe. Comparing mixed hybrid finite element method with standard FEM in swelling simulations involving extremely large deformations. Computational Mechanics 2020, 66, 287 -309.

AMA Style

Cong Yu, Kamyar Malakpoor, Jacques M. Huyghe. Comparing mixed hybrid finite element method with standard FEM in swelling simulations involving extremely large deformations. Computational Mechanics. 2020; 66 (2):287-309.

Chicago/Turabian Style

Cong Yu; Kamyar Malakpoor; Jacques M. Huyghe. 2020. "Comparing mixed hybrid finite element method with standard FEM in swelling simulations involving extremely large deformations." Computational Mechanics 66, no. 2: 287-309.

Journal article
Published: 07 March 2020 in Polymers
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The Flory–Rehner theoretical description of the free energy in a hydrogel swelling model can be broken into two swelling components: the mixing energy and the ionic energy. Conventionally for ionized gels, the ionic energy is characterized as the main contributor to swelling and, therefore, the mixing energy is assumed negligible. However, this assumption is made at the equilibrium state and ignores the dynamics of gel swelling. Here, the influence of the mixing energy on swelling ionized gels is quantified through numerical simulations on sodium polyacrylate using a Mixed Hybrid Finite Element Method. For univalent and divalent solutions, at initial porosities greater than 0.90, the contribution of the mixing energy is negligible. However, at initial porosities less than 0.90, the total swelling pressure is significantly influenced by the mixing energy. Therefore, both ionic and mixing energies are required for the modeling of sodium polyacrylate ionized gel swelling. The numerical model results are in good agreement with the analytical solution as well as experimental swelling tests.

ACS Style

Eanna Fennell; Juliane Kamphus; Jacques M. Huyghe. The Importance of the Mixing Energy in Ionized Superabsorbent Polymer Swelling Models. Polymers 2020, 12, 609 .

AMA Style

Eanna Fennell, Juliane Kamphus, Jacques M. Huyghe. The Importance of the Mixing Energy in Ionized Superabsorbent Polymer Swelling Models. Polymers. 2020; 12 (3):609.

Chicago/Turabian Style

Eanna Fennell; Juliane Kamphus; Jacques M. Huyghe. 2020. "The Importance of the Mixing Energy in Ionized Superabsorbent Polymer Swelling Models." Polymers 12, no. 3: 609.

Review
Published: 28 September 2019 in Molecules
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A hydrogel is a polymeric three-dimensional network structure. The applications of this material type are diversified over a broad range of fields. Their soft nature and similarity to natural tissue allows for their use in tissue engineering, medical devices, agriculture, and industrial health products. However, as the demand for such materials increases, the need to understand the material mechanics is paramount across all fields. As a result, many attempts to numerically model the swelling and drying of chemically responsive hydrogels have been published. Material characterization of the mechanical properties of a gel bead under osmotic loading is difficult. As a result, much of the literature has implemented variants of swelling theories. Therefore, this article focuses on reviewing the current literature and outlining the numerical models of swelling hydrogels as a result of exposure to chemical stimuli. Furthermore, the experimental techniques attempting to quantify bulk gel mechanics are summarized. Finally, an overview on the mechanisms governing the formation of geometric surface instabilities during transient swelling of soft materials is provided.

ACS Style

Eanna Fennell; Jacques M. Huyghe. Chemically Responsive Hydrogel Deformation Mechanics: A Review. Molecules 2019, 24, 3521 .

AMA Style

Eanna Fennell, Jacques M. Huyghe. Chemically Responsive Hydrogel Deformation Mechanics: A Review. Molecules. 2019; 24 (19):3521.

Chicago/Turabian Style

Eanna Fennell; Jacques M. Huyghe. 2019. "Chemically Responsive Hydrogel Deformation Mechanics: A Review." Molecules 24, no. 19: 3521.

Journal article
Published: 27 May 2019 in Polymers
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In numerous industrial applications, the microstructure of materials is critical for performance. However, finite element models tend to average out the microstructure. Hence, finite element simulations are often unsuitable for optimisation of the microstructure. The present paper presents a modelling technique that addresses this limitation for superabsorbent polymers with a partially cross-linked surface layer. These are widely used in the industry for a variety of functions. Different designs of the cross-linked layer have different material properties, influencing the performance of the hydrogel. In this work, the effects of intrinsic properties on the fracture nucleation and propagation in cross-linked hydrogels are studied. The numerical implementation for crack propagation and nucleation is based on the framework of the extended finite element method and the enhanced local pressure model to capture the pressure difference and fluid flow between the crack and the hydrogel, and coupled with the cohesive method to achieve crack propagation without re-meshing. Two groups of numerical examples are given: (1) effects on crack propagation, and (2) effects on crack nucleation. Within each example, we studied the effects of the stiffness (shear modulus) and ultimate strength of the material separately. Simulations demonstrate that the crack behaviour is influenced by the intrinsic properties of the hydrogel, which gives numerical support for the structural design of the cross-linked hydrogel.

ACS Style

Jingqian Ding; Ernst W. Remij; Joris J. C. Remmers; Jacques M. Huyghe. Effects of Intrinsic Properties on Fracture Nucleation and Propagation in Swelling Hydrogels. Polymers 2019, 11, 926 .

AMA Style

Jingqian Ding, Ernst W. Remij, Joris J. C. Remmers, Jacques M. Huyghe. Effects of Intrinsic Properties on Fracture Nucleation and Propagation in Swelling Hydrogels. Polymers. 2019; 11 (5):926.

Chicago/Turabian Style

Jingqian Ding; Ernst W. Remij; Joris J. C. Remmers; Jacques M. Huyghe. 2019. "Effects of Intrinsic Properties on Fracture Nucleation and Propagation in Swelling Hydrogels." Polymers 11, no. 5: 926.

Original paper
Published: 04 September 2018 in Computational Mechanics
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Ionized hydrogels, as osmoelastic media, swell enormously (1000 times its original volume in unionized water) due to the osmotic pressure difference caused by the presence of the negatively charged ion groups attached to the solid matrix (polymer chains). The coupling between the extremely large deformations (induced by swelling) and fluid permeation is a field of application that regular poroelasticity formulations cannot handle. In this work, we present a mixed hybrid finite element (MHFE) computational framework featuring a three-field (deformation-chemical potential-flux) formulation. This formulation guarantees that mass conservation is preserved both locally and globally. The impact of such a property on the swelling simulations is demonstrated by four numerical examples in 2D. This paper focuses on the implementation aspects of the MHFE model and shows that it stays robust and accurate for a volume increase of more than 3000%.

ACS Style

Cong Yu; Kamyar Malakpoor; Jacques M. Huyghe. A mixed hybrid finite element framework for the simulation of swelling ionized hydrogels. Computational Mechanics 2018, 63, 835 -852.

AMA Style

Cong Yu, Kamyar Malakpoor, Jacques M. Huyghe. A mixed hybrid finite element framework for the simulation of swelling ionized hydrogels. Computational Mechanics. 2018; 63 (5):835-852.

Chicago/Turabian Style

Cong Yu; Kamyar Malakpoor; Jacques M. Huyghe. 2018. "A mixed hybrid finite element framework for the simulation of swelling ionized hydrogels." Computational Mechanics 63, no. 5: 835-852.

Journal article
Published: 12 July 2018 in Journal of Applied Mechanics
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Stepwise crack propagation is evidently observed in experiments both in geomaterials and in hydrogels. Pizzocolo et al. (2012, “Mode I Crack Propagation in Hydrogels is Step Wise,” Eng. Fract. Mech., 97(1), pp. 72–79) show experimental evidence that mode I crack propagation in hydrogel is stepwise. The pattern of the intermittent crack growth is influenced by many factors, such as porosity of the material, the permeability of the fluid, the stiffness of the material, etc. The pause duration time is negatively correlated with the stiffness of the material, while the average propagation length per step is positively correlated. In this paper, we integrate extended finite element method (XFEM) and enhanced local pressure (ELP) method, and incorporate cohesive relation to reproduce the experiments of Pizzocolo et al. in the finite deformation regime. We investigate the stepwise phenomenon in air and in water, respectively, under mode I fracture. Our simulations show that despite the homogeneous material properties, the crack growth under mode I fracture is stepwise, and this pattern is influenced by the hydraulic permeability and the porosity of the material. Simulated pause duration is negatively correlated with stiffness, and the average propagating length is positively correlated with stiffness. In order to eliminate the numerical artifacts, we also take different time increments into consideration. The staccato propagation does not disappear with smaller time increments, and the pattern is approximately insensitive to the time increment. However, we do not observe stepwise crack growth scheme when we simulate fracture in homogeneous rocks.

ACS Style

Jingqian Ding; Ernst W. Remij; Joris J. C. Remmers; Jacques M. Huyghe. Swelling-Driven Crack Propagation in Large Deformation in Ionized Hydrogel. Journal of Applied Mechanics 2018, 85, 101011 .

AMA Style

Jingqian Ding, Ernst W. Remij, Joris J. C. Remmers, Jacques M. Huyghe. Swelling-Driven Crack Propagation in Large Deformation in Ionized Hydrogel. Journal of Applied Mechanics. 2018; 85 (10):101011.

Chicago/Turabian Style

Jingqian Ding; Ernst W. Remij; Joris J. C. Remmers; Jacques M. Huyghe. 2018. "Swelling-Driven Crack Propagation in Large Deformation in Ionized Hydrogel." Journal of Applied Mechanics 85, no. 10: 101011.

Article
Published: 16 March 2018 in Transport in Porous Media
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ACS Style

Jacques M. Huyghe; Ehsan Nikooee; S. Majid Hassanizadeh. Reply to the Comments on “Bridging Effective Stress and Soil Water Retention Equations in Deforming Unsaturated Porous Media: A Thermodynamic Approach”—by Nasser Khalili and Arman Khoshghalb. Transport in Porous Media 2018, 122, 521 -526.

AMA Style

Jacques M. Huyghe, Ehsan Nikooee, S. Majid Hassanizadeh. Reply to the Comments on “Bridging Effective Stress and Soil Water Retention Equations in Deforming Unsaturated Porous Media: A Thermodynamic Approach”—by Nasser Khalili and Arman Khoshghalb. Transport in Porous Media. 2018; 122 (3):521-526.

Chicago/Turabian Style

Jacques M. Huyghe; Ehsan Nikooee; S. Majid Hassanizadeh. 2018. "Reply to the Comments on “Bridging Effective Stress and Soil Water Retention Equations in Deforming Unsaturated Porous Media: A Thermodynamic Approach”—by Nasser Khalili and Arman Khoshghalb." Transport in Porous Media 122, no. 3: 521-526.

Article
Published: 04 March 2017 in Transport in Porous Media
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The finite deformation of an unsaturated porous medium is analysed from first principles of mixture theory. An expression for Bishop’s effective stress is derived from (1) the deformation-dependent Brooks and Corey’s water retention curve and (2) the restrictions on the constitutive relationships of an unsaturated medium subject to finite deformation. The resulting expression for the effective stress parameter \(\chi \) is reasonably consistent with experimental data from the literature. Hence, it is shown that Bishop’s equation is constitutively linked to water retention curves in deforming media.

ACS Style

J. M. Huyghe; E. Nikooee; S. M. Hassanizadeh. Bridging Effective Stress and Soil Water Retention Equations in Deforming Unsaturated Porous Media: A Thermodynamic Approach. Transport in Porous Media 2017, 117, 349 -365.

AMA Style

J. M. Huyghe, E. Nikooee, S. M. Hassanizadeh. Bridging Effective Stress and Soil Water Retention Equations in Deforming Unsaturated Porous Media: A Thermodynamic Approach. Transport in Porous Media. 2017; 117 (3):349-365.

Chicago/Turabian Style

J. M. Huyghe; E. Nikooee; S. M. Hassanizadeh. 2017. "Bridging Effective Stress and Soil Water Retention Equations in Deforming Unsaturated Porous Media: A Thermodynamic Approach." Transport in Porous Media 117, no. 3: 349-365.

Journal article
Published: 01 March 2017 in Mechanics Research Communications
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Highlights•Investigation of the step-wise propagation of a mode-II fracture in a poroelastic medium•It is possible to cut multiple elements within one time increment.•The global response of the material is found to be insensitive to the mesh size.•No evidence for step wise progression in mode II failure was found. AbstractIn this paper we use an eXtended Finite Element Method based model for the simulation of shear fracture in fully saturated porous materials. The fracture is incorporated as a strong discontinuity in the displacement field by exploiting the partition of unity property of finite element shape functions. The pressure is assumed to be continuous across the fracture. However, the pressure gradient, i.e. the fluid flow, can be discontinuous. The failure process is described by the cohesive zone approach and a Tresca fracture condition without dilatancy. We investigate the propagation of a shear fracture under compression asking the question whether or not a Tresca criterion can result in stepwise propagation in a poroelastic medium. In order to evaluate possible numerical artefacts, we also look at the influence of the element size and the magnitude of a time increment. The performance of the X-FEM model and the influence of the pore pressure on the fracture propagation are addressed. Our simulations do not show evidence for step wise progression in mode II failure.

ACS Style

E.W. Remij; J.J.C. Remmers; J.M. Huyghe; D.M.J. Smeulders. An investigation of the step-wise propagation of a mode-II fracture in a poroelastic medium. Mechanics Research Communications 2017, 80, 10 -15.

AMA Style

E.W. Remij, J.J.C. Remmers, J.M. Huyghe, D.M.J. Smeulders. An investigation of the step-wise propagation of a mode-II fracture in a poroelastic medium. Mechanics Research Communications. 2017; 80 ():10-15.

Chicago/Turabian Style

E.W. Remij; J.J.C. Remmers; J.M. Huyghe; D.M.J. Smeulders. 2017. "An investigation of the step-wise propagation of a mode-II fracture in a poroelastic medium." Mechanics Research Communications 80, no. : 10-15.

Journal article
Published: 01 October 2016 in Mechanics Research Communications
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We address stepwise crack tip advancement and pressure fluctuations, which have been observed in the field and experimentally in fracturing saturated porous media. Both fracturing due to mechanical loading and pressure driven fracture are considered. After presenting the experimental evidence and the different explanations for the phenomena put forward and mentioning briefly what has been obtained so far by published numerical and analytical methods we propose our explanation based on Biot’s theory. A short presentation of three methods able to simulate the observed phenomena namely the Central Force Model, the Standard Galerkin Finite Element Method SGFEM and extended finite element method XFEM follows. With the Central Force Model it is evidenced that already dry geomaterials break in an intermittent fashion and that the presence of a fluid affects the behavior more or less depending on the loading and boundary conditions. Examples dealing both with hydraulic fracturing and mechanical loading are shown. The conditions needed to reproduce the observed phenomena with FE models at macroscopic level are evidenced. They appear to be the adoption of a crack tip advancement/time step algorithm which interferes the least possible with the three interacting velocities, namely the crack tip advancement velocity on one side, the seepage velocity of the fluid in the domain and from the crack (leak-off), and the fluid velocity within the crack on the other side. Further the crack tip advancement algorithm must allow for reproducing jumps observed in the experiments.

ACS Style

Toan Duc Cao; Enrico Milanese; Ernst W. Remij; Paolo Rizzato; Joris J.C. Remmers; Luciano Simoni; Jacques Huyghe; Fazle Hussain; Bernhard A. Schrefler. Interaction between crack tip advancement and fluid flow in fracturing saturated porous media. Mechanics Research Communications 2016, 80, 24 -37.

AMA Style

Toan Duc Cao, Enrico Milanese, Ernst W. Remij, Paolo Rizzato, Joris J.C. Remmers, Luciano Simoni, Jacques Huyghe, Fazle Hussain, Bernhard A. Schrefler. Interaction between crack tip advancement and fluid flow in fracturing saturated porous media. Mechanics Research Communications. 2016; 80 ():24-37.

Chicago/Turabian Style

Toan Duc Cao; Enrico Milanese; Ernst W. Remij; Paolo Rizzato; Joris J.C. Remmers; Luciano Simoni; Jacques Huyghe; Fazle Hussain; Bernhard A. Schrefler. 2016. "Interaction between crack tip advancement and fluid flow in fracturing saturated porous media." Mechanics Research Communications 80, no. : 24-37.

Journal article
Published: 01 April 2015 in Computer Methods in Applied Mechanics and Engineering
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ACS Style

E.W. Remij; J.J.C. Remmers; Jacques Huyghe; D.M.J. Smeulders. The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials. Computer Methods in Applied Mechanics and Engineering 2015, 286, 293 -312.

AMA Style

E.W. Remij, J.J.C. Remmers, Jacques Huyghe, D.M.J. Smeulders. The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials. Computer Methods in Applied Mechanics and Engineering. 2015; 286 ():293-312.

Chicago/Turabian Style

E.W. Remij; J.J.C. Remmers; Jacques Huyghe; D.M.J. Smeulders. 2015. "The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials." Computer Methods in Applied Mechanics and Engineering 286, no. : 293-312.

Journal article
Published: 01 April 2015 in MRS Bulletin
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Lumbar intervertebral disc (IVD) degeneration is the leading cause of lower back pain. While lumbar IVDs have low cellularity and limited capacity of regeneration, they bear high mechanical loads. Accelerated disc degeneration may happen because of undue cell stimulation, and cell nutrition also seems to be particularly influent in the disc. Cell nutrition depends on exchange of oxygen, glucose, and lactate between the periphery and the various regions of the IVD, which in turn depends on mechanical deformations. The mechanical regulation of disc cell nutrition, known as indirect mechanotransduction, is difficult to study in vivo or in vitro. This review reports on an important alternative in the form of numerical methods, which are based on the ability of poromechanical models to be coupled to solute transport-reaction models. Models need to address intricate nonlinear and time-dependent phenomena, but have allowed for important mechanisms to be proposed, complementing current knowledge gained from in vivo or in vitro observations.

ACS Style

Andrea Malandrino; Alicia R. Jackson; Jacques M. Huyghe; Jérôme Noailly. Poroelastic modeling of the intervertebral disc: A path toward integrated studies of tissue biophysics and organ degeneration. MRS Bulletin 2015, 40, 324 -332.

AMA Style

Andrea Malandrino, Alicia R. Jackson, Jacques M. Huyghe, Jérôme Noailly. Poroelastic modeling of the intervertebral disc: A path toward integrated studies of tissue biophysics and organ degeneration. MRS Bulletin. 2015; 40 (4):324-332.

Chicago/Turabian Style

Andrea Malandrino; Alicia R. Jackson; Jacques M. Huyghe; Jérôme Noailly. 2015. "Poroelastic modeling of the intervertebral disc: A path toward integrated studies of tissue biophysics and organ degeneration." MRS Bulletin 40, no. 4: 324-332.

Journal article
Published: 19 March 2015 in Annals of Biomedical Engineering
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NMR is used to measure sodium flow driven by a 1D concentration gradient inside poly-acrylamid (pAA) hydrogel. A sodium concentration jump from 0.5 M NaCl to 0 M NaCl is applied at the bottom of a cylindrical pAA sample. The sodium level and hydrogen level are measured as a function of time and position inside the sample for 5 days. Then a reversed step is applied, and ion flow is measured for another 5 days. During the measurement, the cylindrical sample is radially confined and allowed to swell in the axial direction. At the same time, sodium and moisture in the sample are measured on a 1D spatial grid in the axial direction. A quadriphasic mixture model (Huyghe and Janssen in Int J Eng Sci 35:793, 1997) is used to simulate the results and estimate the diffusion coefficient of sodium and chloride. The best fit results were obtained for D[Formula: see text] cm(2)/s and D[Formula: see text] cm(2)/s, at 25 degrees centigrade. Different time constants were observed for swelling and deswelling.

ACS Style

R. W. Roos; L. Pel; H. P. Huinink; J. M. Huyghe. 1D Measurement of Sodium Ion Flow in Hydrogel After a Bath Concentration Jump. Annals of Biomedical Engineering 2015, 43, 1706 -11.

AMA Style

R. W. Roos, L. Pel, H. P. Huinink, J. M. Huyghe. 1D Measurement of Sodium Ion Flow in Hydrogel After a Bath Concentration Jump. Annals of Biomedical Engineering. 2015; 43 (7):1706-11.

Chicago/Turabian Style

R. W. Roos; L. Pel; H. P. Huinink; J. M. Huyghe. 2015. "1D Measurement of Sodium Ion Flow in Hydrogel After a Bath Concentration Jump." Annals of Biomedical Engineering 43, no. 7: 1706-11.

Journal article
Published: 28 December 2014 in Transport in Porous Media
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In this paper, we present a general partition of unity-based cohesive zone model for fracture propagation and nucleation in saturated porous materials. We consider both two-dimensional isotropic and orthotropic media based on the general Biot theory. Fluid flow from the bulk formation into the fracture is accounted for. The fracture propagation is based on an average stress approach. This approach is adjusted to be directionally depended for orthotropic materials. The accuracy of the continuous part of the model is addressed by performing Mandel’s problem for isotropic and orthotropic materials. The performance of the model is investigated with a propagating fracture in an orthotropic material and by considering fracture nucleation and propagation in an isotropic mixed-mode fracture problem. In the latter example we also investigated the influence of the bulk permeability on the numerical results.

ACS Style

Ernst W. Remij; Joris J. C. Remmers; Francesco Pizzocolo; David M. J. Smeulders; Jacques M. Huyghe. A Partition of Unity-Based Model for Crack Nucleation and Propagation in Porous Media, Including Orthotropic Materials. Transport in Porous Media 2014, 106, 505 -522.

AMA Style

Ernst W. Remij, Joris J. C. Remmers, Francesco Pizzocolo, David M. J. Smeulders, Jacques M. Huyghe. A Partition of Unity-Based Model for Crack Nucleation and Propagation in Porous Media, Including Orthotropic Materials. Transport in Porous Media. 2014; 106 (3):505-522.

Chicago/Turabian Style

Ernst W. Remij; Joris J. C. Remmers; Francesco Pizzocolo; David M. J. Smeulders; Jacques M. Huyghe. 2014. "A Partition of Unity-Based Model for Crack Nucleation and Propagation in Porous Media, Including Orthotropic Materials." Transport in Porous Media 106, no. 3: 505-522.