F Famke Kraaijeveld

Two-Dimensional Mode I Crack Propagation in Saturated Ionized Porous Media Using Partition of Unity Finite Elements

Shales, clays, hydrogels, and tissues swell and shrink under changing osmotic conditions, which may lead to failure. The relationship between the presence of cracks and fluid flow has had little attention. The relationship between failure and osmotic conditions has had even less attention. The aim of this research is to study the effect of osmotic conditions on propagating discontinuities under different types of loads for saturated ionized porous media using the finite element method (FEM). Discontinuous functions are introduced in the shape functions of the FEM by partition of unity method, independently of the underlying mesh. Damage ahead of the crack-tip is introduced by a cohesive zone model. Tensile loading of a crack in an osmoelastic medium results in opening of the crack and high pressure gradients between the crack and the formation. The fluid flow in the crack is approximated by Couette flow. Results show that failure behavior depends highly on the load, permeability, (osmotic) prestress and the stiffness of the material. In some cases it is seen that when the crack propagation initiates, fluid is attracted to the crack-tip from the crack rather than from the surrounding medium causing the crack to close. The results show reasonable mesh-independent crack propagation for materials with a high stiffness. Stepwise crack propagation through the medium is seen due to consolidation, i.e., crack propagation alternates with pauses in which the fluid redistributes. This physical phenomenon challenges the numerical scheme. Furthermore, propagation is shown to depend on the osmotic prestressing of the medium. This mechanism may explain the tears observed in intervertebral disks as degeneration progresses.

Singularity solution of Lanir’s osmoelasticity: verification of discontinuity simulations in soft tissues

The literature characterizes cartilaginous tissues as osmoviscoelastic. Understanding the damage and failure of these tissues is essential for designing treatments. To determine tissue strength and local stresses, experimental studies—both clinical and animal—are generally supported by computational studies. Verification methods for computational studies of ionized porous media including cracks are hardly available. This study provides a method for verification and shows its performance. For this purpose, shear loading of a finite crack is addressed analytically and through a commercial finite element code. Impulsive shear loading by two-edge dislocation of a crack was considered in a 2D plane strain model for an ionized porous medium. To derive the analytical solution, the system of equation is decoupled by stress functions. The shear stress distribution at the plane of the crack is derived using Fourier and Laplace transformations. The analytical solution for the shear stress distribution is compared with computer simulations in ABAQUS version 6.4-5. Decoupling of the equations makes it possible to solve some boundary value problems in porous media taking chemical effects into account. The numerical calculations underestimate the shear stress at the crack-tips. Mesh refinement increases accuracy, but is still low in the neighborhood of the crack-tips.

Discontinuous Versus Continuous Chemical Potential Across a Crack in a Swelling Porous Medium

Understanding and prediction of mechanisms of failure is needed to develop methods for prevention and treatment of failure. To increase the accuracy for the prediction of failure, advanced computational models are developed. Mesh-independent modeling of cracks in porous media is obtained by enriching the displacement field with a discontinuous shape function describing the crack. In a poroelastic finite element modeling, an enrichment of the pressure field is mandatory around the crack. Two options are available to account for the sharp pressure gradient around the crack. One is to resolve the pressure gradient using a continuous pressure enrichment, the other is not to resolve the steep gradients and use discontinuous jumps across the crack surface. In the latter case, analytical solutions of the pressure field at an interface is used to evaluate the real pressure gradient. This paper formulates criteria to decide whether to use one or the other approach. The techniques are applied to swelling media in which the pressure degree of freedom takes the form of a chemical potential.

3D Finite Strains in Bovine Annulus Fibrosus Tissue

Intervertebral disc tissue consists of a fluid-filled extra-cellular matrix, in which living cells are sparsely dispersed. The mechanical function is highly dependent on the composition of the extra-cellular matrix, which primary consists of collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the proteoglycans (PG’s), the cation concentration inside the tissue is higher than physiological. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue [1]. Because the intervertebral disc is gripped between two vertebrae, the swelling is constrained in vivo, resulting in a intradiscal pressure of 0.1 to 0.2 MPa in supine position. It has been shown that the osmotic pressure inside cartilaginous tissues is much higher than would be expected based on its FCD [2]. This is because part of the water in the tissue is absorbed by the collagen fibers. The proteoglycan molecules, because of their large size, are excluded from this intra-fibrillar space. This means that their effective concentrations are much higher in the extra-fibrillar space than if they were distributed uniformly throughout the entire matrix. Hence, the effective fixed charge density is higher than if computed from total tissue water content. A recent study demonstrates that intrafibrillar water increases osmolarity within the annulus fibrosus substantially [3]. On the other hand, Wognum et al. [4] showed by means of a physical and a numerical model of the disc that high osmolarity within the disc has a protective effect against crack propagation within the disc. Hence, the decrease in osmolarity associated with degeneration may be an explanation of (1) the growing number of cracks observed in the degenerating disc as well as (2) the poor correlation between external loading and crack propagation [5]. The purpose of the present study is to test the hypothesis of Wognum et al. [4] through direct observation of the deformation of annulus fibrosus tissue around discontinuities within its collagen network.Copyright