Amin Ajdari

The indentation of pressurized elastic shells: from polymeric capsules to yeast cells

Pressurized elastic capsules arise at scales ranging from the 10 m diameter pressure vessels used to store propane at oil refineries to the microscopic polymeric capsules that may be used in drug delivery. Nature also makes extensive use of pressurized elastic capsules: plant cells, bacteria and fungi have stiff walls, which are subject to an internal turgor pressure. Here, we present theoretical, numerical and experimental investigations of the indentation of a linearly elastic shell subject to a constant internal pressure. We show that, unlike unpressurized shells, the relationship between force and displacement demonstrates two linear regimes. We determine analytical expressions for the effective stiffness in each of these regimes in terms of the material properties of the shell and the pressure difference. As a consequence, a single indentation experiment over a range of displacements may be used as a simple assay to determine both the internal pressure and elastic properties of capsules. Our results are relevant for determining the internal pressure in bacterial, fungal or plant cells. As an illustration of this, we apply our results to recent measurements of the stiffness of bakers yeast and infer from these experiments that the internal osmotic pressure of yeast cells may be regulated in response to changes in the osmotic pressure of the external medium.

In Vitro and Computational Thrombosis on Artificial Surfaces With Shear Stress

Implantable devices in direct contact with flowing blood are associated with the risk of thromboembolic events. This study addresses the need to improve our understanding of the thrombosis mechanism and to identify areas on artificial surfaces susceptible to thrombus deposition. Thrombus deposits on artificial blood step transitions are quantified experimentally and compared with shear stress and shear rate distributions using computational fluid dynamics (CFD) models. Larger steps, and negative (expanding) steps result in larger thrombus deposits. Fitting CFD results to experimental deposit locations reveals a specific shear stress threshold of 0.41 Pa or a shear rate threshold of 54 s(-1) using a shear thinning blood viscosity model. Thrombosis will occur below this threshold, which is specific to solvent-polished polycarbonate surfaces under in vitro coagulation conditions with activated clotting time levels of 200-220 s. The experimental and computational models are valuable tools for thrombosis prediction and assessment that may be used before proceeding to clinical trials and to better understand existing clinical problems with thrombosis.

Effect of pulsatile blood flow on thrombosis potential with a step wall transition.

It is well known that thrombus can be formed at stagnation regions in blood flow. However, studies of thrombus formation have typically focused on steady state flow. We hypothesize that pulsating flow may reduce persistent stagnation at the sites of low shear stress by decreasing exposure time. In this study, a step-wall transition, which is commonly found on implantable devices, is used as a test bed causing a recirculation vortex. Stagnation at such a step is considered using computational fluid dynamics studies and flow visualization experiments. Parametric studies were performed with varying step height, pulsatility, and velocity. The percentage of time along the wall with shear stresses below a threshold for thrombosis and the total length of wall that maintains contact with stagnant flow throughout the cardiac cycle are calculated. Persistent stagnation occurs at the corner of a step-wall transition in all cases and is observed to decrease with a decrease in step height, an increase in mean velocity, and an increase in pulsatility. Under steady flow conditions, a flow reattachment point resulting from recirculation is observed with expanding steps, whereas a flow separation point is observed with contracting steps. Pulsatility decreases persistent stagnation at the flow separation point with contracting steps, whereas it completely eliminates persistent stagnation at the flow reattachment point with expanding steps. The results of this work conclusively show that stagnation can be reduced by increasing pulsatility and flow velocity and by decreasing step height.

Mechanical Properties of Open-Cell Cellular Structures With Rhombic Dodecahedron Cells

We present a series of analytical models and finite element results (FE) for special 3-D open cellular foam to determine the effective material properties of a 3D rhombic dedecahedron open-cell cellular structure. The analytical approach is based on minimizing the total energy associated with small deformation of a single unit cell of the cellular structure. The finite element models were developed for both a single unit cell and three dimensional foam structure and used to obtain the mechanical properties in all three principal directions.Copyright

Effect of Blood Viscosity on Thrombosis Potential Near a Step Wall Transition

Thrombosis and hemolysis are two problems encountered when processing blood in artificial organs. Physical factors of blood flow alone can influence the interaction of proteins and cells with the vessel wall, induce platelet aggregation and influence coagulation factors responsible for the formation of thrombus, even in the absence of chemical factors in the blood. These physical factors are related to the magnitude of the shear rate/stress, the duration of the applied force and the local geometry. Specifically, high blood shear rates (or stress) lead to damage (hemolysis, platelet activation), while low shear rates lead to stagnation and thrombosis [1].Copyright

Hierarchical Cellular Structures with Tailorable Proparties

Abstract Hierarchical structures are found in many natural and man-made materials [1]. This structural hierarchy play an important role in determining the overall mechanical behavior of the structure. It has been suggested that increasing the hierarchical level of a structure will result in a better performing structure [2]. Besides, honeycombs are well known structures for lightweight and high strength applications [3]. In this work, we have studied the mechanical properties of honeycombs with hierarchical organization using theoretical, numerical, and experimental methods. The hierarchical organization is made by replacing the edges of a regular honeycomb structure with smaller regular honeycomb. Our results showed that honeycombs with structural hierarchy have superior properties compared to regular honeycombs. The results show that a relatively broad range of elastic properties, and thus behavior, can be achieved by tailoring the structural organization of hierarchical honeycombs, and more specificall...

MECHANICAL BEHAVIOR OF FUNCTIONALLY GRADED 2-D CELLULAR STRUCTURES: A FINITE ELEMENT STUDY

Functionally graded cellular structures such as bioinspired functionally graded materials for manufacturing implants or bone replacement, are a class of materials with low densities and novel physical, mechanical, thermal, electrical and acoustic properties. A gradual increase in cell size distribution, can impart many improved properties which may not be achieved by having a uniform cellular structure. The material properties of functionally graded cellular structures as a function of density gradient have not been exclusively addressed within the literature. In this study, the finite element method is used to investigate the compressive uniaxial and biaxial behavior of functionally graded Voronoi structures. Furthermore, the effect of missing cell walls on its overall mechanical (elastic, plastic, and creep) properties is investigated. The finite element analysis showed that the overall effective elastic modulus and yield strength of structures increased by increasing the density gradient. However, the overall elastic modulus of functionally graded structures was more sensitive to density gradient than the overall yield strength. The study also showed that the functionally graded structures with different density gradient had similar sensitivity

Effect of Defect on Elastic/Plastic and Creep Behavior of Bone: A Finite Element Study

Three-dimensional structure of trabecular bone can be modeled by 2D or 3D Voronoi structure. The effect of missing cell walls on the mechanical properties of 2D honeycombs is a first step towards understanding the effect of local bone resorption due to osteoporosis. In patients with osteoporosis, bone mass is lost first by thinning and then by resorption of the trabeculae [1].Furthermore, creep response is important to analyze in cellular solids when the temperature is high relative to the melting temperature. For trabecular bone, as body temperature (38 °C) is close to the denaturation temperature of collagen (52 °C), trabecular bone creeps [1]. Over the half of the osteoporotic vertebral fractures that occur in the elderly, are the result of the creep and fatigue loading associated with the activities of daily living [2].The objective of this work is to understand the effect of missing walls and filled cells on elastic-plastic behavior of both regular hexagonal and non-periodic Voronoi structures using finite element analysis.The results show that the missing walls have a significant effect on overall elastic properties of the cellular structure. For both regular hexagonal and Voronoi materials, the yield strength of the structure decreased by more than 60% by introducing 10% missing walls. In contrast, the results indicate that filled cells have much less effect on the mechanical properties of both regular hexagonal and Voronoi materials.Copyright

Effect of Defect on Elastic-Plastic and Creep Behavior of Cellular Materials

Cellular solids, such as foams, are widely used in engineering applications. In these applications, it is important to know their mechanical properties and the variation of these properties with the presence of defects. Several models have been proposed to obtain the mechanical properties of cellular materials. However, some of these models are based on idealized unit cell structures, and are not suitable for finding the mechanical properties of cellular materials with defects. Furthermore, the creep response changes in cellular solids when the exposed temperature is higher than 1/3 of the material’s melting temperature. The objective of this work is to understand the effect of missing walls and filled cells on mechanical and creep behavior of both the regular hexagonal and non-periodic Voronoi structures using finite element analysis. The finite element analysis showed that on average the non periodic structures have inferior mechanical properties compared to that of the regular hexagonal structures with the same relative density. The yield stress of Voronoi structures had a mean of 27% lower compared to that of the hexagonal structure with the same relative densities. Defects, introduced by removing cell walls at random locations, caused a sharp decrease in the effective mechanical properties of both Voronoi and periodic hexagonal honeycombs. However, our results indicated that elastic properties of Voronoi Structures are more sensitive to missing walls when compared to those of regular honeycomb structures. The yield strength of Voronoi and regular honeycombs exhibited the similar sensitivity to cell wall removal. For creep analysis, the results suggest that removal of struts dramatically increases the creep rate. In the case of filled cells, regular honeycomb structures showed less sensitivity to the defect compared to Voronoi structures. The overall elastic modulus of the structure increased by 11% when 5% of cells were filled in regular hexagonal honeycombs while for Voronoi structure it had more significant effect (22% increase). The results also show that filled cell did not have a significant effect on yield strength of the regular and Voronoi structures.Copyright

The Influence of Muscle Loadings on the Density Distribution of the Proximal Femur

This paper presents an efficient method for simulating the bone remodeling procedure. This method is based on the trajectorial architecture theory of optimization and employs a truss-like model for bone. The truss was subjected to external loads including 5 point loads simulating the hip joint contact forces and 3 muscular forces at the attachment sites of the muscles to the bone. The strain in the links was calculated and the links with high strains were identified. The initial truss is modified by introducing new links wherever the strain exceeds a prescribed value; each link undergoing a high strain is replaced by several new links by adding new nodes around it using the Delaunay method. Introduction of these new links to the truss, which is conducted according to a weighted arithmetic mean formula, strengthens the structure and reduces the strain within the respective zone. This procedure was repeated for several steps. Convergence was achieved when there were no critical links remaining. This method was used to study the 2D shape of proximal femur in the frontal plane and provided results that are consistent with CT data. The proposed method exhibited capability similar to more complicated conventional nonlinear algorithms, however, with a much higher convergence rate and lower computation costs.© 2006 ASME