Tsegay Belay - Academia.edu (original) (raw)

Papers by Tsegay Belay

Research paper thumbnail of Internal Notched Flexure (INF) Test for Measurement of Mode II Interlaminar Fracture Toughness of Fiber Composites

Materials Performance and Characterization, 2014

A revised analysis to derive the expression for the mode II interlaminar fracture toughness of fi... more A revised analysis to derive the expression for the mode II interlaminar fracture toughness of fiber-reinforced polymers from internal notched flexure (INF) testing in small deformation is presented here. The approach adopted for the derivation takes into account the interlaminar shear load in the overhanging section outside the span. This improves the prediction accuracy for the initial specimen compliance, as evident from a finite element (FE) model of the INF specimen. The FE model also suggests that extensive damage develops at the crack tip before the delamination growth. Therefore, rather than using the physical crack length to calculate the interlaminar fracture toughness, one should use the effective crack length, which can be determined based on the measured specimen stiffness from experimental testing. With that, the analytical expression yields an inerlaminar fracture toughness that is consistent with the input value for the cohesive elements of the FE model.

Research paper thumbnail of On the mechanics of lipid membranes: budding formation, diffusion of transmembrane proteins and line tension

We study the formation of membrane budding in model lipid bilayers with the budding assumed to be... more We study the formation of membrane budding in model lipid bilayers with the budding assumed to be driven by means of diffusion of trans-membrane proteins over a composite membrane surface. The theoretical model for the lipid membrane incorporates a modified Helfrich-type formulation as a special case. In addition, a spontaneous curvature is introduced into the model in order to accommodate the effect of the non-uniformly distributed proteins in the bending response of the membrane. Further, we discuss the effects of line tension on the budding of the membrane, and the necessary adjustments to the boundary conditions. The resulting shape equation is solved numerically for the parametric representation of the surface which has one to one correspondence to the membrane surface in consideration. Our numerical results successfully predict the vesicle formation phenomenon on a flat lipid membrane surface, since the present analysis is not restricted to the conventional Monge representatio...

Research paper thumbnail of Mechanics of a lipid bilayer subjected to thickness distension and membrane budding

Mathematics and Mechanics of Solids, 2016

We study the distension-induced gradient capillarity in membrane bud formation. The budding proce... more We study the distension-induced gradient capillarity in membrane bud formation. The budding process is assumed to be primarily driven by diffusion of transmembrane proteins and acting line tensions on the protein-concentrated interface. The proposed model, based on the Helfrich-type potential, is designed to accommodate inhomogeneous elastic responses of the membrane, non-uniform protein distributions over the membrane surface and, more importantly, the thickness distensions induced by bud formations in the membrane. The latter are employed via the augmented energy potential of bulk incompressibility in a weakened manner. By computing the variations of the proposed membrane energy potential, we obtained the corresponding equilibrium equation (membrane shape equation) describing the morphological transitions of the lipid membrane undergoing bud formation and the associated thickness distensions. The effects of lipid distension on the shape equation and the necessary adjustments to th...

Research paper thumbnail of Bud formation of lipid membranes in response to the surface diffusion of transmembrane proteins and line tension

Mathematics and Mechanics of Solids, 2016

We study the formation of membrane budding in model lipid bilayers with the budding assumed to be... more We study the formation of membrane budding in model lipid bilayers with the budding assumed to be driven by means of diffusion of trans-membrane proteins over a composite membrane surface. The theoretical model for the lipid membrane incorporates a modified Helfrich-type formulation as a special case. In addition, a spontaneous curvature is introduced into the model in order to accommodate the effect of the non-uniformly distributed proteins in the bending response of the membrane. Furthermore, we discuss the effects of line tension on the budding of the membrane, and the necessary adjustments to the boundary conditions. The resulting shape equation is solved numerically for the parametric representation of the surface, which has one to one correspondence to the membrane surface in consideration. Our numerical results successfully predict the vesicle formation phenomenon on a flat lipid membrane surface, since the present analysis is not restricted to the conventional Monge representation often adopted to the problems of this kind for the obvious computational simplicity, despite its limited capability to describe the deformed configuration of membranes. In addition, we show that line tension at the interface of the protein-concentrated domain makes a significant contribution to the bud formation of membranes.

Research paper thumbnail of Analytical solution of lipid membrane morphology subjected to boundary forces on the edges of rectangular membranes

Continuum Mechanics and Thermodynamics, 2015

We develop a complete analytical solution predicting the deformation of rectangular lipid membran... more We develop a complete analytical solution predicting the deformation of rectangular lipid membranes resulting from boundary forces acting on the perimeter of the membrane. The shape equation describing the equilibrium state of a lipid membrane is taken from the classical Helfrich model. A linearized version of the shape equation describing membrane morphology (within the Monge representation) is obtained via a limit of superposed incremental deformations. We obtain a complete analytical solution by reducing the corresponding problem to a single partial differential equation and by using Fourier series representations for various types of boundary forces. The solution obtained predicts smooth morphological transition over the domain of interest. Finally, we note that the methods used in our analysis are not restricted to the particular type of boundary conditions considered here and can accommodate a wide class of practical and important edge conditions.

Research paper thumbnail of Interaction-Induced Morphological Transitions of Lipid Membranes in Contact With an Elliptical Cross Section of a Rigid Substrate

Journal of Applied Mechanics, 2015

We present a complete analysis for the deformation profiles of lipid membranes induced by their i... more We present a complete analysis for the deformation profiles of lipid membranes induced by their interactions with solid elliptical cylinder substrates (e.g., proteins). The theoretical framework for the mechanics of lipid membranes is described in terms of the classical Helfrich model, and the resulting shape equation is formulated in general curvilinear coordinates to accommodate the elliptical shape of the contour surrounding the contact area. Admissible boundary conditions for the contact region are taken from the existing literature but reformulated and adapted to the current framework. A complete semi-analytic solution (in terms of Mathieu functions) is obtained within the limitation of superposed incremental deformations and the Monge representation in the deformed configuration functions. The results predict smooth morphological transitions over the domain of interest when a lipid membrane interacts with a rigid substrate through an elliptical contact region.

Research paper thumbnail of Internal Notched Flexure (INF) Test for Measurement of Mode II Interlaminar Fracture Toughness of Fiber Composites

Materials Performance and Characterization, 2014

Research paper thumbnail of Internal Notched Flexure (INF) Test for Measurement of Mode II Interlaminar Fracture Toughness of Fiber Composites

Materials Performance and Characterization, 2014

A revised analysis to derive the expression for the mode II interlaminar fracture toughness of fi... more A revised analysis to derive the expression for the mode II interlaminar fracture toughness of fiber-reinforced polymers from internal notched flexure (INF) testing in small deformation is presented here. The approach adopted for the derivation takes into account the interlaminar shear load in the overhanging section outside the span. This improves the prediction accuracy for the initial specimen compliance, as evident from a finite element (FE) model of the INF specimen. The FE model also suggests that extensive damage develops at the crack tip before the delamination growth. Therefore, rather than using the physical crack length to calculate the interlaminar fracture toughness, one should use the effective crack length, which can be determined based on the measured specimen stiffness from experimental testing. With that, the analytical expression yields an inerlaminar fracture toughness that is consistent with the input value for the cohesive elements of the FE model.

Research paper thumbnail of On the mechanics of lipid membranes: budding formation, diffusion of transmembrane proteins and line tension

We study the formation of membrane budding in model lipid bilayers with the budding assumed to be... more We study the formation of membrane budding in model lipid bilayers with the budding assumed to be driven by means of diffusion of trans-membrane proteins over a composite membrane surface. The theoretical model for the lipid membrane incorporates a modified Helfrich-type formulation as a special case. In addition, a spontaneous curvature is introduced into the model in order to accommodate the effect of the non-uniformly distributed proteins in the bending response of the membrane. Further, we discuss the effects of line tension on the budding of the membrane, and the necessary adjustments to the boundary conditions. The resulting shape equation is solved numerically for the parametric representation of the surface which has one to one correspondence to the membrane surface in consideration. Our numerical results successfully predict the vesicle formation phenomenon on a flat lipid membrane surface, since the present analysis is not restricted to the conventional Monge representatio...

Research paper thumbnail of Mechanics of a lipid bilayer subjected to thickness distension and membrane budding

Mathematics and Mechanics of Solids, 2016

We study the distension-induced gradient capillarity in membrane bud formation. The budding proce... more We study the distension-induced gradient capillarity in membrane bud formation. The budding process is assumed to be primarily driven by diffusion of transmembrane proteins and acting line tensions on the protein-concentrated interface. The proposed model, based on the Helfrich-type potential, is designed to accommodate inhomogeneous elastic responses of the membrane, non-uniform protein distributions over the membrane surface and, more importantly, the thickness distensions induced by bud formations in the membrane. The latter are employed via the augmented energy potential of bulk incompressibility in a weakened manner. By computing the variations of the proposed membrane energy potential, we obtained the corresponding equilibrium equation (membrane shape equation) describing the morphological transitions of the lipid membrane undergoing bud formation and the associated thickness distensions. The effects of lipid distension on the shape equation and the necessary adjustments to th...

Research paper thumbnail of Bud formation of lipid membranes in response to the surface diffusion of transmembrane proteins and line tension

Mathematics and Mechanics of Solids, 2016

We study the formation of membrane budding in model lipid bilayers with the budding assumed to be... more We study the formation of membrane budding in model lipid bilayers with the budding assumed to be driven by means of diffusion of trans-membrane proteins over a composite membrane surface. The theoretical model for the lipid membrane incorporates a modified Helfrich-type formulation as a special case. In addition, a spontaneous curvature is introduced into the model in order to accommodate the effect of the non-uniformly distributed proteins in the bending response of the membrane. Furthermore, we discuss the effects of line tension on the budding of the membrane, and the necessary adjustments to the boundary conditions. The resulting shape equation is solved numerically for the parametric representation of the surface, which has one to one correspondence to the membrane surface in consideration. Our numerical results successfully predict the vesicle formation phenomenon on a flat lipid membrane surface, since the present analysis is not restricted to the conventional Monge representation often adopted to the problems of this kind for the obvious computational simplicity, despite its limited capability to describe the deformed configuration of membranes. In addition, we show that line tension at the interface of the protein-concentrated domain makes a significant contribution to the bud formation of membranes.

Research paper thumbnail of Analytical solution of lipid membrane morphology subjected to boundary forces on the edges of rectangular membranes

Continuum Mechanics and Thermodynamics, 2015

We develop a complete analytical solution predicting the deformation of rectangular lipid membran... more We develop a complete analytical solution predicting the deformation of rectangular lipid membranes resulting from boundary forces acting on the perimeter of the membrane. The shape equation describing the equilibrium state of a lipid membrane is taken from the classical Helfrich model. A linearized version of the shape equation describing membrane morphology (within the Monge representation) is obtained via a limit of superposed incremental deformations. We obtain a complete analytical solution by reducing the corresponding problem to a single partial differential equation and by using Fourier series representations for various types of boundary forces. The solution obtained predicts smooth morphological transition over the domain of interest. Finally, we note that the methods used in our analysis are not restricted to the particular type of boundary conditions considered here and can accommodate a wide class of practical and important edge conditions.

Research paper thumbnail of Interaction-Induced Morphological Transitions of Lipid Membranes in Contact With an Elliptical Cross Section of a Rigid Substrate

Journal of Applied Mechanics, 2015

We present a complete analysis for the deformation profiles of lipid membranes induced by their i... more We present a complete analysis for the deformation profiles of lipid membranes induced by their interactions with solid elliptical cylinder substrates (e.g., proteins). The theoretical framework for the mechanics of lipid membranes is described in terms of the classical Helfrich model, and the resulting shape equation is formulated in general curvilinear coordinates to accommodate the elliptical shape of the contour surrounding the contact area. Admissible boundary conditions for the contact region are taken from the existing literature but reformulated and adapted to the current framework. A complete semi-analytic solution (in terms of Mathieu functions) is obtained within the limitation of superposed incremental deformations and the Monge representation in the deformed configuration functions. The results predict smooth morphological transitions over the domain of interest when a lipid membrane interacts with a rigid substrate through an elliptical contact region.

Research paper thumbnail of Internal Notched Flexure (INF) Test for Measurement of Mode II Interlaminar Fracture Toughness of Fiber Composites

Materials Performance and Characterization, 2014