Bhavani V Sankar

• Ph.D.
• Professor (Full) at University of Florida

Translaminar reinforcements (TLR) are effective means of improving the interlaminar fracture toughness of laminated fiber composites. The three methods to provide such reinforcements are: stitching, z-pinning and three-dimensional weaving. Although TLR are effective in improving the interlaminar fracture toughness, there is an optimum amount of rei...

The four-point bend test is one of the simplest and often the preferred flexural strength evaluation method for brittle materials. In this loading mode, fracture often initiates from a critical surface (or subsurface) flaw when subjected to a tensile stress state. However, if the critical flaw exists on the compression side of the test specimen, it...

In the micromechanical analysis of braided composite tubes, the effects of curvature are often ignored. This approach is acceptable for thin-walled tubes with a large radius. However, in case of small diameter thick-walled tubes, such an approach may lead to inaccurate results. Therefore, it is of interest to determine when the curvature effects of...

Many piezoelectric microelectromechanical systems (MEMS) measure or generate acoustic signals via the motion of radially non-uniform, thin film composite plates. The composite layers provide piezoelectric actuation, structural support, electrode metallization, passivation, etc. Often, the layers are non-uniform over the plate and contain residual s...

Bend-twist coupling refers to the ability of a structure (beam, plate, shaft, etc.) to twist when subjected to pure bending. This characteristic is used in wind turbine blades, marine propellers, and beams subjected to off-axis loadings. A method is presented for designing carbon fiber shafts to maximize the degree of bend twist coupling while main...

A simple analytical model is derived for composite tubes subjected to bending and torsion. The model is applied to a novel design of composite tube that exhibits bend–twist coupling such that the shear center of the cross section is away from the tube axis. Analytical expressions are derived for the shear center distance – distance of the shear cen...

Bend-twist coupling is a property of certain specially designed composite beams that when subjected to loading conditions that would normally result in pure bending, undergo both bending and twisting. This phenomenon is called bend-twist coupling. To fully characterize the degree of bend-twist coupling in the beam, shear center per unit length (e y...

A new and unique way of orienting carbon fiber lamina in cylindrical shafts results in bend-twist coupling. A beam is said to possess bend-twist coupling when a pure bending moment applied to the beam results in simultaneous bending and twisting. This effect is normally associated with asymmetric cross-sections (such as c-shaped sections) but can r...

A novel method involving the use of micromechanical analysis to predict elastic constants of a unidirectional fiberreinforced composite is proposed. The method revolves around a model called the two-parameter model. The two parameters are obtained by performing one micromechanical analysis of the composite unit cell along one of its transverse dire...

Finite element models are developed to predict potential failure initiation sites and associated failure modes in S2-Glass/SC15 three-dimensional (3D) woven composites under quasi-static indentation. As part of this modeling effort, experimental micrographs of the composite specimen obtained from a previous experimental study1,2 are analyzed. In co...

The objectives of this paper include identifying important architectural parameters that describe the SiC/SiC five-harness satin weave composite and characterizing the statistical distributions and correlations of those parameters from photomicrographs of various cross sections. In addition, realistic artificial cross sections of a 2D representativ...

Randomness in woven ceramic matrix composite architecture has been found to cause large variability in stiffness and strength. The inherent voids are an aspect of the architecture that may cause a significant portion of the variability. A study is undertaken to investigate the effects of many voids of random sizes and distributions. Response surfac...

Delamination initiation and propagation in plain woven laminates and 3D orthogonal woven composites during short beam shear (SBS) test were analyzed using finite element (FE) analyses. Two kinds of 3D woven composites, containing single z-yarns and double z-yarns, were considered. The FE models were guided by experimental observations from SBS test...

The problem of contact between a rigid cylindrical indenter and a functionally graded (FG) beam is studied. The elastic modulus of the material varies in an exponential fashion across the thickness of the beam. For the sake of comparison indentation of a homogeneous beam is also considered. In the case of FG beams indentation of both soft and hard...

The design of engineering systems is often based on analysis models with substantial errors in predicting failures, that is epistemic uncertainty. The epistemic uncertainty is reduced by post design tests, and the safety of unsafe designs restored by redesign. When this process of design, test and redesign is to be based on probabilistic analysis,...

The stiffness and strength properties of foams with tetrakaidecahedral unit cells are evaluated using both finite element-based micromechanics and analytical methods. The finite element analysis models the varying cross section of the struts exactly. The analytical methods assume the struts have constant cross section along the length. Equivalent c...

Most components undergo tests after they are designed and are redesigned if necessary. Tests help designers find unsafe and overly conservative designs, and redesign can restore safety or reduce mass. In general, the changes to the mass and reliability of the design after the test and redesign are not considered. This paper examines the effect of c...

A new test method for performing dynamic short-beam shear tests using a momentum trapped Hopkinson pressure bar is proposed. Angle-interlock 3D woven composite specimens were tested under quasi-static and dynamic loading conditions to determine the effect of loading rate on damage evolution. The equilibrium condition in the composite specimen under...

Many micromachined electroacoustic devices use thin plates in conjunction with electrical components to measure acoustic signals. Composite layers are needed for electrical passivation, moisture barriers, etc. The layers often contain residual stresses introduced during the fabrication process. Accurate models of the composite plate mechanics are c...

This paper is concerned with homogenization of a corrugated-core sandwich panel, which is a candidate structure for integrated thermal protection systems for space vehicles. The focus is on determining the local stresses in an integrated thermal protection system panel subjected to mechanical and thermal loads. A micromechanical method is developed...

The objectives of this paper are to identify important architectural parameters that describe the SiC/SiC five harness-satin weave composite and characterize the statistical distributions and correlations of parameters from photomicrographs of cross sections; generate artificial specimens of a 2D representative volume element (RVE) of the composite...

It is common to test components after they are designed and redesign if necessary. The reduction of the uncertainty in the probability of failure that can occur after a test is usually not incorporated in reliability calculations at the design stage. This reduction in uncertainty is accomplished by additional knowledge provided by the test and by r...

It is computationally expensive to evaluate the overall system level reliability when several interacting failure modes are present. Therefore, it is even more expensive to optimize considering the system level reliability that accounts for the interactions between failure modes. In this paper, we decompose the system level reliability based optimi...

Toughening mechanisms in hard, metal oxide nanoparticle reinforced epoxy systems were analyzed using a multi-scale approach. Samples on varying scales were fabricated using a shear mixing device and the dispersion of the particles was characterized. On the macro-scale, four-point bend testing showed a maximum of an 80% increase in fracture toughnes...

This paper presents a reduced analytical modeling method for the initial optimal design of thermoelastic micromachined actuators. The key aspects of the model are a Green’s function formulation of the axisymmetric heat conduction equation that incorporates an internal heat source and the solution of the thermoelastically forced bending wave equatio...

Integrated thermal protection systems (ITPS) are multi-functional structures that combine the functions of conventional TPS (heat shields) and load bearing structural panels of a hypersonic vehicle. Because of its complex design, an ITPS panel could fail due to multiple failure modes. This paper focuses on uncertainty characterization and uncertain...

Short beam shear tests may be used to examine a composites resistance to delamination by creating a state of stress conducive to delamination. Both static and dynamic short beam shear tests were conducted. Results indicate that the baseline had the highest damage resistance at all loading rates when compared to the 3D woven composites tested. When...

The homogenization of a corrugated core sandwich panel as a two dimensional (2-D) orthotropic plate was performed. A representative volume element of the panel was analyzed to obtain the equivalent stiffness properties through finite element based homogenization. A method is also proposed to estimate the transverse shear stiffness of the equivalent...

Monotonic, multi-step and cyclic short beam shear tests were conducted on 2D and 3D woven composites. The test results were used to determine the effect of z-yarns on the inter-laminar shear strength as well as the multi-loading behavior. The presence of z-yarns was found to affect not only the inter-laminar shear strength of the composite but also...

Reliability-based design often uses the Monte-Carlo method as a sampling procedure for predicting failure. The combination of designing for very small failure probabilities (similar to 10(-8) - 10(-6)) and using computationally expensive finite element models, makes Monte-Carlo simulations very expensive. This paper uses an improved sampling proced...

When composite laminates are operated at cryogenic temperatures, thermal stresses arise. This is due to the difference in coefficients of thermal expansion of different plies and also between the fiber and matrix. While the former is taken into account in the composite structural analysis, the latter, called micro-thermal stresses, has not been giv...

Finite element method based micromechanics has been used for predicting the multi-axial failure strengths of open cell foams which have tetrakaidecahedral unit-cells. Low density foams with equi-sided and Kelvin-elongated tetrakaidecahedron as unit cells are studied. The struts are modeled using three-dimensional beam elements. The effect of varyin...

Integrated Thermal protection Systems (ITPS) are the features incorporated into a spacecraft's design to protect it from severe aerodynamic heating combining both the load bearing structure and the thermal protection system (TPS) into one single structure. Previous work studied an ITPS concept with a corrugated-core sandwich structure made of face...

Current thermal protection systems (TPS) in hypersonic vehicles do not carry significant loads. One potential method of saving weight is to have a load-bearing TPS that performs some structural functions. One such concept, the Integrated Thermal Protection System (ITPS), uses a corrugated-core sandwich structure. Design-optimization of an ITPS requ...

A finite element method based micromechanics has been used for predicting the orthotropic properties of foams which have tetrakaidecahedral unit-cells. Both equi-sided and Kelvin-elongated tetrakaidecahedrons are studied. The results for elastic constants from the FE models agree well with that of available analytical models. The struts were modele...

Through-the-thickness stitching is a method that increases the translaminar strength and apparent fracture toughness of laminated composites. A novel test fixture was developed to measure mixed mode fracture toughness under combined Mode I and Mode II loadings. This fixture allowed the ratio between Mode I and Mode II to be varied in order to perfo...

This paper is concerned with homogenization of a corrugated-core sandwich panel, which is a candidate structure for integral thermal protection systems for space vehicles. The focus was on determination of thermal stresses in the face sheets and the web caused by through-the-thickness temperature variation. A micromechanical method was developed to...

The objective of this work is to model the response of S2-Glass/SC-15 three-dimensional (3D) woven composites subjected to quasi-static loads, especially indentation type loads that are typical of impact situations. In particular, the focus is on quantifying the role of throughthickness reinforcements known as warp weavers or Z-yarns vis-à-vis load...

Toughening mechanisms in hard, metal oxide nanoparticle reinforced epoxy systems were analyzed using a multi-scale approach. Samples on varying scales were fabricated using a shear mixing device and the dispersion of the particles was characterized. On the macro-scale, four point bend testing showed an 80 percent increase in fracture toughness over...

Micro-mechanics tools investigating the in-plane elastic and strength properties of 3D woven composites are developed in this work. Particular attention is directed toward constructing detailed geometry and finite element models of an example 3D weave architecture available in the literature. The models are then modified to investigate the effect o...

of the maximum bottom face temperature is needed. The finite element model used to evaluate the maximum temperature depended on 15 parameters of interest for the design. A small number of assumptions simplified the thermal equations, allowing easy nondimensionalization, which together with a global sensitivity analysis showed that the maximum tempe...

The primary function of a Thermal Protection System (TPS) is to protect the space vehicle from extreme aerodynamic heating and to maintain the underlying structure within acceptable temperature limits. Typically TPS are not load bearing members. One potential method of saving weight is to have a load-bearing TPS that performs some structural functi...

Bayesian identification provides a framework that can handle both measurement and modeling errors. Furthermore it identifies a probability distribution function thus providing information on both variance and correlation of the identified properties. However, the procedure can be very costly computationally. In order to address the computational co...

An integrated thermal protection system for spacecraft reentry based on a corrugated core sandwich panel concept fulfilling both thermal and structural functions is optimized for minimal mass. We seek the optimal dimensions and the best materials, but directly optimizing both continuous geometric parameters and discrete material choices is difficul...

A qualitative analysis of experimental results from small caliber ballistic impact and dynamic indentation on a 3D glass fiber reinforced composite are presented. Microscopic analysis of the damaged specimens revealed that the current 3D weaving scheme creates inherently two weak planes which act as potential sites for delamination in the above exp...

a b s t r a c t A method that uses a structured grid to perform micromechanical analysis for determining effective properties of a composite microstructure is presented. This approach eliminates the need for constructing a mesh that has nodes along the interfaces between constituent materials of the composite. Implicit boundary method is used to en...

Finite element methods have been used to simulate and understand the physical basis behind surface cracks leading to interface delamination in thermal barrier coatings. Traditionally energy release rate has been used as a criterion for crack propagation in thermal barrier coatings. There have been some conceptual difficulties in using this approach...

The basic formulation of the least squares method, based on the L2 norm of the misfit, is still widely used today for identifying elastic material properties from experimental data. An alternative statistical approach is the Bayesian method. We seek here situations with significant difference between the material properties found by the two methods...

Stitch cracks in multidirectional laminates were observed by many researchers in the literature. In the present work, the damage evolution in multidirectional laminates is investigated using the strain energy release rate concept. Two methods are used to compute the strain energy release rate. The effects of ply angle and ply thickness on stitch cr...

The paper considers probabilistic optimization of integrated thermal protection system (ITPS) that combines the thermal protection function with the structural load carrying function. For ITPS design, structural and thermal requirements usually conflict. Increased structural thickness helps carry loads but increases heat conduction. Designers need...

Experiments were performed to investigate the effect of cryogenic cycling on the gas permeability of various composite laminates for cryogenic storage systems. Textile composites have lower permeability than laminated composites even with increasing number of cryogenic cycles. Nano-particles dispersed in one of the ply-interfaces in tape laminates...

A finite-element based method is developed to predict gas permeability in cross-ply laminates. Based on Poiseuille's Law and Darcy's Law, the gas permeability is presented in terms of crack densities, microcrack opening displacements and an experimentally determined constant. The crack densities in each ply are predicted using finite element analys...

Currently fiber composites are used in thick structures with significant out of plane stresses for which new 3D failure criteria are required. In this article the direct micromechanics method is used to determine the exact failure envelope of a unidirectional graphite/epoxy composite. A hexagonal unit cell of the composite is modeled using finite e...

The meshless local Petrov-Galerkin (MLPG) method is used in the micromechanical analysis of a unidirectional fiber composite. The methods have been extended to include shear loadings, thus permitting a more complete micromechanical analysis of the composite subjected to combined loading states. The MLPG formulation is presented for the analysis of...

This paper develops an efficient computational technique to perform reliability-based optimization of structural design and an inspection schedule for fatigue crack growth. Calculating structural reliability in the presence of inspection is computationally challenging because crack size distribution has to be updated after each inspection to simula...

This study investigates several available sandwich beam theories for their suitability of application to one-dimensional sandwich plates with functionally graded core. Two equivalent single-layer theories based on assumed displacements, a higher-order theory, and the Fourier—Galerkin method are compared. The results are also compared with the finit...

Designs of several micromachined electroacoustic devices use thin composite plates in conjunction with electrical components to measure acoustic signals. Composite layers are needed for electrical passivation, moisture barriers, structure for electrical components, etc. The layers often contain residual stresses introduced during the fabrication pr...

Micromechanical methods to predict the fracture behavior and estimate the fracture toughness of cellular solids and foams are presented in this paper. The microstructure of the foam is modeled using finite elements. The struts of foam are modeled using either structural elements such as beams or three-dimensional solid elements. A portion of the fo...

The axisymmetric post-buckling behavior of a circular plate with initial in-plane compression loading is investigated. The von Karman plate equations are solved numerically for a clamped plate and solutions are presented for a range of transverse and in-plane loadings. These solutions can be used to predict the post-buckled behavior of microscale d...

Previously developed micromechanical methods for stiffness and strength prediction are adapted for analysis of multi-layer plain weave textile composites. Utilizing the direct micromechanics method (DMM) via finite element modeling, three methods are presented: (a) direct simulation of a multi-layer plain weave textile composite; (b) micromechanica...

The dynamic behavior of an axisymmetric post- buckled circular plate with initial in-plane compression loading is investigated. The static von Karman plate equations are solved numerically for clamped boundary conditions. The static solution is presented for a range of transverse and in-plane loads. Lumped element modeling is used to calculate the...

A composite corrugated-core sandwich panel was investigated as a potential candidate for an integral thermal protection system. This multifunctional integral thermal protection system concept can protect the space vehicle from extreme reentry temperatures, and possess load-carrying capabilities. The corrugated core is composed of two, thin, flat sh...

Certain diffraction-based techniques that measure strains in bulk samples are limited to determination of normal strains. A numerical inverse method is developed to determine full field stresses from the experimentally determined normal strains in isotropic solids under plane stress conditions. The method is based on satisfying the equations of equ...

In this paper we present the meshless local Petrov-Galerkin formulation for the generalized plane strain problem with specific emphasis on micromechanics of composite materials containing material discontinuities. The problem requires the introduction of an extra discrete degree of freedom, the out-of-plane uniform normal strain. The treatment of m...

Three-dimensional finite element models are used to study the influence of various parameters on the gas permeability of cross-ply composite laminate. It is shown that the intersection area, which is formed between two adjacent plies due to crack opening, is the most crucial factor in determining the permeability. It is found that the intersection...

Stress singularity of a transverse crack normal to ply-interface in a composite laminate is investigated using analytical and finite element methods. Four-point bending tests were performed on single-notch bend specimens of graphite/epoxy laminates containing a transverse crack perpendicular to the ply-interface. The experimentally determined fract...

Out of many exciting and unique unmanned air vehicles (UAVs) being developed at the University of Florida, one UAV design utilizes a bendable wing concept. To minimize the storage volume, the wing is rolled and the UAV is stored inside a canister. By design, the carbon/epoxy composite wing is made compliant in one direction while it is designed for...

Response surface approximations (RSA) are a common tool in engineering, often constructed based on finite element (FE) simulations. For some design problems, the FE models can involve a high number of parameters. However it is advantageous to construct the RSA as function of a small number of variables. The purpose of this paper is to demonstrate t...

Based upon previous results of direct micromechanical method (DMM) analysis of the representative volume element (RVE) of a plain-weave textile composite, two methods for predicting failure envelopes are presented: a parametric ellipse-fitting scheme, and a 27-term quadratic stress-gradient failure criterion. Both include the consideration of micro...

A u t h o r ' s p e r s o n a l c o p y Abstract In this paper, finite element method based micromechanical analysis is used to understand the fracture behavior of func-tionally graded foams. The finite element analysis uses a micro-mechanical model in conjunction with a macro-mechanical model in order to relate the stress intensity factor to the s...

Piezoelectric flap actuators are often used in active flow-control applications. However, effective design tools are lacking in the flow-control community. This paper discusses theoretical modeling, experimental validation, and optimal design of piezoelectric unimorph and bimorph flap actuators. First, two different finite element models are descri...

This paper presents a methodology to predict microcracking and microcrack density in both surface and internal plies of a symmetric cross-ply laminate under biaxial mechanical and thermal loading conditions. The thermoelastic properties of the microcracked laminates at different crack densities were determined by finite element analysis of the unit...

The purpose of this study was to investigate the applicability of an existing lay-up independent fracture criterion for notched composite laminates. A detailed finite element analysis of notched graphite/epoxy laminates was performed to understand the nature of stresses and crack tip parameters in finite-width composite panels. A new laminate param...

This paper presents an analytical two-port, lumped-element model of a piezoelectric composite circular plate. In particular, the individual components of a piezoelectric unimorph transducer are modeled as lumped elements of an equivalent electrical circuit using conjugate power variables. The transverse static deflection field as a function of pres...

A finite element analysis-based micromechanics method is developed to investigate development of microcracks in a graphite/epoxy composite liquid hydrogen tank at cryogenic temperatures. The unit cell of the composite is modeled using finite elements. Periodic boundary conditions are applied to the boundaries of the unit cell. The temperature-depen...

A preliminary design process of an integral thermal protection system (ITPS) has been presented. Unlike the conventional TPS, the ITPS has both thermal protection as well as load bearing capabilities. The objective of this research work is to establish procedures and identify issues in the design of an ITPS. Corrugated-core sandwich construction ha...

In this paper we present the meshless local Petrov-Galerkin (MLPG) formulation for the generalized plane strain problem with specific emphasis on micromechanics of composite materials containing material discontinuities. The problem requires the introduction of an extra discrete degree of freedom, the out-of-plane uniform normal strain. The treatme...

Micromechanical methods for stiffness and strength prediction are presented, the results of which have led to an effective failure theory for prediction of strength. Methods to account for analysis of multi-layer textile composites are also developed. This allows simulation of a single representative volume element (RVE) to be applicable to a layup...

A fracture mechanics approach is proposed to determine the residual strength of debonded honeycomb core composite sandwich panels. Asymmetric double cantilever beam sandwich specimens are tested in order to measure the core/ face sheet interfacial fracture toughness. Graphite/epoxy composite laminates are used as face sheets, and the core is an ara...

The research presented in this paper is an effort to better understand the interlaminar fracture behavior of graphite/epoxy composite laminates in cryogenic conditions. Double cantilever beam tests were performed on different types of specimens, at room and cryogenic temperatures, and the fracture toughness was calculated from their load-displaceme...

The tradeoffs of allowable flight loads and safety of aerospace structures via deterministic and probabilistic design methodologies are analyzed. The methodologies are illustrated by performing allowable flight load calculation of a sandwich panel used in aerospace structures. The effect of using a more accurate prediction technique for interfacial...

A micromechanical analysis of the representative volume element (RVE) of a plain weave textile composite has been performed using the finite element method. Stress gradient effects are investigated, and it is assumed that the stress state is not uniform across the RVE. This is unlike most stiffness and strength models, which start with the premise...

Polymer matrix composites are candidate materials for cryogenic tanks for Crew Exploration Vehicles and Crew Launch Vehicles planned by NASA for future space missions. However gas leakage through microcracks and delaminations remains as a critical problem that needs to be solved. In the present work, gas permeability mechanism through multiple ply...