Yogesh Bansal

A Second Look at the Higher-Order Theory for Periodic Multiphase Materials

In this communication, we present a reformulation, based on the local/global stiffness matrix approach, of the recently developed higher-order theory for periodic multiphase materials, Aboudi et al. [Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials, J. Appl. Mech., 68(5), pp. 697-707]. This reformulation reveals that the higher-order theory employs an approximate, and standard, elasticity approach to the solution of the unit cell problem of periodic multiphase materials based on direct volumeaveraging of the local field equations and satisfaction of the local continuity conditions in a surface-averge sense. This contrasts with the original formulation in which different moments of the local equilibrium equations were employed, suggesting that the theory is a variant of a micropolar, continuum-based model. The reformulation simplifies the derivation of the global system of equations governing the unit cell response, whose size is substantially reduced through elimination of redundant continuity equations employed in the original formulation, allowing one to test the theorys predictive capability in most demanding situations. Herein, we do so by estimating the elastic moduli of periodic composites characterized by repeating unit cells obtained by rotation of an infinite square fiber array through an angle about the fiber axis. Such unit cells possess no planes of material symmetry in the rotated coordinate system, and may contain a few or many fibers, depending on the rotation angle, which the reformulated theory can easily accommodate. The excellent agreement with the corresponding results obtained from the standard transformation equations confirms the new models previously untested predictive capability for a class of periodic composites characterized by nonstandard, multi-inclusion repeating unit cells lacking planes of material symmetry. Comparison of the effective moduli and local stress fields with the corresponding results obtained from the original Generalized Method of Cells, which the higher-order theory supersedes, confirms the need for this new model, and dramatically highlights the original models shortcomings for a certain class of unidirectional composites.

EFFICIENT REFORMULATION OF THE THERMOELASTIC HIGHER-ORDER THEORY FOR FUNCTIONALLY GRADED MATERIALS

The majority of techniques employed in the analysis of functionally graded materials (FGMs) use the so-called uncoupled approach, based on homogenized material property variations, which ignores the effect of local microstructural interaction. The higher-order theory for FGMs (HOTFGM) is a coupled approach that explicitly takes the effect of microstructural gradation and, thus, the local interaction of the spatially variable inclusion phase(s), into account. Despite its demonstrated utility, however, the original formulation of HOTFGM is computationally intensive. Herein, an efficient reformulation of HOTFGM is presented based on the local/global conductivity and stiffness matrix formulations. In this approach, surface-averaged quantities are the primary variables which replace volume-averaged quantities employed in the original formulation. The reformulation eliminates redundant continuity equations and, therefore, decreases the size of the overall systems of equations for the thermal and mechanical problem by approximately 60%, facilitating modeling of realistic microstructures. Explicit expressions for the elements of the local conductivity and stiffness matrices, which relate the surface average heat flux/traction quantities to the corresponding surface average temperatures/displacements, facilitate the theorys implementation, as well as comparison with the finite-element approach. The presented results illustrate the efficiency of the reformulation and its advantages in analyzing FGMs.

Analysis Tools for Adhesively Bonded Composite Joints, Part 2: Unified Analytical Theory

Adhesively bonded joints are currently of interest to the aerospace field due to the heavy reliance on bonded composite structures in new aircraft designs. In response, tools for joint analysis have been developed and examined in this two-part paper. In Part 1, a higher-order theory, considering an explicit discretization of the joint geometry, was investigated. In Part 2, a method for multiaxial stress analysis of composite joints is developed based on Mortensens unified approach, with considerable extension to accommodate transverse in-plane strain and hygrothermal loads and most importantly, to compute the in-plane and interlaminar stresses in the adherends. Compared with other analytical methods for bonded joint analysis, the present method is capable of handling more general situations, including various joint geometries, linear and nonlinear adhesives, asymmetric and unbalanced laminates, and various loading and boundary conditions. The method has been implemented within the commercially available HyperSizer® structural analysis software. Through comparison to finite element and analytical results, it is shown that the new HyperSizer joint analysis method is efficient and accurate and can serve as a capable tool for joint analysis in preliminary design, where rapid and generally accurate stress field estimates, as well as joint strengths and margins are needed.

On the Micromechanics-Based Simulation of Metal Matrix Composite Response

The response of metal matrix composites is affected by factors such as inclusion distribution and shape, inclusion/matrix interfacial bond, residual stresses, and fabrication-altered in situ matrix properties. These effects are studied using a finite-volume micro-mechanics model whose extensive modeling capabilities are sufficient to account for these diverse factors. A consistent micromechanics-aided methodology is developed for extracting the unknown in situ matrix plastic parameters using a minimum amount of experimental data. Subsequent correlation of the micromechanics-based predictions with carefully generated data on off-axis response of unidirectional boron/aluminum composite specimens under tensile and compressive axial loading validates the models predictive capability and quantifies the importance of each factor.

Analysis Tools for Adhesively Bonded Composite Joints, Part 1: Higher-Order Theory

A new application of the higher-order theory to the analysis of adhesively bonded composite joints is investigated. The adhesively bonded joint problem is currently of interest to the aerospace field because of the heavy reliance on bonded composite structures in an extensive number of new aircraft designs. As such, new tools that enable the sizing of joints in the context of the overall vehicle design are being sought. Through comparison of analytical and finite element results from the literature, along with a recently developed unified analytical joint analysis methodology, it is shown that the higher-order theory is a capable tool for joint analysis that serves as a middle ground between the finite element approach and less general analytical methodologies. In Part 2 of the paper, an alternative analytical method for the three-dimensional stress analysis of composite bonded joints will be investigated.

EFFICIENT REFORMULATION OF THE THERMAL HIGHER-ORDER THEORY FOR FGMs WITH LOCALLY VARIABLE CONDUCTIVITY

Functionally graded materials are characterized by spatially variable microstructures introduced to satisfy given performance requirements. The graded microstructure gives rise to continuously or discretely changing properties, complicating the analysis of these materials. The majority of the computational techniques use the so-called uncoupled approach which ignores the effect of microstructural gradation by employing specific spatial material property variations that are either assumed or obtained by local homogenization. In contrast, the higher-order theory for functionally graded materials is a coupled approach which takes the effect of microstructural gradation into consideration and does not ignore the local-global interaction of the spatially variable inclusion phase(s). Despite its demonstrated utility, however, the original formulation of the higher-order theory is computationally intensive. Herein, an efficient reformulation of the higher-order theory for thermal problems, based on the local/glo...

3D Stress Analysis of Adhesively Bonded Composite Joints

A robust and rapid analytical method for 3D stress analysis of composite bonded joints has been recently developed based on Mortensens unified approach, with considerable extension to accommodate hygrothermal loads and most importantly, to compute the in- plane and out-of-plane, through-the-thickness interlaminar peel and shear stresses in the laminate adherends. Compared to other analytical methods for bonded joint analysis the present method is capable of handling more general situations, including various joint geometries, both linear and nonlinear adhesive, asymmetric and unbalanced laminates, and more general loading and boundary conditions. The formulation has been extended from strict cylindrical bending to consider generalized cylindrical bending that allows an arbitrary constant strain to be applied in the out-of-plane direction. Other analytical methods, such as Hart-Smiths, are 1-D and mainly focus on obtaining adhesive stresses, while generally ignoring stresses in laminate adherends, particularly interlaminar stresses, which are known to be key contributors to failure. Joining composite structures using adhesive bonding remains a challenging problem because performance is severely influenced by the characteristics of the composite laminate adherends, which usually have low interlaminar strengths. This new method, most importantly, computes local 3D stress fields in each ply of each adherend, which vary along the joint. Given the realistic 3D local stress fields at the ply level within each adherend, failure criteria can be employed to predict joint strength, which can facilitate better joint designs. This paper addresses the computation of stresses for composite bonded doubler joints. A companion paper, also presented in this conference, addresses failure prediction.

Analysis of Adhesively Bonded Composite Joints Using a Higher-Order Theory

*† ‡ § ** A new application of the higher-order theory to the analysis of adhesively bonded composite joints is investigated. The adhesively bonded joint problem is currently of interest to the aerospace field due to the heavy reliance on bonded composite structures in an extensive number of new aircraft designs. As such, new tools that enable the sizing of joints in the context of the overall vehicle design are being sought. Through comparison of analytical and finite element results from the literature, along with a recently developed unified analytical joint analysis methodology, it is shown that the higher-order theory is a capable tool for joint analysis that serves as a middle ground between the finite element approach and less general analytical methodologies.