University of Viginia

University Center, VA, United States

University of Viginia

University Center, VA, United States
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Cavalcante M.A.A.,Federal University of Alagoas | Pindera M.-J.,University of Viginia
International Journal of Plasticity | Year: 2016

Generalized FVDAM theory for the analysis of periodic heterogeneous materials with elastic-plastic phases undergoing infinitesimal deformation is constructed to overcome the limitations of the original or 0th-order version of the theory, and to concomitantly extend the theory's range of modeling capabilities. The 0th-order theory suffers from intrinsic constraints stemming from limited displacement field representation at the local level, which results in the deterioration of pointwise continuity of interfacial tractions and displacements with increasing plasticity, requiring greater unit cell discretization. The generalization is based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain, in contrast with the second-order expansion employed in the 0th-order theory. The higher-order displacement field is expressed in terms of elasticity-motivated surface-averaged kinematic variables which are subsequently related to corresponding static variables through a generalized local stiffness matrix. Comparison of local fields in metal matrix composites with large moduli contrasts obtained using the generalized FVDAM theory, its predecessor and finite-element method illustrates substantial improvement in the pointwise satisfaction of interfacial continuity conditions at adjacent subvolume faces in the presence of plasticity, producing smoother stress and plastic strain distributions and excellent interfacial conformability with smaller unit cell discretizations. The generalized theory offers several advantages relative to the Q9-based finite-element method, including direct relationship between static and kinematic variables across subvolume faces and superior satisfaction of pointwise traction continuity which facilitate modeling of various interfacial phenomena, such as fiber/matrix cracks illustrated herein. © 2015 Elsevier Ltd.

Cavalcante M.A.A.,University of Viginia | Pindera M.-J.,University of Viginia | Khatam H.,University of Texas at Austin
Composites Part B: Engineering | Year: 2012

The finite-volume method is now a well-established tool in the numerical engineering community for simulation of a wide range of problems in fluid and solid mechanics. Its acceptance by the mechanics of heterogeneous media community, however, continues to be slow, often characterized by confusion with the finite-element method or so-called higher-order theories. Herein, we provide a brief historical perspective on the evolution of this important technique in the fluid mechanics community, its transition to the solution of solid mechanics boundary-value problems initiated in Europe in 1988, and the recent developments aimed at the solution of unit cell problems of periodic heterogeneous media. The differences and similarities with the finite-element method are highlighted, and the resulting tangible advantages of the finite-volume technique discussed and illustrated. Finally, our most recent results in this area are presented which demonstrate the method's capability of solving unit cell problems with complex architectures in a variety of settings and applications, while revealing undocumented effects of interest in the development of new material microstructures with targeted response. Recent attempts to develop alternative versions of this technique are also discussed, together with our ongoing work to generalize the finite-volume micromechanics approach in order to further enhance its predictive capabilities and efficiency. © 2011 Elsevier Ltd. All rights reserved.

Katz A.,University of Viginia | Trinh C.,University of Viginia | Wright J.,University of Viginia | Tu W.,University of Viginia | Pindera M.-J.,University of Viginia
Composites Part B: Engineering | Year: 2014

Biomimetic or bio-inspired microstructures are increasingly being explored as a source of inspiration for material innovation. The goal of this study is to aid future design of biomimetic materials by conducting analysis of material architectures that resemble brick-and-mortar microstructures found in nacre. Specifically, this study explores the thus-far undocumented combined effects of waviness and platelet architecture on composite material ductility under unidirectional loading parallel and perpendicular to the reinforcing platelets. Model material architectures, comprised of discontinuous silicon carbide platelets suspended in aluminum matrix, that mimic nacre's microstructure were constructed for analysis with the finite-volume direct averaging micromechanics (FVDAM) theory. The silicon carbide platelets play the role of nacre's load-bearing calcite phase while the aluminum matrix mimics the combined effects of hierarchical load transferring mechanisms and organic protein matrix. The FVDAM simulations indicate that the introduction of waviness leads to an increase in ductility. Just as significant to material performance is the degree of relative shift between wavy rows of discontinuous hard-phase platelets. The effect of shift on ductility was found to be most significant when introduced to a degree that disrupted unit cell symmetry and when applied to configurations with low amplitude-to-wavelength ratios. The differences in the observed homogenized response are rooted in the local microstructure-controlled stress and resulting plastic strain fields that are identified in this investigation. © 2014 Elsevier B.V. All rights reserved.

Tu W.,University of Viginia | Pindera M.-J.,University of Viginia
Composites Part B: Engineering | Year: 2016

The classical phenomenon of progressive cracking of 90°plies in polymeric matrix cross-ply laminates, and potential or subsequent delamination along the 0°/90°ply interface, is critically revisited using a finite-volume homogenization theory with damage evolution capability. Progressive separation of adjacent phases or subdomains as well as crack evolution may be simulated with this capability within a unified framework that employs discontinuity functions in conjunction with the cohesive-zone model. The finite-volume simulations of evolving damage in graphite/epoxy cross-ply laminates on the fly and its effect on the homogenized axial stress-strain and transverse Poisson's responses, as well as crack density, are compared with available experimental results, taking account of residual stresses, interfacial resin-rich region and variable strength of the 90°plies. The comparison demonstrates the theory's ability to capture the dramatic effect of transverse cracking on the homogenized transverse Poisson's ratio that increases with increasing 90°ply thickness, and the damage mode bifurcation from transverse cracking to interfacial delamination. Moreover, the finite-volume simulations indicate that many features observed in the transverse and through-thickness Poisson's response of graphite/epoxy cross-ply laminates may be related to the underpinning damage modes more readily than in the axial response. The developed finite-volume framework offers a unified methodology for simulating damage evolution in a class of composite laminates due to cracking and/or progressive interfacial degradation, and for identifying features observed in the homogenized response that reflect the underpining local failure mechanisms. © 2015 Elsevier Ltd. All rights reserved.

Cavalcante M.A.A.,University of Viginia | Pindera M.-J.,University of Viginia
International Journal of Mechanics and Materials in Design | Year: 2013

The transformation field analysis (TFA) proposed by Dvorak et al. in a sequence of papers in the 1990s is an important conceptual cornerstone of the elastic-plastic analysis of heterogeneous materials. However, the need for highly discretized unit cells required to attain converged homogenized response using finite-element based calculation of the plastic influence matrices employed in TFA simulations has given rise to further developments, including the recent nonlinear TFA approach. This variant leverages characteristic plastic modes that arise in elastic-plastic heterogeneous materials. Herein, we re-visit the TFA approach in the context of periodic materials with large phase moduli contrast, and first quantify the unit cell discretization required to attain the same level of convergence as with full unit cell finite-element based analysis. Subsequently we demonstrate that the finite-volume based calculation of strain concentration and plastic influence matrices requires substantially smaller unit cell discretizations to achieve the same degree of macroscopic and microscopic level accuracy, resulting in large execution time reductions and fewer parameters that describe the underpinning plastic deformation mechanisms. Further reductions may be achieved by explicitly leveraging plastic field localization that assumes distinct spatial distributions or characteristic modes. © 2013 Springer Science+Business Media Dordrecht.

Wang G.,University of Viginia | Pindera M.-J.,University of Viginia
Mechanics of Materials | Year: 2016

The elasticity-based, locally-exact homogenization theory for periodic materials with hexagonal and tetragonal symmetries is extended to accommodate linearly viscoelastic phases via the correspondence principle. The theory employs Fourier series representations for fiber and matrix displacement fields in the cylindrical coordinate system that satisfy exactly equilibrium equations and continuity conditions in the interior of the unit cell. The inseparable exterior problem requires satisfaction of periodicity conditions efficiently accomplished using previously introduced balanced variational principle which ensures rapid displacement and stress field convergence in the presence of linearly viscoelastic phases with relatively few harmonic terms. The solution's stability and efficiency, with concommitant simplicity of input data construction, facilitate rapid identification of the impact of phase viscoelasticity and array type on homogenized moduli and local fields in wide ranges of fiber volume fraction. We illustrate the theory's utility by investigating the impact of fiber array type and matrix viscoelastic response (constant Poisson's ratio vs constant bulk modulus) on the homogenized response and local stress fields, reporting previously undocumented differences. Specifically, we show that initially small differences between hexagonal and square arrays are magnified substantially by viscoelasticity. New results on the transmission of matrix viscoelastic features to the macroscale are also generated in support of construction of homogenized viscoelastic functions from experimental data. © 2016 Elsevier Ltd

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