Showing papers on "Micromechanics published in 2007"

Finite element analysis of composite materials

Abstract: MECHANICS OF ORTHOTROPIC MATERIALS Material Coordinate System Displacements Strain Stress Contracted Notation Equilibrium and Virtual Work Boundary Conditions Continuity Conditions Compatibility Coordinate Transformations Transformation of Constitutive Equations 3D Constitutive Equations Engineering Constants From 3D to Plane Stress Equations Apparent Laminate Properties Suggested Problems References INTRODUCTION TO THE FINITE ELEMENT METHOD Basic FEM Procedure General FEM Procedure FE Analysis with CAE Systems Suggested Problems References ELASTICITY AND STRENGTH OF LAMINATES Kinematics of Shells FE Analysis of Laminates Failure Criteria Suggested Problems References BUCKLING Bifurcation Methods Continuation Methods Suggested Problems References FREE EDGE STRESSES Poisson's Mismatch Coefficient of Mutual Influence Suggested Problems References COMPUTATIONAL MICROMECHANICS Analytical Homogenization Numerical Homogenization Local-Global Analysis Laminated RVE Suggested Problems References VISCOELASTICITY Viscoelastic Models Boltzmann Superposition Correspondence Principle Frequency Domain Spectrum Representation Micromechanics of Viscoelastic Composites Macro-Mechanics of Viscoelastic Composites FEA of Viscoelastic Composites Suggested Problems References DAMAGE MECHANICS One-Dimensional Damage Mechanics Multi-Dimensional Damage and Effective Spaces Thermodynamics Formulation Kinetic Law in Three-Dimensional Space Damage and Plasticity Suggested Problems References A DAMAGE MODEL FOR FIBER REINFORCED COMPOSITES Theoretical Formulation Numerical Implementation Model Identification Laminate Damage References Bibliography DELAMINATIONS Two-Dimensional Delamination Delamination in Composite Plates Suggested Problems References APPENDIX A: TENSOR ALGEBRA Principal Directions of Stress and Strain Tensor Symmetry Matrix Representation of a Tensor Inner-Product Tensor Multiplication Tensor Inversion Tensor Differentiation APPENDIX B: STRAIN CONCENTRATION TENSORS APPENDIX C: SECOND ORDER DIAGONAL DAMAGE MODELS Effective and Damaged Spaces Thermodynamic Force Y Damage Surface Unrecoverable-Strain Surface APPENDIX D: NUMERICAL INVERSE LAPLACE TRANSFORM APPENDIX E: INTRODUCTION TO THE SOFTWARE INTERFACE ANSYS BMI3 References INDEX

Transport Properties of Engineered Cementitious Composites under Chloride Exposure

Abstract: This paper presents the results of an experimental investigation on the chloride transport properties of engineered cementitious composites (ECC) under combined mechanical and environmental loads. ECC is a newly developed, high-performance, fiber-reinforced cementitious composite with substantial benefit in both high ductility and improved durability due to tight crack width. By employing micromechanics-based material design, maximum ductility in excess of 3% under uniaxial tensile loading can be attained with only 2% fiber content by volume, and the typical single crack fracture behavior commonly observed in normal concrete or mortar is converted to multiple microcracking in ECC. In this study, immersion and salt ponding tests were conducted to determine chloride ion transport properties. Under high imposed bending deformation, the preloaded ECC beam specimens reveal microcracks less than 50 μm and an effective diffusion coefficient significantly lower than that of the similarly preloaded reinforced mortar beam because of the tight crack width control in ECC. In contrast, cracks larger than 150 μm are easily produced under the same imposed deformation and have significant effects on effective diffusion coefficient of reinforced mortar. Moreover, through the formation of microcracks, a significant amount of self-healing was observed within the ECC cracks subjected to NaCl solution exposure.

Micromechanics of Heterogeneous Materials

Abstract: The micromechanics of random structure heterogeneous materials is a burgeoning multidisciplinary research area which overlaps the scientific branches of materials science, mechanical engineering, applied mathematics, technical physics, geophysics, and biology. Micromechanics of Heterogeneous Materials features rigorous theoretical methods of applied mathematics and statistical physics in materials science of microheterogeneous media. The prediction of the behavior of heterogeneous materials by the use of properties of constituents and their microstructures is a central issue of micromechanics. This book is the first in micromechanics to provide a useful and effective demonstration of the systematic and fundamental research of the microstructure of the wide class of heterogeneous materials of natural and synthetic nature. Micromechanics of Heterogeneous Materials is suitable as a reference for researchers involved in applied mathematics, physics, geophysics, materials science, and electrical, chemical, civil and mechanical engineering working in micromechanics of heterogeneous media. Micromechanics of Heterogeneous Materials is also appropriate as a textbook for advanced graduate courses.

A numerical method for homogenization in non-linear elasticity

Abstract: In this work, homogenization of heterogeneous materials in the context of elasticity is addressed, where the effective constitutive behavior of a heterogeneous material is sought. Both linear and non-linear elastic regimes are considered. Central to the homogenization process is the identification of a statistically representative volume element (RVE) for the heterogeneous material. In the linear regime, aspects of this identification is investigated and a numerical scheme is introduced to determine the RVE size. The approach followed in the linear regime is extended to the non-linear regime by introducing stress–strain state characterization parameters. Next, the concept of a material map, where one identifies the constitutive behavior of a material in a discrete sense, is discussed together with its implementation in the finite element method. The homogenization of the non-linearly elastic heterogeneous material is then realized through the computation of its effective material map using a numerically identified RVE. It is shown that the use of material maps for the macroscopic analysis of heterogeneous structures leads to significant reductions in computation time.

The Eshelby Tensors in a Finite Spherical Domain—Part I: Theoretical Formulations

Abstract: This work is concerned with the precise characterization of the elastic fields due to a spherical inclusion embedded within a spherical representative volume element (RVE) The RVE is considered having finite size, with either a prescribed uniform displacement or a prescribed uniform traction boundary condition Based on symmetry and group theoretic arguments, we identify that the Eshelby tensor for a spherical inclusion admits a unique decomposition, which we coin the “radial transversely isotropic tensor” Based on this notion, a novel solution procedure is presented to solve the resulting Fredholm type integral equations By using this technique, exact and closed form solutions have been obtained for the elastic disturbance fields In the solution two new tensors appear, which are termed the Dirichlet‐Eshelby tensor and the Neumann‐Eshelby tensor In contrast to the classical Eshelby tensor they both are position dependent and contain information about the boundary condition of the RVE as well as the volume fraction of the inclusion The new finite Eshelby tensors have far-reaching consequences in applications such as nanotechnology, homogenization theory of composite materials, and defects mechanics DOI: 101115/12711227

Computational Micromechanics of Clustering and Interphase Effects in Carbon Nanotube Composites

Abstract: Computational micromechanical analysis of high-stiffness hollow fiber nanocomposites is performed using the finite element method. The high-stiffness hollow fibers are modeled either directly as isotropic hollow tubes or equivalent transversely isotropic effective solid cylinders with properties computed using a micromechanics based composite cylinders method. Using a representative volume element for clustered high-stiffness hollow fibers embedded in a compliant matrix with the appropriate periodic boundary conditions, the effective elastic properties are obtained from the finite element results. These effective elastic properties are compared to approximate analytical results found using micromechanics methods. The effects of an interphase layer between the high-stiffness hollow fibers and matrix to simulate imperfect load transfer and/or functionalization of the hollow fibers is also investigated and compared to a multi-layer composite cylinders approach. Finally the combined effects of clustering with...

Deterministic material-based averaging theory model of collagen gel micromechanics.

Abstract: Mechanics of collagen gels, like that of many tissues, is governed by events occurring on a length scale much smaller than the functional scale of the material. To deal with the challenge of incorporating deterministic micromechanics into a continuous macroscopic model, we have developed an averaging-theory-based modeling framework for collagen gels. The averaging volume, which is constructed around each integration point in a macroscopic finite-element model, is assumed to experience boundary deformations homogeneous with the macroscopic deformation field, and a micromechanical problem is solved to determine the average stress at the integration point. A two-dimensional version was implemented with the microstructure modeled as a network of nonlinear springs, and 500 segments were found to be sufficient to achieve statistical homogeneity. The method was then used to simulate the experiments of Tower et al. (Ann. Biomed. Eng., 30, pp. 1221-1233) who performed uniaxial extension of prealigned collagen gels. The simulation captured many qualitative features of the experiments, including a toe region and the realignment of the fibril network during extension. Finally, the method was applied to an idealized wound model based on the characterization measurements of Bowes et al. (Wound Repair Regen., 7, pp. 179-186). The model consisted of a strongly aligned "wound" region surrounded by a less strongly aligned "healthy" region. The alignment of the fibrils in the wound region led to reduced axial strains, and the alignment of the fibrils in the healthy region, combined with the greater effective stiffness of the wound region, caused rotation of the wound region during uniaxial stretch. Although the microscopic model in this study was relatively crude, the multiscale framework is general and could be employed in conjunction with any microstructural model.

Micromechanical modeling of solid-type and plate-type deformation patterns within softwood materials. A review and an improved approach

Abstract: Wood exhibits a highly diverse microstructure. It appears as a solid-type composite material at a length scale of some micrometers, while it resembles an assembly of plate-like elements arranged in a honeycomb fashion at the length scale of some hundreds of micrometers. These structural features result in different load-carrying mechanisms at different observation scales and under different loading conditions. In this paper, we elucidate the main load-carrying mechanisms by means of a micromechanical model for softwood materials. Representing remarkable progress with respect to earlier models reported in the literature, this model is valid across various species. The model is based on tissue-independent stiffness properties of cellulose, lignin, hemicellulose, and water obtained from direct testing and lattice-dynamics analyses. Sample-specific characteristics are considered in terms of porosity and the contents of cellulose, lignin, hemicelluloses and water, which are obtained from mass density measurements, environmental scanning micrographs, analytical chemistry, and NMR spectroscopy. The model comprises three homogenization steps, two based on continuum micromechanics and one on the unit cell method. The latter represents plate-like bending and shear of the cell walls due to transverse shear loading and axial straining in the tangential stem direction. Accurate representation of these deformation modes results in accurate (orthotropic) stiffness estimates across a variety of softwood species. These stiffness predictions deviate, on average, by less than 10% from corresponding experimental results obtained from ultrasonic or quasi-static testing. Thus, the proposed model can reliably predict microscopic and macroscopic mechanical properties from internal structure and composition, and is therefore expected to significantly support wood production technology (such as drying techniques) and mechanical analyses of timber structures.

A thermo-viscoelastic analysis of process-induced residual stress in fibre-reinforced polymer–matrix composites

Abstract: Process-induced residual stress in fibre-reinforced thermoset polymer–matrix composites was analysed using a thermo-viscoelastic micromechanical model and the finite element method. A three-dimensional unit cell with glass fibre and epoxy polymer–matrix, representing the periodic microstructure of unidirectional fibre-reinforced composites, was considered to compute cure residual stress of fibre composites induced by chemical shrinkage of the epoxy resin and thermal cooling contraction of the whole fibre and resin system. The constitutive behaviour of the epoxy matrix was described by a cure and temperature-dependent viscoelastic material model. Compared to an elasticity solution, a reduction in residual stress was predicted due to the stress-relaxation caused by the viscoelastic behaviour of the epoxy matrix. Calculated residual stress shows strong dependency on the fibre volume fraction and fibre packing. After the cure process is complete, residual stress tends to relax to a constant value. The effect of residual stress on damage and failure of the model was also studied using the maximum stress failure criterion combined with a post-failure stiffness reduction technique. Damage onset, in terms of the location and the load level, was shown to be clearly influenced by the residual stress for both normal and shear loading. Initial and final failure envelopes, predicted for biaxial normal (longitudinal and transverse) loading and combined shear (longitudinal) and normal (transverse) loading, were shown to be shifted and contracted by the inclusion of residual stress. For final failure, residual stress was seen to have little effect on the load levels for longitudinal failure but greatly affected the load levels for transverse and shear failure. Residual stress could be detrimental or beneficial depending on the state of existing residual stress and the loading conditions.

Reinforcing mechanisms of single-walled carbon nanotube-reinforced polymer composites.

Abstract: The reinforcing mechanisms of single-walled carbon nanotube-reinforced epoxy composites were studied by micromechanics models. The modeling results obtained from both Halpin-Tsai and Mori-Tanaka models are in good agreement with the experimental results. It has been found that these two models are also applicable to other single-walled carbon nanotube-reinforced, amorphous-polymer composites, given the existence of efficient load transfer. The reinforcing mechanisms that work in polymer-carbon nanotube composites were studied. The reasons responsible for the low mechanical property enhancement of single-walled carbon nanotube in polymer composites were discussed in conjunction with the effective fiber length concept, interface between nanotube bundles and the matrix, properties of the reinforcements and matrix, bundle effects, bundle curvature, and alignment.