Homogenization of plain weave composites with imperfect microstructure: Part II--Analysis of real-world materials

A two-layer statistically equivalent periodic unit cell is offered to predict a macroscopic response of plain weave multilayer carbon-carbon textile composites. Falling-short in describing the most typical geometrical imperfections of these material systems the original formulation presented in (Zeman and \v{S}ejnoha, International Journal of Solids and Structures, 41 (2004), pp. 6549--6571) is substantially modified, now allowing for nesting and mutual shift of individual layers of textile fabric in all three directions. Yet, the most valuable asset of the present formulation is seen in the possibility of reflecting the influence of negligible meso-scale porosity through a system of oblate spheroidal voids introduced in between the two layers of the unit cell. Numerical predictions of both the effective thermal conductivities and elastic stiffnesses and their comparison with available laboratory data and the results derived using the Mori-Tanaka averaging scheme support credibility of the present approach, about as much as the reliability of local mechanical properties found from nanoindentation tests performed directly on the analyzed composite samples.Comment: 28 pages, 14 figure

An Integrated Flow-Curing Model for Predicting Residual Stresses in Textile Composites

Fiber-reinforced composites have been widely employed in structural applications due to their high stiffness-to-weight ratio and easily-tailored mechanical properties. However, manufacturing of these lightweight materials involves an infusion and curing process, and flow-induced defects and residual stresses can easily occur, which can compromise the mechanical performance of the composite structures. The purpose of this work is to develop an integrated flow-curing processing model to accurately predict the resin flow front and the residual stresses in the Liquid Composite Molding (LCM) process. In the infusion model, the fiber fabrics are treated as a homogeneous and porous material, and the resin flow movement is governed by the Navier-Stokes equations. The resin flow can be solved using the Volume of Fluid (VOF) method. Due to the pressure equilibrium, the resin flow movement and the compaction of the fiber preform are two-way coupled, and the coupling between the flow and compaction models can be captured in the proposed model. After the infusion simulation, the residual stresses are predicted through a curing model. Since the thermal and chemical strains are major contributing factors to the residual stresses, the temperature and cure progression inside the composite are first predicted through a thermal-chemical analysis. Based on the predicted temperature and cure progression, the residual stress development can be captured through a thermo-viscoelastic model. Based on the elastic moduli of the fiber and viscoelastic properties of the resin, the effective relaxation moduli of the composite can be predicted through the correspondence principle and micromechanics models. The effective composite properties are then included in a 3D anisotropic viscoelastic constitutive law, and the differential form of the constitutive law is developed for numerical implementation to improve the computational efficiency. The accuracy of the processing model is assessed by comparing the simulation results against experiments through a set of benchmark examples. The proposed coupled flow-curing processing model is physics-based and experimentally-validated, which can be employed to understand the variability in composite manufacturing and identify the root causes of processing-induced defects. The integrated model shows great promise as a modeling toolkit to guide the design of optimal manufacturing procedures with minimized defects

Simulation of damage mechanisms in weave reinforced materials based on multiscale modeling

A weave reinforced composite material with a thermoplastic matrix is investigated by using a multiscale chain to predict the macroscopic material behavior. A large-strain framework for constitutive modeling with focus on material non-linearities, i.e. plasticity and damage is defined. The ability of the geometric and constitutive models to predict the deformation and failure behavior is demonstrated by means of selected examples

Virtual testing of advanced composites, cellular materials and biomaterials: A review

This paper documents the emergence of virtual testing frameworks for prediction of the constitutive responses of engineering materials. A detailed study is presented, of the philosophy underpinning virtual testing schemes: highlighting the structure, challenges and opportunities posed by a virtual testing strategy compared with traditional laboratory experiments. The virtual testing process has been discussed from atomistic to macrostructural length scales of analyses. Several implementations of virtual testing frameworks for diverse categories of materials are also presented, with particular emphasis on composites, cellular materials and biomaterials (collectively described as heterogeneous systems, in this context). The robustness of virtual frameworks for prediction of the constitutive behaviour of these materials is discussed. The paper also considers the current thinking on developing virtual laboratories in relation to availability of computational resources as well as the development of multi-scale material model algorithms. In conclusion, the paper highlights the challenges facing developments of future virtual testing frameworks. This review represents a comprehensive documentation of the state of knowledge on virtual testing from microscale to macroscale length scales for heterogeneous materials across constitutive responses from elastic to damage regimes

Evaluation of Effective Thermal Conductivities of Porous Textile Composites

An uncoupled multi-scale homogenization approach is used to estimate the effective thermal conductivities of plain weave C/C composites with a high degree of porosity. The geometrical complexity of the material system on individual scales is taken into account through the construction of a suitable representative volume element (RVE), a periodic unit cell, exploiting the information provided by the image analysis of a real composite system on every scale. Two different solution procedures are examined. The first one draws on the classical first order homogenization technique assuming steady state conditions and periodic distribution of the fluctuation part of the temperature field. The second approach is concerned with the solution of a transient flow problem. Although more complex, the latter approach allows for a detailed simulation of heat transfer in the porous system. Effective thermal conductivities of the laminate derived from both approaches through a consistent homogenization on individual scales are then compared with those obtained experimentally. A reasonably close agreement between individual results then promotes the use of the proposed multi-scale computational approach combined with the image analysis of real material systems.Comment: 17 pages, 7 figure

Mini-Workshop: Numerical Upscaling for Flow Problems: Theory and Applications

The objective of this workshop was to bring together researchers working in multiscale simulations with emphasis on multigrid methods and multiscale finite element methods, aiming at chieving of better understanding and synergy between these methods. The goal of multiscale finite element methods, as upscaling methods, is to compute coarse scale solutions of the underlying equations as accurately as possible. On the other hand, multigrid methods attempt to solve fine-scale equations rapidly using a hierarchy of coarse spaces. Multigrid methods need “good” coarse scale spaces for their efficiency. The discussions of this workshop partly focused on approximation properties of coarse scale spaces and multigrid convergence. Some other presentations were on upscaling, domain decomposition methods and nonlinear multiscale methods. Some researchers discussed applications of these methods to reservoir simulations, as well as to simulations of filtration, insulating materials, and turbulence

Multiscale Modeling of Advanced Materials for Damage Prediction and Structural Health Monitoring

abstract: Advanced aerospace materials, including fiber reinforced polymer and ceramic matrix composites, are increasingly being used in critical and demanding applications, challenging the current damage prediction, detection, and quantification methodologies. Multiscale computational models offer key advantages over traditional analysis techniques and can provide the necessary capabilities for the development of a comprehensive virtual structural health monitoring (SHM) framework. Virtual SHM has the potential to drastically improve the design and analysis of aerospace components through coupling the complementary capabilities of models able to predict the initiation and propagation of damage under a wide range of loading and environmental scenarios, simulate interrogation methods for damage detection and quantification, and assess the health of a structure. A major component of the virtual SHM framework involves having micromechanics-based multiscale composite models that can provide the elastic, inelastic, and damage behavior of composite material systems under mechanical and thermal loading conditions and in the presence of microstructural complexity and variability. Quantification of the role geometric and architectural variability in the composite microstructure plays in the local and global composite behavior is essential to the development of appropriate scale-dependent unit cells and boundary conditions for the multiscale model. Once the composite behavior is predicted and variability effects assessed, wave-based SHM simulation models serve to provide knowledge on the probability of detection and characterization accuracy of damage present in the composite. The research presented in this dissertation provides the foundation for a comprehensive SHM framework for advanced aerospace materials. The developed models enhance the prediction of damage formation as a result of ceramic matrix composite processing, improve the understanding of the effects of architectural and geometric variability in polymer matrix composites, and provide an accurate and computational efficient modeling scheme for simulating guided wave excitation, propagation, interaction with damage, and sensing in a range of materials. The methodologies presented in this research represent substantial progress toward the development of an accurate and generalized virtual SHM framework.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201

Mechanics of Materials

All up-to-date engineering applications of advanced multi-phase materials necessitate a concurrent design of materials (including composition, processing routes, microstructures and properties) with structural components. Simulation-based material design requires an intensive interaction of solid state physics, material physics and chemistry, mathematics and information technology. Since mechanics of materials fuses many of the above fields, there is a pressing need for well founded quantitative analytical and numerical approaches to predict microstructure-process-property relationships taking into account hierarchical stationary or evolving microstructures. Owing to this hierarchy of length and time scales, novel approaches for describing/ modelling non-equilibrium material evolution with various degrees of resolution are crucial to linking solid mechanics with realistic material behavior. For example, approaches such as atomistic to continuum transitions (scale coupling), multiresolution numerics, and handshaking algorithms that pass information to models with different degrees of freedom are highly relevant in this context. Many of the topics addressed were dealt with in depth in this workshop