Multiscale modeling of materials by a multifield approach: Microscopic stress and strain distribution in fiber–matrix composites☆ (original) (raw)
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A Multiscale Approach for Composite Materials as Multifield Continua
Materials Science Forum, 2007
A continuum model for composite materials made of short, stiff and tough fibres embedded in a more deformable matrix with distributed microflaws is proposed. Based on the kinematics of a lattice system made of fibres, perceived as rigid inclusions, and of microflaws, represented by slit microcracks, the stress-strain relations of an equivalent multifield continuum is obtained. These relations account for the shape and the orientation of the internal phases and include internal scale parameters, which allow taking into account size effects. Some numerical analyses effected on a sample fibre-reinforced composite pointed out the influence of the size and orientation of the fibres on the gross behaviour of the material.
A Multiscale Micro-Continuum Model to Capture Strain Localization in Composite Materials
International Journal for Multiscale Computational Engineering, 2012
This paper presents a plasticity/damage formulation in the context of the physically based micro-continuum theory for multiphase materials described in a companion paper (see Vernerey, A physically-based micro-continuum theory, Mech. Adv. Mater. Struct., 2012). Based on a micro-structurally motivated decomposition of the deformation, the presented inelastic formulation is capable of characterizing the independent plastic/damage processes occurring in different phases (such as fiber or inclusions) and predicting the overall material behavior. The inelastic constitutive relation can thus be cast in a simple, physically motivated form, compared to conventional models. Such a formulation is thus very attractive for establishing a link between materials structure and properties. To illustrate the presented framework, we apply the micro-continuum model to the tensile failure of fiber-reinforced composite and compare it to a "brute force" approach in which the microstructure is explicitly modeled. We show that the model captures accurately the evolution of various features that cannot be calculated with conventional methods such as the independent stress, strain, and damage in the matrix and fibers and the fiber/matrix interface. Moreover, the existence of a size effect during failure is accounted for correctly.
A constitutive model for fibre composite materials based on microscopic descriptions
Constitutive equations for composite materials with reinforcing fibres and micro-flaws are derived in the framework of continua with microstructure (multi-field continua). These equations are based on the kinematics and the statics of the material at the microscopic level and account for the geometry and the texture of the material internal phases. Considering homogeneous deformations for the microscopic model (lattice model) the equivalent macroscopic model proves to be a multi-field continuum. Differently from the classical continuous models, this continuum includes internal scale parameters which allow taking into account size effects. The study of a one-dimensional problem points out the influence of the microstructure on the macroscopic behaviour of the composite material.
A Hierarchical Coupled Multi-Scale Model for Short Fiber Composites
14th WCCM-ECCOMAS Congress, 2021
Short Fiber Reinforced Composites (SFRCs) are being increasingly used in a variety of applications due to their interesting mechanical properties and ease of processing. For SFRCs, different micro-structural parameters (in addition to the constitutive behaviour of the matrix and reinforcement fibers), such as fiber orientation distribution, fiber aspect ratio and fiber/matrix interface strength play important roles in the macroscopic mechanical behaviour. Hence, to have an accurate and reliable modelling approach, using multi-scale models is a natural choice. In this study, a coupled multi-scale model is proposed using a recently developed micromechanical model and the Finite Element Method. The proposed model enables analysis of macroscopic specimens considering micro-structural properties.
Science and Engineering of Composite Materials, 2008
Behavior of a viscoelastic material under mechanical loading has been systematically investigated in this study in the scope of continuum mechanics, where the material was brought to a composite state by non-expansive fiber family considered as topological objects constituting only anisotropy. In this model no constraint was applied that would prevent realization of fiber reinforcement on molecular dimensions or on nano scale. Matrix part of the object has a viscoelastic anisotropy and, in addition to that, due to the fiber reinforcement, the object will wholly have an anisotropic structure. In terms of behavior the object responds to the environment prompting it through elastic stress and dissipative stress, whose constitutive equations have been obtained. While elastic stress is derived from the thermodynamic potential, dissipative stress was formed as a tensorial function that depends on certain arguments. After necessary information was obtained on the constitutive functions, power series expansions were made based on the assumption that such functions are analytic. Considering physical application conditions where mechanical interactions are assumed to be linear, orders of the terms in power series have been determined accordingly. As a result, constitutive equations obtained were used as substitutes in balance equations, yielding field equations.
A multiscale continuum model for inelastic behavior of woven composite
Composite Structures, 2019
A multiscale continuum model to predict the anisotropic non-linear behavior and strength of 2D and 3D woven composite has been proposed. The proposed approach is based on representative volume element (RVE), which serves as a two-level approximation, first at the microscale via fibers enclosed with cohesive interphase embedded in a matrix and second at the mesoscale via tows interlaced with each other and reinforced inside a matrix. The constitutive property fields of the RVE's at two scales are evaluated under periodic boundary conditions and quasi-static loading in six different directions. The mechanism's such as built-in imperfections at the surface, residual stresses and glitches that are generally neglected in such models have been incorporated combinedly in the form of cohesive interphase at lower scale. The accuracy of the proposed approach is assessed by a comparison of the literature data and the predicted results. The fundamental failure mechanism at both the scales have been addressed using preeminent failure criterions. From the various techniques used, homogenization in conjunction with finite element analysis is a precise and consistent way to analyze the nonlinear mechanical response and prediction of failure in woven composites and their tows.
International Journal of Solids and Structures, 2010
The present paper is devoted to the study of the mechanical behavior of an ethylene propylene diene monomer (EPDM) rubber reinforced by polypropylene (PP) particles, revealed as compressible. The hyperlastic behavior of this blend has been characterized under cyclic uni-axial tensile tests. The experimental results show a significant effect of the fraction of (PP) particles (5%, 10%, 25% and 30% by weight) on the macroscopic behavior of the composite. In order to model this behavior, we first develop and implement a micromechanically-based nonlinear model for hyperelastic composites. The approach is based on the second order homogenization method proposed by Ponte Castaneda and Tiberio (2000) and for which suitable energy densities are adopted for the matrix and the inclusions phases, both assumed as compressible. We then proceed to the model verification by comparison with Finite Element simulations on a unit cell. Finally, we propose an extension of the model in order to take into account damage due to voids growth phenomena. The comparison of the multiscale damage model predictions with the experimental data obtained on the EPDM/PP composite indicates a very good agreement.
A Numerical Investigation of Structure-Property Relations in Fiber Composite Materials
International Journal for Multiscale Computational Engineering, 2007
A multifield continuous model is adopted to investigate the mechanical behaviour of heterogeneous materials made of short, stiff and tough fibres embedded in a more deformable matrix. This continuum accounts for the presence of internal structure by means of non-standard field descriptors. The constitutive relations, obtained by a multiscale approach linking the material description at different scales, depend on the geometry and the arrangement of the internal phases and include internal scale parameters, which allow taking into account size effects. A multiscale finite element technique has been used for obtaining the numerical solution of the multifield and the corresponding Cauchy model. The numerical results obtained on a sample fibre reinforced composite show the effectiveness of the former in pointing out the influence of the size, the shape and the orientation of the fibres on the gross behaviour of the material.
Composites Science and Technology, 2007
An effective integration of a three-dimensional (3D) micromechanical and finite element (FE) modeling framework is proposed for the analysis of thick-section fiber reinforced plastic (FRP) composite materials and structures. The proposed modeling framework is applied to a pultruded composite system. It consists of two alternating layers with unidirectional fiber (roving) and continuous filaments mat (CFM) reinforcements. Nonlinear 3D micromechanical models representing the different composite layers are used to generate through-thickness composite's effective responses. Approximate traction continuity and strain compatibility relations in the micromechanical models are expressed in terms of the average stresses and strains of the sub-cells that recognize the fiber and matrix responses. The nonlinear elastic behavior is attributed only to the matrix sub-cells. The nested nonlinear micromechanical models are implemented at each integration (Gaussian) point in the FE structural analyses. A linearized structural response will produce a trial strain increment for each Gaussian integration point and an iterative solution is performed until a structural-level convergence criterion is met. At every iteration, the micromechanical models are called to provide effective material responses. An efficient numerical implementation of the micromodels is required in order to achieve accurate solutions and accelerate the structural-level convergence. Thus, stress correction algorithm is performed in each level of the nested micromodels. Axial tension and compression tests on off-axis E-glass/vinylester coupons and notched specimens are used to calibrate the in situ material properties of the fiber and matrix and verify the prediction ability of the nested micromodels. The nonlinear calibration of the matrix is done by using the overall axial shear stress-strain response generated from Iosipescu (V-notched) specimens. Good agreement is shown for all off-axis angles when comparing the experimental stress-strain curves with those predicted by the analyses with the proposed micromodels.
Predicting the nonlinear mechanical response of short fiber reinforced composites (SFRCs) is a crucial and challenging task. In this paper, a computationally efficient multi-scale strategy is proposed to predict the anisotropic elasto-plastic behavior of SFRCs using the intrinsic mechanical behavior of the pure polymer and fibers without the requirements for reverse engineering. In doing so, different simple unit cells are first examined to find the one that can adequately describe the nonlinear mechanical response of SFRCs' representative volume elements (RVE) with aligned fibers. Considering the effects of packing configuration, fiber aspect ratio, volume fraction and material properties, the performance of different unit cells is investigated. Then, the homogenized mechanical responses of unit cells are linked to Hill's anisotropic plasticity model to correlate the mechanical response of the suggested unit cell to the continuum domain. Using the pseudo-grain approach and a numerical orientation averaging framework, the effects of fiber misalignment are taken into account. A multi-step homogenization strategy is also employed to consider the variation of fiber orientation tensor and volume fraction through the thickness. Finally, the validity and robustness of the proposed multi-scale strategy are extensively investigated based on the RVE-generated results and the available experimental observations.