Full-field Simulations Research Articles

“pyGDM” - new functionalities and major improvements to the python toolkit for nano-optics full-field simulations

pyGDM is a python toolkit for electro-dynamical simulations of individual nano-structures, based on the Green Dyadic Method (GDM). pyGDM uses the concept of a generalized propagator, which allows to solve cost-efficiently monochromatic problems with a large number of varying illumination conditions such as incident angle scans or focused beam raster-scan simulations. We provide an overview of new features added since the initial publication [Wiecha, Comput. Phys. Commun. 233 (2018) 167–192]. The updated version of pyGDM is implemented in pure python, removing the former dependency on fortran-based binaries. In the course of this re-write, the toolkit's internal architecture has been completely redesigned to offer a much wider range of possibilities to the user such as the choice of the dyadic Green's functions describing the environment. A new class of dyads allows to perform 2D simulations of infinitely long nanostructures. While the Green's dyads in pyGDM are based on a quasistatic description for interfaces, we also provide as new external python package “pyGDM2_retard” a module with retarded Green's tensors for an environment with two interfaces. We have furthermore added functionalities for simulations using fast-electron excitation, namely electron energy loss spectroscopy and cathodoluminescence. Along with several further new tools and improvements, the update includes also the possibility to calculate the magnetic field and the magnetic LDOS inside nanostructures, field-gradients in- and outside a nanoparticle, optical forces or the chirality of nearfields. All new functionalities remain compatible with the evolutionary optimization module of pyGDM for nano-photonics inverse design. Program summaryProgram Title: pyGDM2CPC Library link to program files:https://doi.org/10.17632/5zdrppdc3j.1Licensing provisions: GPLv3Programming language: pythonNature of problem: Full-field electrodynamical simulations of photonic nanostructures. This includes calculations of the optical extinction, scattering and absorption, as well as the near-field distribution or the interaction of quantum emitters with nanostructures as well as fast electron beam simulations. The toolkit includes a module for automated evolutionary optimization of nanostructure geometries to obtain a user-defined optical response.Solution method:: The optical response of photonic nanostructures is calculated using field susceptibilities (“Green Dyadic Method”, GDM) via a volume discretization. The approach is formally similar to the coupled dipole approximation.Additional comments including restrictions and unusual features: 2D and 3D nanostructures. On typical office PCs (8-16GB RAM) the discretization is limited to about 10000-15000 meshpoints, therefore it applies best to single, small nanostructures.

Theoretical Modelling of Droplet Extension on Hydrophobic Surfaces

In this work, droplet impact dynamics on hydrophobic surfaces under different wettability and impact conditions are examined numerically. Multi-phase finite volume simulations are carried out by employing volume-of-fluid scheme and are validated against experimental results. Numerous droplet impact experiments are performed by varying Weber number, Reynolds number and substrate contact angle. Sticking, bouncing and splitting regimes are identified. It is observed that, for the same Reynolds number, the droplet attaches, rebounds or fragments depending on the Weber number. A semi-analytical representation using a single mass-spring-dashpot model is employed for the prediction of droplet height evolution during spreading and retraction. The spring and damping coefficients required for the model are estimated from the empirical correlations for contact time and restitution coefficients obtained from the simulations. Even though the Reynolds number is found to influence the coefficient of restitution significantly, it is found to have negligible influence on contact time. The theoretical forecasting exhibited good agreement with simulated results and it gives a significant reduction in computational time compared to the conventional full-field continuum simulations.

Damping in a row of locally-resonant inclusions: Dynamic homogenization and scattering of transient shear waves

The scattering of scalar waves by a periodic row of inclusions is theoretically and numerically investigated. The wavelength in the background medium is assumed to be much larger than the typical sizes of the inclusions. The latter are also much softer than the matrix, yielding localized resonances within the microstructure. Previous works in the inviscid case have concerned: (i) the derivation of effective resonant jump conditions, that are non local in time (Touboul et al. (2020) [41]); (ii) the introduction of auxiliary fields along the interface, providing a time-domain formulation of the scattering problem (Touboul et al. (2020) [40]). The present contribution extends the analysis to dissipative cases, which allows to be closer from real devices. The effective jump conditions with damping are obtained, both in the frequency domain and in the time domain. An exact plane-wave solution is proposed. A balance of energy is written, and new auxiliary fields are introduced. Practical implementation of the simulation methods is discussed. Then, numerical experiments are proposed to validate the auxiliary-field approach. The effect of dissipation is examined, and the relevance of the homogenized simulations in comparison with full-field simulations of transient waves is assessed. As an application, a numerical experiment of Coherent Perfect Absorption is finally proposed: at critical values of the attenuation parameter and close to the resonant frequencies, the waves impacting the dissipative resonant interface are fully absorbed.

Large-deformation crystal plasticity simulation of microstructure and microtexture evolution through adaptive remeshing

The capability of high-resolution modeling of crystals subjected to large plastic strain is essential in predicting many important phenomena occurring in polycrystalline materials, such as microstructure, deformation localization and in-grain texture evolution. However, due to the heterogeneity of the plastic deformation in polycrystals, the simulation mesh gets distorted during the deformation. This mesh distortion deteriorates the accuracy of the results, and after reaching high local strain levels, it is no longer possible to continue the simulation. In this work, two different adaptive remeshing approaches are introduced for simulating large deformation of 3D polycrystals with high resolution under periodic boundary conditions. In the first approach, a new geometry with a new mesh is created, and then the simulation is restarted as a new simulation in which the initial state is set based on the last deformation state that had been reached. In the second approach, the mesh is smoothened by removing the distortion part of the deformation, and then the simulation is continued after finding a new equilibrium state for the smoothed mesh and geometry. The first method is highly efficient for conducting high-resolution large-deformation simulations. On the other hand, the second method’s primary advantage is that it can overcome periodicity issues related to shear loading, and it can be used in conjunction with complex loading conditions. The merits of the methodologies are demonstrated using full-field simulations performed using a dislocation-density-based crystal plasticity model for Interstitial free (IF-) steel. Particular emphasis is put on studying the effect of resolution and adaptive meshing. The algorithms presented have been implemented into the free and open-source software package, DAMASK (Düsseldorf Advanced Material Simulation Kit).

Linking a phase field model for polymer crystallization to full-field micromechanical simulations of semi-crystalline polymers

An enhanced phase field model recently proposed by the authors enables to model polymer crystallization and to predict spherulite growth and representative semi-crystalline micro-structures in 2D or 3D. After solidification, the value of the phase field variable in each subcell (2D pixel or 3D voxel) indicates whether the material is amorphous or crystalline. In the present paper, full-field micromechanical simulations are conducted on the microstructures generated by the enhanced phase field model in order to predict the effective mechanical properties. A Fast Fourier Transform (FFT) method with periodic boundary conditions is used. Care is taken to obtain representative volume elements (RVEs) by computing the number of subcells in each spherulite and the number of spherulite nucleations in each RVE. Numerical FFT predictions of elastic properties for a range of crystallinity ratios are validated against experimental data and compared to simpler composite inclusion models. Finite element simulations of thermal shrinkage are also shown. The approach was numerically implemented in a research version of the Digimat software.

Differentiated Strain-Control of Localized Magnetic Modes in Antidot Arrays.

The control of localized magnetic modes has been obtained in Ni60Fe40 square lattice (600 nm) antidot arrays. This has been performed by tailoring the magnetoelastic field at the scale of the antidot primitive cell. The corresponding heterogeneous strain field distributions have been generated by a PZT substrate and enhanced by the incorporation of a supporting compliant layer. It has been highlighted by a differentiated variation of magnetic energy directly due to the local magnetoelastic field felt by each magnetic mode, probed by ferromagnetic resonance spectroscopy. A modeling, involving micromagnetic simulations (to locate the magnetic modes), full-field simulations (to evaluate the strain field distributions), and an analytical model generally dedicated to continuous film that we have extended to those magnetic modes, shows a good agreement with the experimental data. This approach is very promising to develop multichannel systems with simultaneous and differentiated controlled frequencies in magnetic devices.

An FE–DMN method for the multiscale analysis of short fiber reinforced plastic components

In this work, we propose a fully coupled multiscale strategy for components made from short fiber reinforced composites, where each Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN) which covers the different fiber orientation states varying within the component. These DMNs need to be identified by linear elastic precomputations on representative volume elements, and serve as high-fidelity surrogates for full-field simulations on microstructures with inelastic constituents.We discuss how to extend direct DMNs to account for varying fiber orientation, and propose a simplified sampling strategy which significantly speeds up the training process. To enable concurrent multiscale simulations, evaluating the DMNs efficiently is crucial. We discuss dedicated techniques for exploiting sparsity and high-performance linear algebra modules, and demonstrate the power of the proposed approach on an injection molded quadcopter frame as a benchmark component. Indeed, the DMN is capable of accelerating two-scale simulations significantly, providing possible speed-ups of several magnitudes.

Acoustic radiation force for multiple particles over a wide size-scale by multiple ultrasound sources

In recent years, the manipulation of microparticles by ultrasound transducer arrays becomes possible. However, the contributions of rescattered waves among the particles have not to be taken into account in designs. The theoretical results are typically valid for small particles. This study considers the acoustic forces exerted by time-harmonic waves on large particles. The theory accounting for the scattering effect is developed for multiple sources (or transducers) and multiple particles of various sizes, levitated in an inviscid fluid. The external waves from multiple sources are expanded by equivalent plane wave series with the translation addition theorem. The multiple scattering field and the acoustic force can then be expressed under the plane wave series structure. The key to predicting the particle trajectory is the updating of the coordinate information of moving particles. The computed acoustic pressure field and the acoustic forces by this semi-analytical method are first validated by the full-field finite element simulation with a few particles. It is then used to calculate the more complex and interesting cases of multiple particles of various sizes manipulated by multiple transducers in the air. It is found that, in general, the contribution of scattering wave becomes significant when the size parameter ka>2, and it increases quadratically with the amplitude parameter of the transducers. A typical example also shows that the scattering force overtakes the gradient force when the source amplitude for a large particle is two times higher than that for a neighboring particle.

Experimental study and micromechanical modelling of the effective elastic properties of Fe–TiB2 composites

The aim of this paper is to investigate the effective properties of Fe–TiB2 composites obtained after hot or cold rolling. The elastic moduli of both hot and cold rolled composites are measured experimentally using several methods. Microstructure analyses based on SEM observations are performed to characterize the distribution of particles and cracks, and are then used to generate 3D representative microstructures using the RSA method. This allows the numerical determination of the overall elastic behavior of Fe–TiB2 composites using full-field FFT-based simulations. In addition, Young’s moduli of the hot rolled Fe–TiB2 composites are also determined analytically using the mean-field homogenization scheme of Mori–Tanaka. The elastic properties determined experimentally, analytically and numerically are in a good agreement. Overall, a significant improvement of the specific stiffness in comparison to standard steels is achieved irrespective of the processing conditions.

MENP: an open-source MATLAB implementation of multipole expansion for nanophotonics

In modern nanophotonics, multipolar interference plays an indispensable role to realize novel optical devices represented by metasurfaces with unprecedented functionalities. Not only to engineer sub-wavelength structures that constitute such devices but also to realize and interpret unnatural phenomena in nanophotonics, a program that efficiently carries out multipole expansion is highly demanded. MENP is a MATLAB program for computation of multipole contributions to light scattering from current density distributions induced in nanophotonic resonators. The main purpose of MENP is to carry out post-processing of a rigid multipole expansion for full-field simulations that in principle provide the information of all near- and far-field interactions (e.g., as a total scattering cross section). MENP decomposes total scattering cross sections into partial ones due to electric and magnetic dipolar and quadrupolar terms based on recently developed exact multipole expansion formulas. We validate the program by comparing results for ideal and realistic nanospheres with those obtained with the Mie theory. We also demonstrate the potential of MENP for analysis of anapole states by calculating the multipole expansion under the long-wavelength approximation, which enables us to introduce toroidal dipole moments.

Stochastic evaluation of stress and strain distributions in duplex steel

Austenite–ferrite duplex steels generally consist of two differently textured polycrystalline phases with different glide mechanisms. For estimating the effective mechanical behavior of heterogeneous materials, there exist well established approaches, two of which are the classes of mean-field and full-field methods. In this work, the local fields resulting from these different approaches are compared using analytical calculations and full-field simulations. Duplex steels of various textures measured using X-ray diffraction are considered. Special emphasis is given to the influence of the crystallographic texture on the stress and strain distributions.

Self-consistent, polycrystal rate-independent crystal plasticity modeling for yield surface determination

The evolution of the macroscopically observed yield surface has been the subject of many studies due to its significant effect on the numerical simulation of metal forming processes. Although macroscopic models exist that aim to define this evolution accurate data for calibration as well as validation of these models are difficult to obtain. One common approach is to use crystal plasticity simulations for analyzing the mesoscopic behavior followed by a homogenization scheme for gathering the aggregate behavior. In this study a similar approach is followed the difference being the choice of the crystal plasticity and homogenization methods. A rate-independent crystal plasticity framework where all slip system activities are solved implicitly using a backward Euler approach in combination with an interior point method for constrained optimization is used for single crystal behavior. The aggregate behavior is obtained using a self-consistent analytical homogenization scheme. The results of the homogenization scheme are compared against full-field crystal plasticity finite element simulations. The determination of the yield surface is done by considering the macroscopic behavior where the strain rate direction and magnitude changes over a threshold during stress-based loading.

Free or Bound? Thomeer and NMR Porosity Partitioning in Carbonate Reservoirs, Alta Discovery, Southwestern Barents Sea

The main etrophysical challenges in carbonate reservoirs are often to define meaningful rock types, then to establish robust permeability and saturation models for these rock types, as well as to develop a realistic estimation of irreducible water saturation (Swirr). Realistic Swirr estimation is important for predicting production behavior (expected development of water cut) and thus ultimately for planning the future development scheme of a discovery. In this study, we present the 2014 Alta discovery, located in the southwestern Barents Sea. More than 50% of the expected hydrocarbon resources reside within complex carbonate reservoirs of Permo-Carboniferous age that display highly variable rock properties. The initial screening revealed that primary rock textures and pore geometries were, for a large part, overprinted by diagenetic processes. Hence, better control on the reservoir’s diagenetic evolution will be needed to apply a full-scale rock typing workflow. In the meantime, it was decided to proceed with a simplified reservoir characterization approach based on the main stratigraphic building blocks. Sufficient core coverage allowed for using permeability measurements on core samples as direct input to a 3D reservoir model. A customized core analysis program, using whole-core samples, was designed to characterize the effect of large-scale vuggy pores. For modeling water saturation, a workflow based on the Thomeer hyperbola was developed that describes mercury injection capillary pressure (MICP) curves. The results adequately specify the saturation in all the stratigraphic building blocks. However, saturation uncertainty in the reservoir is high due to a highly variable cementation factor (m), unknown wettability, and the presence of residual oil below the current free-water level (FWL). The Alta structure has been and still is leaking gas, causing the FWL to rise over time. To address the otherwise underestimated volumes in the transition zone above the current FWL, a deeper pseudo-FWL was created and used as input to the saturation height function. Despite log-based water saturation (Archie) and core measurements (Dean-Stark) indicating more than 80% water saturation for less permeable reservoir rocks within the oil leg, production tests did not produce water at normal rates. This clearly demonstrated the need to distinguish “nonproductive” pore systems (with capillary-bound fluids; in this case, water) from pore systems contributing to production (“free” fluids). A large MICP data set confirmed that most reservoir rocks exhibit a mix of different pore types and pore-throat diameters. To model this accurately, porosity partitioning in nonproductive microporosity and movable porosity using the NMR logs was performed. Calibrating appropriate T2 cutoffs by matching core MICP to NMR logs in these heterogeneous rocks is seriously hampered by the large difference in sample size. Applying both MICP and NMR measurements to a subset of core plugs helped to resolve this challenge. Comparing the corresponding movable (“free”) porosity to total porosity revealed near-linear relationships for different reservoir rocks. For irreducible water saturation (Swirr), Swimmobile is calculated using the NMR-based movable porosity. Swimmobile is considered to be a close approximation of Swirr. The resulting full-field simulation showed a significantly improved match between model output and recorded well test data.

Cellular Automata-based computational library for development of digital material representation models of heterogenous microstructures

The development of an efficient numerical approach for the generation of a wide range of heterogeneous microstructures models with the application of the lean workflow concept is presented in the paper. First, the idea and implementation details of the developed cellular automata-based computational library allowing the development of digital material representation models within a workflow are presented in the paper. Such an approach provides the desired flexibility in the generation of various digital models of heterogenous microstructures. Therefore, the proposed library is mostly implemented within the object-oriented C + + programming language with the assumption of modularity. In this case, the main part of the application consists of classes and methods, which can be treated like base elements to be inherited and extended in other libraries. Each additional dynamic link library implements particular algorithms for the generation of specific microstructure features in the digital model within the unified data structures that allow the application of the workflow concept. The set of developed libraries and their assumptions are described as case studies to show the capabilities of the presented solution. Finally, examples of practical applications of the developed library in the full-field numerical simulations of complex material deformation are presented at the end of the paper.

Impact of Relaxation of Low-Sulfate Seawater Parameters on Scaling Risk

SummaryInjection of low-sulfate seawater (LSSW) instead of untreated full-sulfate seawater (FSSW) is widely used to mitigate barium sulfate scaling risk at the production wells. LSSW injection may no longer be required when the barium concentrations in the produced water drop below a certain threshold. Such a trigger value could be estimated from the barium sulfate precipitation tendency. Relaxation of requirements for the sulfate reduction plant (SRP) can significantly reduce operational costs. This study investigates the impact of several parameters on the timing and degree of relaxation of the output sulfate concentration by the SRP. Finally, the optimal switching strategy is proposed for a field case.The strategy for switching from LSSW to FSSW (e.g., time and method; direct or gradual increase in the sulfate concentration) was initially investigated using generic 2D areal and vertical models. The sensitivity study included the impact of reservoir heterogeneity and the initial barium and sulfate ion concentrations. Findings were later applied on a full-field reservoir simulation model followed by a mineral scale prediction software to investigate the specific switching strategy for a field that has multiple wells and significantly more complex heterogeneity.The results show that barium concentrations in the formation brine affect the choice of switching time more than the output sulfate concentration produced by the SRP. The degree of heterogeneity around the producers also has a significant impact on the switching time. Another parameter is the contrast in the permeability between layers; higher contrast allows a longer period of coproduction of the scaling ions and thus delays the switching time. In the field case, switching to FSSW at early times allows higher consumption of barium ions because of its in-situ precipitation. Barium is no longer a limiting ion, and so a higher degree of deep reservoir precipitation reduces the requirement for prolonged LSSW injection. Another strategy is a gradual relaxation of LSSW output, which allows even earlier buildup of the injected sulfate concentration compared with the direct FSSW switch.The study investigates the reservoir parameters that affect sulfate relaxation of LSSW injection for a field. After the proposed workflow, the optimal relaxation strategy can be designed for other field cases.

A poroelastic simulator with hydraulic fracture propagation using cohesive finite elements

Oil and gas production projects rely on hydraulic fracturing for improved well stimulation and profitability. Research progress on numerical simulation enables design teams to estimate rock behavior and ensure the success of such operations. Stimulation operations usually take only a few hours, and fluid diffusion around the well is normally unimportant. In long-term improved oil recovery injection projects, however, injected water and gas significantly modify reservoir pore pressure and geomechanical conditions around injection wells. This paper proposes a fully coupled hydromechanical full-field reservoir simulator to consider the effects of such coupled effects in the propagation of tensile hydraulic fractures in short- and long-term processes. The numerical approach uses finite elements to represent the poroelastic medium and lower dimension cohesive interface elements to represent fragile interfaces. Numerical accuracy is validated against asymptotic analytical solutions. The results show significant impact of fluid injection and production history in the attributes of the fracture generated. For long-term projects, designers must avoid the use of off-the-shelf hydraulic fracturing simulators designed typically for stimulation operations. This paper encourages using fully coupled, full-field reservoir simulators and considering, in detail, the variety of physical phenomena present in the process. The main contributions of this work comprise an incremental damage control algorithm for fracture propagation and a geometrical analysis technique for avoiding mesh overlap on damaged compressive interfaces.

Wavefront shaping and modulation with resonant electro-optic phase gradient metasurfaces

Phase gradient metasurfaces have revolutionized modern optical components by significantly reducing the path length of bulk optics while maintaining high performance. However, their geometric design makes dynamic modulation challenging, with devices facing a trade-off between the modulation range and efficiency. Here, we introduce Silicon-on-Lithium Niobate (LNO) high-Quality-factor (high-Q) metasurfaces for efficient electro-optic wavefront shaping and modulation. Periodic perturbations within Si metasurface elements allow incident light to be weakly coupled into guided modes, generating high-Q resonances that manifest in the far-field diffraction spectrum. The near field of each Si element spatially overlaps with the LNO substrate, enabling electrically tunable modulation of the resonant frequency. Using full-field simulations, we demonstrate near-infrared, dynamically tunable beamsteering, and beamsplitting metasurfaces. First, we demonstrate beamsteering metasurfaces whose +1st order diffracted intensity can be modulated from 70% to 7% absolute efficiency near the resonant frequency with applied electric fields of order V/μm. Next, we design a tunable beam splitter, switching between direct, 0th order transmission and beamsplitting with the application of 30 V across the metasurface. Our high-Q electro-optic metasurfaces provide a foundation for efficient, time-dependent transfer functions in subwavelength footprints.

Composite Material Failure Model Updating Approach Leveraging Nondestructive Evaluation Data

Abstract A novel failure model updating methodology is presented in this paper for composite materials. The innovation in the approach presented is found in both the experimental and computational methods used. Specifically, a dominant bottleneck in data-driven failure model development relates to the types of data inputs that could be used for model calibration or updating. To address this issue, nondestructive evaluation data obtained while performing mechanical testing at the laboratory scale are used in this paper to form a damage metric based on a series of processing steps that leverage raw sensing inputs and provide progressive failure curves that are then used to calibrate the damage initiation point computed by full-field three-dimensional finite element simulations of fiber-reinforced composite material that take into account both intra- and interlayer damage. Such curves defined based on nondestructive evaluation data are found to effectively monitor the progressive failure process, and therefore, they could be used as a way to form modeling inputs at different length scales.

Effective dynamics for low-amplitude transient elastic waves in a 1D periodic array of non-linear interfaces

This article focuses on the time-domain propagation of elastic waves through a 1D periodic medium that contains non-linear imperfect interfaces, i.e. interfaces exhibiting a discontinuity in displacement and stress governed by a non-linear constitutive relation. The array considered is generated by a, possibly heterogeneous, cell repeated periodically and bonded by interfaces that are associated with transmission conditions of non-linear “spring–mass” type. More precisely, the imperfect interfaces are characterized by a linear dynamics but a non-linear elasticity law. The latter is not specified at first and only key theoretical assumptions are required. In this context, we investigate transient waves with both low-amplitude and long-wavelength, and aim at deriving homogenized models that describe their effective motion. To do so, the two-scale asymptotic homogenization method is deployed, up to the first-order. To begin, an effective model is obtained for the leading zeroth-order contribution to the microstructured wavefield. It amounts to a wave equation with a non-linear constitutive stress–strain relation that is inherited from the behavior of the imperfect interfaces at the microscale. The next first-order corrector term is then shown to be expressed in terms of a cell function and the solution of a linear elastic wave equation. Without further hypothesis, the constitutive relation and the source term of the latter depend non-linearly on the zeroth-order field, as does the cell function. Combining these zeroth- and first-order models leads to an approximation of both the macroscopic behavior of the microstructured wavefield and its small-scale fluctuations within the periodic array. Finally, particularizing for a prototypical non-linear interface law and in the cases of a homogeneous periodic cell and a bilaminated one, the behavior of the obtained models are then illustrated on a set of numerical examples and compared with full-field simulations. Both the influence of the dominant wavelength and of the wavefield amplitude are investigated numerically, as well as the characteristic features related to non-linear phenomena.

Effective viscoelastic behavior of polymer composites with regular periodic microstructures

Polymer matrix exhibit linear viscoelasticity during processing of composites. The viscoelastic homogenization problem in the time-domain play a vital role in the virtual process simulations. In this paper, full-field simulations using finite element (FE) are carried out for different regular periodic microstructures of unidirectional (UD) fiber reinforced polymer (FRP) (i.e., short, and long fiber) composite and particulate composites. The incremental variational based mean-field homogenization (MFH) as proposed by Lahellec and Suquet (Lahellec and Suquet, 2007a) is used here for comparing with the full-field solutions. Two different elastic bounds-based homogenization methods are coupled with this scheme. Implementation is validated with benchmark problems of particulate composites. These are then compared with the solutions of different particulate microstructures (face centered cubic (FCC), body centered cubic (BCC) and simple cubic (SC)). Mean-field response is closer to FCC arrangement. Additionally, FCC and BCC arrangement indicated nearly the same response with different local field statistics. Relaxation in the effective modulus of UD FRP composites obtained from the MFH compared well with the full-field solution as a function of direction and time for hexagonal arrangement of long fiber and staggered arrangement of ellipsoidal short fibers. The effect of different aspect ratio, volume fraction and contrast in properties on the macroscopic response is additionally investigated. Glass and carbon fiber with an isotropic approximation is used for studying the effect of contrast. Double inclusion MFH scheme coupled with the incremental variational approach indicated better comparisons with the full-field solution of UD FRP composites.