Macro-scale Model Research Articles

Numerical simulation for deformation of laminates combining the novel shell element with the decoupled two-scale viscoelastic analysis of FRP

This study proposes a numerical simulation for the deformation of laminates incorporating a combination of the novel shell element, whose thickness is allowed to change in a macro-scale model, with a decoupled two-scale viscoelastic analysis of FRP. The dependence of resin properties on the degree of cure (DOC) is considered in the simulation. Because the shell element of interest is enriched with degrees of freedom (DOFs) to represent the transverse deformations, it is capable of evaluating and controlling the thickness change during curing process of laminates. Since the additional DOFs are introduced to each element independently, they are condensed out at the element level in assembling the global finite element (FE) equation. Besides the force, the displacement can also be imposed on the outermost DOFs to control the change in thickness. Thus, numerical simulations where the plate thickness is controlled according to the requirements for molded products can be realized without introducing solid-shell-type formulations. The macroscopic mechanical behavior of FRP can be represented by the orthotropic version of the model employed for resin whose DOC-dependent macroscopic viscoelastic properties (the macroscopic coefficient of thermal expansions (CTEs) and coefficient of cure shrinkages (CCSs)) are identified from the relaxation curves obtained by results of numerical material tests (NMTs) conducted on the periodic microstructure (unit cell). The usefulness of the proposed approach was clarified by the results of the numerical verifications.

Postbuckling response of unitized stiffened textile composite panels: Computational modeling

A computational investigation of unitized stiffened textile composite panels that are manufactured from triaxially braided textile composites and loaded in axial compression into the postbuckling regime is presented. The stiffened panels are unitized because the textile nature of the constituent material, in conjunction with an alternative stiffener design, form a near-net shape one-piece stiffened panel structure where the textile laminae that form the skin section of the panel are also used, without discontinuity of material, to form the stiffener. A multiscale computational model is presented where the architecture-dependent behavior of a discretely modeled mesoscale representative volume element is passed up to the orthotropic homogenized macroscale stiffened panel shell model. The mesoscale model is automatically executed based on input from the macroscale shell model. Progressive damage initiation and propagation is accomplished by implementing a crack band model in the macroscale model to simulate a material softening behavior. The experimental results are compared to the computational multiscale framework analysis results where a mesoscale triaxially braided textile composite architecture-based model serves as the damage initiation criterion for a smeared progressive damage crack band model in the orthotropic homogenized stiffened panel macroscale shell model.

GeoChemFoam: Direct Modelling of Multiphase Reactive Transport in Real Pore Geometries with Equilibrium Reactions

GeoChemFoam is an open-source OpenFOAM-based toolbox that includes a range of additional packages that solve various flow processes from multiphase transport with interface transfer, to single-phase flow in multiscale porous media, to reactive transport with mineral dissolution. In this paper, we present a novel multiphase reactive transport solver for simulations on complex pore geometries, including microfluidic devices and micro-CT images, and its implementation in GeoChemFoam. The geochemical model includes bulk and surface equilibrium reactions. Multiphase flow is solved using the Volume-Of-Fluid method, and the transport of species is solved using the continuous species transfer method. The reactive transport equations are solved using a sequential operator splitting method, with the transport step solved using GeoChemFoam, and the reaction step solved using Phreeqc, the US geological survey’s geochemical software. The model and its implementation are validated by comparison with analytical solutions in 1D and 2D geometries. We then simulate multiphase reactive transport in two test pore geometries: a 3D pore cavity and a 3D micro-CT image of Bentheimer sandstone. In each case, we show the pore-scale simulation results can be used to develop upscaled models that are significantly more accurate than standard macro-scale equilibrium models.

A two-scale strategy for the modeling of hook and loop fasteners

Hook-and-loop-like joints have been widely used in many engineering applications and even observed in nature. The demand for computational models to predict the behavior of fasteners is increasing as they will be key for reducing design process time and manufacturing costs. Here, we develop a bottom-up two-scale modeling strategy, which enables us to capture the mechanical performance of a hook-and-loop fastener at both micro- and macroscales. In particular, we employ a two-scale homogenization approach capable of predicting the mechanical behavior of the hook-and-loop fastener. The model starts with a micromechanical model of a hook-and-loop fastener which considers the detailed geometry of the individual building blocks of the hook-and-loop fastener and their statistical geometrical variability through a so-called Representative Hook and Loop Element (RHLE) computational domain. The second scale considers the homogenization of the micromechanical model into a Detachment Process Zone (DPZ) which reveals an emerging length scale. The resulting effective traction-separation law concept is then employed at the macroscale with a Double Cantilever Beam (DCB) test using a macroscale model, which is then validated with experiments. The results suggest that the two-scale model strategy is able to predict the mechanical behavior of hook-and-loop fastener and to capture the main deformation and dissipative mechanisms at the relevant length scales.

Opportunities for flexible electricity loads such as hydrogen production from curtailed generation

• Least-cost electricity systems have unused generation capacity during most hours. • Flexible loads can initially be added to systems with minimal generation expansion. • Initially, flexible loads may operate at low marginal cost with high capacity factors. • Increasing flexible loads beyond ∼ 25% of total load accelerates generation expansion. • Increasing electricity system flexibility lessens unused and/or curtailed generation. Variable, low-cost, low-carbon electricity that would otherwise be curtailed may provide a substantial economic opportunity for entities that can flexibly adapt their electricity consumption. We used historical hourly weather data over the contiguous U.S. to model the characteristics of least-cost electricity systems dominated by variable renewable generation that powered firm and flexible electricity demands (loads). Scenarios evaluated included variable wind and solar power, battery storage, and dispatchable natural gas with carbon capture and storage, with electrolytic hydrogen representing a prototypical flexible load. When flexible loads were small, excess generation capacity was available during most hours, allowing flexible loads to operate at high capacity factors. Expanding the flexible loads allowed the least-cost systems to more fully utilize the generation capacity built to supply firm loads, and thus reduced the average cost of delivered electricity. The macro-scale energy model indicated that variable renewable electricity systems optimized to supply firm loads at current costs could supply ∼ 25% or more additional flexible load with minimal capacity expansion, while resulting in reduced average electricity costs ( ∼ 10% or less capacity expansion and ∼ 10% to 20% reduction in costs in our modeled scenarios). These results indicate that adding flexible loads to electricity systems will likely allow more full utilization of generation assets across a wide range of system architectures, thus providing new energy services with infrastructure that is already needed to supply firm electricity loads.

Multiscale numerical investigation on failure behaviour of three-dimensional orthogonal woven carbon/carbon composites subjected to pin-loading

On the basis of the experimental results in previous work, a multiscale numerical modeling strategy on the failure behaviour of three-dimensional orthogonal woven carbon/carbon composites under pin-loading was presented. In consideration of the complexity of internal woven architecture, the finite element analysis at micro-/meso-/macro-scale levels was performed to exhibit the effective material properties and mechanical behaviour. The geometric models were reconstructed via X-ray tomography technology to obtain feasible configurations based on actual microstructure, meanwhile the models considered the fibers random arrangement in the yarn and voids stochastic distribution in the matrix. The anisotropic composites damage evolution was characterized by Murakami-Ohno damage theory. Additionally, for a further exploration on the practical bearing failure mode, the macro-scale open-hole plate model was established using mesh superposition method to expose the damage mechanism of each component in composites at hole edge, and the numerical predictions agreed reasonably well with the experimental results.

A Multi-Scale Submodel Method for Fatigue Analysis of Braided Composite Structures.

A multi-scale fatigue analysis method for braided ceramic matrix composites (CMCs) based on sub-models is developed in this paper. The finite element shape function is used as the interpolation function for transferring the displacement information between the macro-scale and meso-scale models. The fatigue failure criterion based on the shear lag theory is used to implement the coupling calculation of the meso-scale and micro-scale. Combining the meso-scale cell model and the fatigue failure criterion based on the shear lag theory, the fatigue life of 2D SiC/SiC is analyzed. The analysis results are in good agreement with the experimental results, which proves the accuracy of the meso-scale cell model and the fatigue life calculation method. A multi-scale sub-model fatigue analysis method is used to study the fatigue damage of 2D SiC/SiC stiffened plates under random tension–tension loads. The influence of the sub-models at different positions in the macro-model element on the analysis results was analyzed. The results shows that the fatigue analysis method proposed in this paper takes into account the damage condition of the meso-structured of composite material, and at the same time has high calculation efficiency, and has low requirements for modeling of the macro finite element model, which can be better applied to the fatigue analysis of CMCs structure.

A novel multiscale modeling strategy of the low-velocity impact behavior of plain woven composites

A novel multiscale modeling strategy is proposed to investigate the low-velocity impact (LVI) behavior of plain woven composites. Initially, the effective properties of the yarn are obtained from the microscale modeling, in which a microscopic representative volume element (RVE) is constructed by considering carbon fibers and resin matrix. Meanwhile, a mesoscopic RVE is established using the internal fabric structure. Combined with the effective properties of the yarn and continuum damage mechanics (CDM) approaches, the damage initiation and evolution are predicted for the mesoscale models subjected to various loading conditions. A local homogenization approach is developed to transfer the warp and fill yarns, as well as the resin, into 0° and 90° subcells, respectively. Moreover, an equivalent cross-ply laminate (ECPL) cell is constructed by assembling these subcells, to represent the internal fabric structure. Finally, the LVI behavior of plain woven composites is investigated using the macroscale model obtained by extending the ECPL cells. The numerical results are in good agreement with the experimental measurements, confirming the reliability of the multiscale modeling strategy. The LVI damage mechanisms of plain woven composites are analyzed using the numerical simulations, indicating that the delamination and matrix-based damages are the prevailing failure modes.

Homogenized Balance Equations for Nonlinear Poroelastic Composites

Within this work, we upscale the equations that describe the pore-scale behaviour of nonlinear porous elastic composites, using the asymptotic homogenization technique in order to derive the macroscale effective governing equations. A porous hyperelastic composite can be thought of as being comprised of a matrix interacting with a number of subphases and percolated by a fluid flowing in the pores (which is chosen to be Newtonian and incompressible here). A general nonlinear macroscale model is derived and is then specified for a particular choice of strain energy function, namely the de Saint-Venant function. This leads to a macroscale system of PDEs, which is of poroelastic type with additional terms and transformations to account for the nonlinear behaviour of the material. Our new porohyperelastic-type model describes the effective behaviour of nonlinear porous composites by prescribing the stress balance equations, the conservation of mass and Darcy’s law. The coefficients of these macroscale equations encode the detailed microstructure of the material and are to be found by solving pore-scale differential problems. The model reduces to the following limit cases of (a) linear poroelastic composites when the deformation gradient approaches the identity, (b) nonlinear composites when there are no pores and (c) nonlinear poroelasticity when only the matrix–fluid interaction is considered. This model is applicable when the interactions between various hyperelastic solid phases occur at the pore-scale, as in biological tissues such as artery walls, the myocardium, lungs and liver.

A Random Walk Approach to Transport in Tissues and Complex Media: From Microscale Descriptions to Macroscale Models.

The biological processes necessary for the development and continued survival of any organism are often strongly influenced by the transport properties of various biologically active species. The transport phenomena involved vary over multiple temporal and spatial scales, from organism-level behaviors such as the search for food, to systemic processes such as the transport of oxygen from the lungs to distant organs, down to microscopic phenomena such as the stochastic movement of proteins in a cell. Each of these processes is influenced by many interrelated factors. Identifying which factors are the most important, and how they interact to determine the overall result is a problem of great importance and interest. Experimental observations are often fit to relatively simple models, but in reality the observations are the output of complicated functions of the physicochemical, topological, and geometrical properties of a given system. Herein we use multistate continuous-time random walks and generalized master equations to model transport processes involving spatial jumps, immobilization at defined sites, and stochastic internal state changes. The underlying spatial models, which are framed as graphs, may have different classes of nodes, and walkers may have internal states that are governed by a Markov process. A general form of the solutions, using Fourier-Laplace transforms and asymptotic analysis, is developed for several spatially infinite regular lattices in one and two spatial dimensions, and the theory is developed for the analysis of transport and internal state changes on general graphs. The goal in each case is to shed light on how experimentally observable macroscale transport coefficients can be explained in terms of microscale properties of the underlying processes. This work is motivated by problems arising in transport in biological tissues, but the results are applicable to a broad class of problems that arise in other applications.

Application of a Stochastic Multicriteria Acceptability Analysis to support decision-making within a macro-scale energy model: Case study of the electrification of the road European transport sector

Energy system models based on the TIMES framework can explore possible energy futures through the construction of a network of technological processes, to satisfy a set of exogenously imposed service demands at the least-cost system configuration. This work presents a methodology aimed at supporting decision-makers in finding optimal energy-system configuration in a complex energy environment, characterized by uncertain information. First, the EUROfusion TIMES Model is used to assess the sensitivity of different long-term evolutions of the European energy system, with particular reference to the road transport sector, considering different trends for the prescribed future variations of investment cost and vehicle efficiency. In a second step, the Stochastic Multicriteria Acceptability Analysis is used to critically evaluate the alternative optimal configurations proposed by the model simulations under a set of economic and environmental criteria. The results of the analysis allow the discussion of the influence of such criteria on the different alternative cases, complementing the cost minimization approach. In the case study considered here, high penetrations of electric vehicles in the road fleet are favored by economic, environmental and energy-related priorities.

Mesoscale modeling of fracture in cement and asphalt concrete

In this paper, mesoscale modeling is performed to simulate and understand fracture behavior of two concrete composites: cement and asphalt concrete using disk-shaped compact tension (DCT) tests. Mesoscale models are used as alternative to macroscale models to obtain better realistic behavior of composite and heterogeneous materials such as cement and asphalt concrete. In mesoscale models, aggregate and matrix are represented as distinct materials and each material has its characteristic properties. Disk-shaped compact tension test is used to obtain tensile strength and fracture energy of materials. This test can be used as a better alternative to other tests such as three points bending tests because it is more convenient for both field and laboratory specimens in addition to its accurate results. Comparing the numerical results of the mesoscale models of cement and asphalt concrete specimens with experimental data shows that these models can predict the behavior of these composite materials very well as seen in the curves of load-crack mouth opening displacement (CMOD). Also, the mesoscale modeling highlights the variability of crack direction where it is dependent on the random distribution of aggregate.

Homogenized Macroscale Model and Morphological Microscale Model to Understand the Varying Mechanical Properties of Scar Tissue of Hip Capsule Ligaments Grown Around Different Implant Materials

Homogenized Macroscale Model and Morphological Microscale Model to Understand the Varying Mechanical Properties of Scar Tissue of Hip Capsule Ligaments Grown Around Different Implant Materials

Multi-scale modelling of the damage behavior for 3D woven composites with variant structure

In the process of fabricating a three-dimensional (3 D) woven perform, the variant structures introduced during adding and reducing tows, lead to changes of local tow orientation and woven pattern, which affects the mechanical response of 3 D woven composite. In this study, specimens with variant structure were manufactured by adding and reducing tow techniques, and representative unit cells of normal and variant structure were established by topological method. A multi-scale damage model was proposed to analyze the damage behaviors and predict the strength of 3 D woven composites with the user subroutine UMAT of ABAQUS/Standard. The results show that the variation of tensile modulus and strength between the experimental and simulation value were less than 4%. In addition, it is proved that the damage propagation of the macro-scale model with variant structure can be successfully captured.

Robust simulation of mineral precipitation\u2013dissolution problems with variable mineral surface area

We consider a macroscale model of transport and reaction of chemical species in a porous medium with a special focus on mineral precipitation–dissolution processes. In the literature, it is frequently proposed that the reaction rate should depend on the reactive mineral surface area, and so on the amount of mineral. We point out that a frequently used model is ill posed in the sense that it admits non-unique solutions. We investigate what consequences this non-uniqueness has on the numerical solution of the model. The main novelty in this article is our proposal of a certain substitution which removes the ill-posedness from the system and which leads to better numerical results than some “ad hoc methods.” We think that the proposed substitution is a rather elegant way to get rid of the non-uniqueness and the numerical difficulties and is much less technical than other ideas. As a proof of concept, we present some numerical tests and simulations for the new model.

Numerical modeling of the thermal performance of soil containing microencapsulated PCM

Phase change material (PCM) can be used with soil as an alternative type of thermal regulation of the subgrade, since it has an ability to accumulate and generate heat during the phase change. This paper evaluates the position of PCM microcapsules in the soil by means of scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS) analysis. The SEM image processing method includes an integrated approach to transferring a color pixel image into a numerical matrix, followed by noise removal and precise determination of the position and size of microcapsules. Based on these data, a macroscale model of the soil volumetric unit with the inclusion of the microencapsulated phase change material (mPCM) was created, which made it possible to estimate the temperature of the mixture at a changing external temperature, as well as the nature of the effect of mPCM on the soil temperature regime. Through the analysis of many points in the model, the following results were obtained: 1) mPCM not only reduces the peak temperatures of its own volume, but it also softens the peak temperatures of the surrounding soil, 2) with a decrease in the external temperature, there is a tendency to a decrease in the temperature change rate as the model temperature approaches the phase change temperature range, 3) in the second cycle of changing the outside temperature, the effect of mPCM on peak temperatures is greater than in the first cycle due to the cumulative effect of decreasing the temperature change from cycle to cycle. PCM materials release/absorb a large amount of latent heat during hardening/melting, which can be useful in solving problems associated with seasonal freezing and thawing of pavements.

A continuum mechanical framework for modeling tumor growth and treatment in two- and three-phase systems

The growth and treatment of tumors is an important problem to society that involves the manifestation of cellular phenomena at length scales on the order of centimeters. Continuum mechanical approaches are being increasingly used to model tumors at the largest length scales of concern. The issue of how to best connect such descriptions to smaller-scale descriptions remains open. We formulate a framework to derive macroscale models of tumor behavior using the thermodynamically constrained averaging theory (TCAT), which provides a firm connection with the microscale and constraints on permissible forms of closure relations. We build on developments in the porous medium mechanics literature to formulate fundamental entropy inequality expressions for a general class of three-phase, compositional models at the macroscale. We use the general framework derived to formulate two classes of models, a two-phase model and a three-phase model. The general TCAT framework derived forms the basis for a wide range of potential models of varying sophistication, which can be derived, approximated, and applied to understand not only tumor growth but also the effectiveness of various treatment modalities.

Pressure drop model for fibrous media in depth filtration: Coupling simulation of microstructure and CFD porous media during dust loading

The micro-scale model of fibrous media was simulated to obtain viscous resistance in clean state, which was provided to the CFD porous media. A macro-scale model for predicting the pressure drop during dust loading was established based on the Euler-Lagrangian method by implementing the UDF in ANSYS-Fluent. The trapping mechanism programs were developed to realize different distribution forms of particles in the porous media. The macro-empirical model was used to calibrate the macro-scale model under different SVFs. The 592*592*292-4 V–F9 filter was simplified to CFD porous media and the numerical simulation was carried out during dust loading. The results show that the pressure drop shows different growth trends under different trapping mechanism programs. Very good agreement was found between the experimental and simulated pressure drop during dust loading. Thus, the macro-scale model broadens the way of studying the pressure drop of fibrous media in depth filtration.

Multiscale modeling of tip-leakage cavitating flows by a combined volume of fluid and discrete bubble model

For the tip-leakage cavitating flow, the existence of both interface and microbubbles at scales separated by orders of magnitude makes it difficult to be comprehensively reproduced by numerical modeling. This work aims to develop a multiscale model that directly resolves the large-scale cavities and models small discrete bubbles. The volume of fluid (VOF) method and the Schnerr–Sauer cavitation model are first adopted to represent the phase field of water and vapor from a macroscale point of view. A discrete bubble model (DBM) based on the Lagrangian formulation is then developed to simulate the microscale cavitation bubbles that are smoothed in the macroscale model due to the limited mesh resolution. The transition between DBM and VOF is also implemented to achieve the multiscale simulation. For modeling of the turbulence, the scale adaptive simulation approach is used. The tip-leakage cavitating flows induced by the NACA0009 hydrofoil under the conditions with different gaps according to the reported experiment are simulated. Results show that, using the proposed multiscale model, better agreements can be obtained compared with the macroscale model, and specific phenomena can be well revealed including the bubble nucleation, growth and collapse, the interaction between discrete bubbles and large-scale cavities.

The role of accessibility for land use and land cover change in the Brazilian Amazon

Roads and infrastructure are fundamental preconditions for the large-scale conversion of natural forests into agricultural landscapes. Therefore, geographic differences in accessibility are critical for understanding land use and land cover change (LULCC) dynamics. As one of the most dynamic agricultural frontiers globally, the Amazon has much attention in LULCC research. While most studies account for roads and infrastructure, LULCC research often relies on one-dimensional measures of accessibility (e.g., Euclidean distances), which may not optimally represent the underlying latent variable concept. In this study, we demonstrate how alternative concepts and measures of accessibility (specifically travel time maps) can have considerably different explanatory value in the prediction of LULCC. We adopt a panel-data model to explain the geographical distribution of pasture and crop expansion in the Brazilian Amazon using land cover data and travel time maps generated with high-quality representations of existing official and non-official road infrastructure. Our approach's novelty consists of comparing travel time to different markets during the wet- and the dry season and their effect on the allocation of LULCC within a macro scale modeling approach. Our results suggest that (1) pronounced differences between wet- and rainy season accessibility (due to road quality) increase the likelihood of pasture expansion and reduce the likelihood for crops, and (2) that alternative measures of infrastructure access (e.g., to markets versus towns or processing facilities) can explain different socio-economic aspects of LULCC. Our findings suggest that bad infrastructure quality might severely limit the possibility of establishing a less land-intensive agricultural model in the Amazon and that LULCC research can significantly benefit from improved and context-specific measures of accessibility.