An atomistically-informed multiscale modeling framework to investigate damage evolution and failure in radially-grown carbon nanotube (CNT) architecture is detailed in this paper. Molecular dynamics (MD) simulations are performed to investigate the effects of nano-reinforcements on the elastic-plastic characteristics of the constituent interphase in the radially-grown nanocomposite. An interphase damage model is developed using the continuum damage mechanics approach with damage evolution equations derived using atomistic simulations. The developed damage model is integrated with a high-fidelity micromechanical analysis and captures the underlying physical behavior that could be attributed to the enhancement of the out-of-plane properties at higher length scales. The mechanical properties of the nanocomposite obtained from micromechanical simulations are compared to experimental values reported in the literature, to validate the developed modeling framework. Conclusions are presented by comparing the material response of radially-grown CNT architectures with the traditional fiber reinforced polymer (FRP) with dispersed CNT architecture.

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This paper presents the implementation of an atomistic computational framework to investigate a fuzzy fiber nanocomposite architecture. A polymeric functional coating for the carbon fiber surface, which also serves as a substrate for the CNT growth, is explicitly modeled. Additionally, the carbon fiber surface is modeled through irregularly stacked graphene layers with voids. Radially grown CNTs and epoxy resin and hardener molecules are also included at the nanocomposite interface. The epoxy curing simulation is carried out first, followed by virtual deformation of the simulation volume. The tensile and transverse moduli of the fuzzy fiber nanocomposite interface is computed from the virtual deformation simulations. Results indicate that the out-of-plane interface modulus is significantly improved, compared to the traditional fiber/matrix interface by the addition of the polymer coating and radially-grown CNTs. The in-plane transvers modulus also shows improvement and the atomistic modeling framework is able to capture the physical mechanisms that lead to improvement/degradation of material properties.@en

A methodology that accurately simulates the brittle behavior of epoxy polymers initiating at the molecular level due to bond elongation and subsequent bond dissociation is presented in this paper. The system investigated in this study comprises a combination of crystalline carbon nanotubes (CNTs) dispersed in epoxy polymer molecules. Molecular dynamics (MD) simulations are performed with an appropriate bond order-based force field to capture deformation-induced bond dissociation between atoms within the simulation volume. During deformation, the thermal vibration of molecules causes the elongated bonds to re-equilibrate; thus, the effect of mechanical deformation on bond elongation and scission cannot be captured effectively. This issue is overcome by deforming the simulation volume at zero temperature—a technique adopted from the concept of quasi-continuum and demonstrated successfully in the authors’ previous work. Results showed that a combination of MD deformation tests with ultra-high strain rates at near-zero temperatures provides a computationally efficient alternative for the study of bond dissociation phenomenon in amorphous epoxy polymer. In this paper, the ultra-high strain rate deformation approach is extended to the CNT-epoxy system at various CNT weight fractions and the corresponding bond disassociation energy extracted from the simulation volume is used as input to a low-fidelity continuum damage mechanics (CDM) model to demonstrate the bridging of length scales and to study matrix failure at the microscale. The material parameters for the classical CDM model are directly obtained from physics-based atomistic simulations, thus improving the accuracy of the multiscale approach.

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An atomistic modeling framework to investigate the interface/interphase of composite architecture with carbon fibers containing radially-grown carbon nanotubes (often called fuzzy fibers) is detailed in this paper. A polymeric functional coating for the carbon fiber surface, which also serves as a substrate for the CNT growth, is explicitly modeled. The tensile and transverse moduli of the fuzzy fiber/epoxy interphase is computed from virtual deformation simulations and compared to experimental values reported in literature, in order to validate the nanoscale model. Furthermore, the effect of the polymer substrate is studied by modeling the local interphase mechanics. Various modes of virtual loading provide the cohesive behavior of the local substrate/epoxy interphase. Conclusions are presented by comparing the material response of the interphase with and without the polymeric substrate. The integration of results from the nanoscale to an atomistically-informed subcell-based continuum level model is also demonstrated in the paper.

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A micromechanical modeling framework that integrates an interphase damage model is used to study damage evolution, and failure in radially-grown carbon nanotube (CNT) reinforced nanocomposites. The atomistically-informed damage model is developed using the continuum damage mechanics approach with damage evolution equations derived using molecular dynamics simulations. The developed damage model is integrated with a high-fidelity micromechanical analysis and captures the underlying physical behavior that could be attributed to the enhancement of the out-of-plane properties at the higher length scales. To illustrate the effects of nanoarchitecture, the response of the radially-grown CNT nanocomposite is compared with that of the traditional carbon fiber reinforced polymer (CFRP) composite.@en

A multiscale-modeling framework is presented to understand damage and failure response in carbon nanotube reinforced nanocomposites. A damage model is developed using the framework of continuum damage mechanics with a physical damage evolution equation inspired by molecular dynamics simulations. This damage formulation is applied to randomly dispersed carbon nanotube reinforced nanocomposite unit cells with periodic boundary conditions to investigate preferred sites and the tendency towards damage. The continuum model is seen as successfully capturing much of the unique nonlinear trends observed in the molecular dynamics simulations in a volume 1000 times greater than the molecular dynamics unit cell. Additionally, application of the damage model to the continuum unit cell revealed insights into the failure of carbon nanotube reinforced nanocomposites at the sub-microscale.@en

The carbon fiber/polymer matrix interphase region plays an important role in failure initiation and accurate modeling techniques are integral to study the effects of this complex region on the composite response. In composites infused with nanoparticles such as carbon nanotubes (CNT), the interphase region is more complex due to the presence of multiple constituents and their interactions with each other. An atomistic methodology to simulate the constituent interphases in carbon fiber reinforced CNT/epoxy nanocomposites is presented in this paper. The interphase model consisting of voids in multiple graphene layers enable the simulation of physical entanglement between the polymer matrix and the irregular carbon fiber surface. The voids in graphene layers are generated by removing carbon atoms and hydrogenating the end carbon atoms, which better represent the roughness of the carbon fiber surface. The epoxy curing studies and the response of fiber/matrix interphase under mechanical loading are investigated through molecular dynamic (MD) simulations with appropriate classical/harmonic and bond order-based force fields. Furthermore, the atomistic force-displacement behavior is also extracted to formulate a traction-separation law for interface cohesive zone models. The cohesive behavior determined from molecular models is parameterized in equations that can be integrated with an atomistically informed multiscale modeling framework.

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The carbon fiber/polymer matrix interphase region plays an important role in the behavior and failure initiation of polymer matrix composites and accurate modeling techniques are needed to study the effects of this complex region on the composite response. This paper presents a high fidelity multiscale modeling framework integrating a novel molecular interphase model for the analysis of polymer matrix composites. The interphase model, consisting of voids in multiple graphene layers, enables the physical entanglement between the polymer matrix and the carbon fiber surface. The voids in the graphene layers are generated by intentionally removing carbon atoms, which better represents the irregularity of the carbon fiber surface. The molecular dynamics method calculates the interphase mechanical properties at the nanoscale, which are integrated within a high fidelity micromechanics theory. Additionally, progressive damage and failure theories are used at different scales in the modeling framework to capture scale-dependent failure of the composite. Comparisons between the current molecular interphase model and existing interphase models and experiments demonstrate that the current model captures larger stress gradients across the material interphase. These large stress gradients increase the viscoplasticity and damage effects at the interphase which are necessary for improved prediction of the nonlinear response and multiscale damage in composite materials.

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This paper examines microscale and sub-microscale damage mechanisms in carbon nanotube (CNT) reinforced nanocomposites. A multiscale modeling framework with a damage model developed from molecular dynamics simulation, is employed to study the physical mechanisms of damage initiation and propagation in CNT nanocomposites at the sub-microscale. Two CNT arrangements, randomly dispersed and entangled agglomerates, are examined. This investigation offers insights into damage properties of particular configurations of CNTs in a polymer matrix, in addition to specific understanding related to damage concentration effects around the filler material at the sub-microscale. High spatial CNT concentration differential is observed to affect damage initiation and rate of damage. It is further shown to result in sub-microscale crack initiation at low global strains, a phenomenon that is also observed at agglomeration boundaries, which results in CNT agglomerations to behave as crack initiation sites.

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This article presents a novel approach to model the mechanical response of smart polymeric materials. A cyclobutane-based mechanophore, named "smart particle" in this article, is embedded in an epoxy polymer matrix to form the self-sensing smart material. A spring-bead model is developed based on the results from molecular dynamics simulation at the nanoscale to represent bond clusters of a smart polymer. The spring-bead network model is developed through parametric studies and mechanical equivalence optimization to represent the microstructure of the material. A statistical network model is introduced, which is capable of bridging the high-accuracy molecular dynamics model at the nanoscale and the computationally efficient finite element model at the macroscale. A comparison between experimental and simulation results shows that the multiscale model can capture global mechanical response and local material properties.

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The piezoresistivity of carbon nanotube (CNT) reinforced nanocomposites is modeled using a multiscale damage modeling technique. Two phenomena of piezoresistivity are studied, the inherent piezoresistivity of the CNTs and the electrical tunneling effect. The damage model is developed under the framework of continuum damage mechanics (CDM) with a physical damage evolution equation inspired by Molecular Dynamics (MD) simulations. This damage model is applied to a nanocomposite unit cells with randomly dispersed CNTs. Orders of magnitude change in piezoresistivity is observed as the nanocomposite changes from non-damaged state to damaged state. This study provides insights into the prevailing mechanisms associated with piezoresistivity in the damaged and undamaged state of the CNT reinforced nanocomposites at the sub micro scale.

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An atomistic methodology to simulate the constituent interphases in carbon fiber reinforced CNT/epoxy nanocomposites is presented in this paper. Two critical interphase regions are considered in the study: CNT/polymer interphase and the fiber/matrix interphase. The elastic and inelastic responses of the interphases are investigated through molecular dynamic (MD) simulations with appropriate force fields, and integrated with an atomistically informed multiscale modeling framework. The elastic behavior is studied at the molecular level using harmonic force fields whereas bond elongation and subsequent bond dissociation in epoxy polymer chains, and the fiber/matrix interphase are investigated using a bond order based force field. An MD simulation approach adopted from the concept of quasi-continuum (QC) is employed to calculate the bond dissociation energy during virtual deformation tests. The variation of bond dissociation energy density during the deformation tests is integrated into a continuum damage mechanics model to characterize microscale damage in the epoxy matrix. Furthermore, the atomistic forcedisplacement behavior is also extracted to formulate a tractionseparation law for the microscale cohesive zone models for the fiber/matrix interface.@en

A novel molecular dynamics (MD) simulation methodology to capture brittle fracture in epoxy-based thermoset polymer under mechanical loading is presented. The ductile behavior of amorphous polymers has been captured through traditional MD simulation methods by estimating the stress-strain response beyond the yield point; however, brittle fracture in highly crosslinked polymer materials such as epoxy thermoset has not been addressed appropriately and is the primary objective of this work. In this study, a numerically cured epoxy system comprising molecules of epoxy resin and hardener is generated. During the virtual deformation test, it is observed that the inherent molecular vibration due to temperature re-equilibrates the elongated covalent bonds and this molecular vibration impedes further stretching the covalent bond leading to scission. In order to overcome the influence of thermal vibration, an approach that employs deformation tests at absolute zero temperature condition - a concept borrowed from the quasi-continuum method, is developed. Bond dissociation energy is measured to quantify the extent of failure in the system by calculating the bond potentials during the deformation tests. Applying zero temperature condition to the deformation test, however, requires a large amount of computational time due to intermediate energy minimization processes. To improve the computational efficiency, an ultra-high strain rate (UHSR ≈ 10¹³ s^-1) approach is developed by which the thermal vibration is decoupled from the deformation test using a strain rate higher than molecular vibration frequency. Note that the deformation test performed by traditional MD simulation methods used strain rates ranging 10⁸-10¹⁰ s^-1. Simulation results show that the UHSR approach successfully captures brittle fracture in epoxy polymer due to covalent bond dissociation with high computational efficiency.

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In this paper a multiscale-modeling framework is presented wherein fundamental damage information at the atomic level is coupled with a sectional micromechanics model for the nonlinear and damage analysis of carbon fiber reinforced polymer (CFRP) composites. Damage information in the polymer matrix originating from the atomic scale, as investigated using molecular dynamics (MD) simulations, is transferred to the continuum length scale using a continuum damage mechanics approach with a physical damage evolution equation. Such a framework is shown to be computationally efficient for the linear and damage analysis of CFRP composites and reasonably accurate when compared to experimental data and verified models in literature. Furthermore, material uncertainty, such as curing degree variation in polymers, can be computationally calculated leading to a computational stochastic analysis of the CFRP composites. Thus, such a framework can be used to investigate the damage mechanics of ply level CFRP components at the nano, micro and macro length scales.@en

A comprehensive, point-information-to-continuum-level analysis framework is presented in this paper to accurately characterize the behavior of CNT-enhanced composite materials. Molecular dynamics (MD) simulations are performed to study atomistic interactions of the CNT with the polymeric phase. The effect of cross-linking between the epoxy resin and the hardener on the mechanical properties of the polymer is investigated; furthermore, the effect of CNT weight fraction on the most likely polymer cross-linking degree is also studied through stochastic models. The stochastic distributions obtained from MD simulations provide a basis to simulate local variations in the matrix properties at the fiber-centered continuum model at the microscale. The interfaces at nanoscale (CNT and matrix) and microscale (fiber and CNT-dispersed matrix) are characterized by performing CNT pullout simulations, and a single fiber pullout simulation, respectively.@en

A multiscale methodology that accurately simulates the inelastic behavior of epoxy polymers initiating at the molecular level due to bond elongation and subsequent bond dissociation is presented in this paper. The system investigated in this study comprises a combination of crystalline carbon nanotubes (CNTs) dispersed in amorphous epoxy polymer molecules. Molecular dynamics (MD) simulations are performed with an appropriate bond order based force field to capture deformation-induced bond dissociation between atoms within the simulation volume. In order to overcome the influence of thermal vibrations of bonds on bond dissociation energy (BDE), a quasi-continuum (QC) approach, excluding the effects of temperature, is explored. Results indicate that a QC approach can simulate bond breakage leading to brittle behavior in amorphous epoxy polymer. The novel combination of MD deformation tests with high strain rates at near-zero temperatures, however, is seen to provide a more computationally efficient alternative for the study of bond dissociation phenomenon in amorphous epoxy polymer. The corresponding BDE extracted from the simulation volume is used as input to the continuum damage mechanics (CDM) model to study matrix failure at the microscale. The material parameters for the CDM model are directly obtained from physics-based atomistic simulations, thus, significantly reducing the propagation of errors in the multiscale framework.@en

This paper presents the development of a novel methodology for modeling the interphase between carbon fiber and polymer matrix using atomistic scale simulations. The model is integrated within a multiscale framework for the analysis of polymer matrix composites. The interphase region that exists between carbon fiber and polymer matrix plays an important role in damage initiation and it is critical for modeling damage propagation across length scales. The developed interphase model in this work consists of multiple pseudo-damaged graphene layers, and is capable of capturing the physical entanglement between the polymer matrix and the carbon fiber through the use of molecular dynamics simulations. The pseudo-damage model simulates voids in the graphene layer by removing carbon atoms, while multiple pseudo-damaged graphene layers represent the amorphous structure of the carbon fiber surface. In order to accurately model the chemical structure of the polymer, a numerical curing process is employed that captures the stochastic interactions between resin and hardener molecules for crosslinking (carbon-nitrogen covalent bond generation). The molecular dynamics model also enables extraction of the material properties of the interphase at the nanoscale which is then integrated within a high fidelity generalized method of cells micromechanics theory. A modified Bodner-Partom viscoplastic theory is applied to the polymer matrix subcells. Additionally, progressive damage and failure theories are used at different scales in the modeling framework to accurately capture scale-dependent failure of the composite material. Comparative studies are performed by applying different interphase properties that are obtained from the literature to the interphase subcells. The results indicate that the responses for each type of interphase model are similar, but the transverse tensile strength, obtained using the MD simulated interphase properties, is approximately 7% lower than the other interphase types and also has a maximum difference of 10% in failure strain.@en

A comprehensive, point-information-to-continuum-level analysis framework is presented in this paper to accurately characterize the behavior of carbon nanotube (CNT)-enhanced composite materials. Molecular dynamics (MD) simulations are performed to study sub-nanoscale interactions of the CNT with the polymeric phase of the nanocomposite. The effect of cross-linking between the epoxy resin and the hardener on the mechanical properties of the polymer is investigated; furthermore, the effect of CNT weight fraction on the probability distribution of polymer cross-linking degree is also studied through stochastic models. The stochastic distributions obtained from MD simulations provide a basis to simulate local variations in the matrix properties in the continuum model at the microscale. The inclusion of an atomistically informed elastic-plastic model at the microscale reveals a significant deviation of the mechanical properties from those obtained based on classical homogenization approaches. Microstructural variability arising from heterogeneous cross-linking degree in the polymer phase and variations in fiber geometry and spacing is also found to cause deviations in the mechanical response when compared to the assumption of a perfectly ordered fiber-matrix microstructure.

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This paper presents a multiscale approach for capturing the mechanical response of smart polymer materials. A spring-bead model is developed at the microscale based on results from molecular dynamics simulation to represent a bond cluster of polymer. Through parametric studies and mechanical equivalence optimization, a statistical network model is developed to represent the microstructure of the materials at the mesoscale. The introduction of the spring-bead based network model bridges the high accuracy molecular dynamics model at the microscale and the computationally efficient finite element model at the macroscale. A comparison between experimental and simulation results shows that the multiscale model is capable of capturing global mechanical response and local material properties.@en