Micromechanics-based Model Research Articles

Micromechanics-based binary-medium constitutive model for frozen soil considering the influence of coarse-grained contents and freeze–thaw cycles

Micromechanics-based binary-medium constitutive model for frozen soil considering the influence of coarse-grained contents and freeze–thaw cycles

Micromechanics-based model of single crack propagation in Engineered cementitious composites (ECC)

Engineered Cementitious Composites (ECC) are composites exhibiting strain-hardening behavior accompanied by the formation of multiple cracks. A special feature of ECC is the ability to tune the material composition to meet the different needs of various structural components, which benefits from the special micromechanics-based design theory of ECC. However, these existing micromechanics-based design theories are specific to the case of direct tension and has not been fully discussed and developed for the case where the ECC is subjected to bending load. In this study, a micromechanics-based crack propagation model for ECC under bending load is developed to guide the design of flexural performance of ECC. The entire crack propagation process is simulated by considering the microstructure of ECC and the crack propagation criterion. For ECCs with different types of fiber, the simulated load-crack mouth opening displacement curves agree well with experimental results and the dispersion of the ECC specimens can be captured by imparting randomness to the model. Based on this model, parametric studies of several representative parameters are performed to illustrate the applicability of the model. The results indicate that the material has a higher ultimate flexural bearing capacity near a fiber aspect ratio of 448 for the given material property parameters; and the fiber/matrix bonding should not be excessively strong. Insights from this model can facilitate the design of ECC members with excellent bending properties through fiber tailoring and surface treatment.

Effect of partial asymmetric friction on sliding over fractures

Asymmetric friction refers to different friction forces resisting sliding in opposite directions. This property is found to arise from material anisotropy that can form coupling between normal and shear stress. It is plausible that such material anisotropy can emerge as a result of fractures of asperities or micro-cracks that precedes shear fractures. This study considers a model with multiple blocks where some blocks have asymmetric friction, while others have conventional symmetric friction. This assembly is driven by an external surface that connects to each block through leaf springs in the spirit of the Burrige-Knoppof model. The driving force is considered to undergo harmonic oscillations. It is found that asymmetric friction can induce intermittent regions of tension and compression that can form fractures normal (tension) or parallel (compression) to the sliding surface. Asymmetric friction produces velocity spectra with a frequency falloff of 1/f2, where f is the frequency; these are observed in sliding over shear fracture produced by strain localisation in compression. Opposite to this, symmetric friction leads to the falloff of 1/f observed in sliding over pre-existing fractures or faults. This distinguishes sliding over pre-existing faults from sliding over fractures formed in compression. This model can shed light on the mechanisms of fault sliding and production of geological fractures observed near the faults, as well as to complement the micromechanics-based asperity models in the emerging fields such as surface morphing.

A review on micromechanical modelling of progressive failure in unidirectional fibre-reinforced composites

The recent decades have seen various attempts at the numerical modelling of fibre-reinforced polymer (FRP) composites in the aerospace, auto and marine sectors due to their excellent mechanical properties. However, it is still challenging to accurately predict the failure of the composites because of their anisotropic and inhomogeneous characteristics, multiple failure modes and their interaction, especially under multiaxial loading conditions. Micromechanics-based numerical models, such as representative volume elements (RVEs), were developed to understand the progressive failure mechanisms of composites, and assessing existing failure criteria. To this aim, this review paper summarises the development of micromechanics-based RVE modelling of unidirectional (UD) FRP composites reported in the literature, with a focus on those models developed using finite element (FE) and discrete element (DE) methods. The generation of fibre spatial distribution, constitutive models of material constituents as well as periodic boundary conditions are briefly introduced. The progressive failure mechanisms of UD FRP composites simulated by RVEs under various loadings are discussed and the comparison of failure envelopes predicted by numerical results and classical failure criteria are reviewed.

Crack path predictions in heterogeneous media by machine learning

The interaction between stress fields at the crack-tip and nearby microstructural heterogeneities influences the crack path, and in turn, the effective fracture toughness of a material. In this paper, we assess the ability of artificial neural networks (ANNs) for machine learning to predict the crack paths from given initial void defect distributions in the material, and to provide insights into the underlying crack growth mechanics. Our ANN accurately captures the process zone size, crack growth sequence, and resulting crack patterns in the simplistic case where the proximity of voids to the crack-tip forms the criterion for crack advance. In a ductile medium, pre-existing voids grow with deformation and link up with the primary crack either contiguously or through the formation of multiple unconnected damage zones. The complex crack patterns for both these ductile fracture processes are successfully captured by an ANN, trained on the cracking sequences in a micromechanics-based ductile fracture model containing two size-scales of voids. In addition, the ANN architecture is capable of predicting stochastic crack growth, by providing a multiplicity of possible crack paths, along with a quantified likelihood of each path. Results further demonstrate the utility of autonomous crack path predictions in enabling fracture-by-design.

An efficient micromechanics-based finite element model for failure analysis of laminated composites

Accurately predicting ultimate strength of composite laminate is still a great challenge, especially only based on the constituent properties. In this paper, the micromechanics Bridging Model and systematic failure criteria for the constituent materials with emphasis on matrix failures subjected to three dimensional (3D) loads are compiled into a UMAT subroutine for ABAQUS to analyze failures of a laminated composite structure. The main purpose of this research is to greatly reduce calculation costs for loading conditions of in-plane tension or compression by introducing a simplified 3D finite element model based on the Pipes-Pagano theory. In all calculation cases, only the constituent properties together with the transverse tensile strength of unidirectional composite are needed as input data. Later in this paper, sufficient illustrations of 81 different composite laminates composed of 14 material systems are analyzed to confirm the practicability of this model.

Interplay of manufacturing-induced thermal residual stresses and microvoids in damage and failure of fiber-reinforced composites

Fiber-reinforced composites have inherent thermal residual stresses (TRS) and microvoids that are both generated during the manufacturing process. While the two factors are naturally included in experimental measurements as they preexist in the specimens for testing, theoretical and computational modeling of composites usually neglect these two or include only one. Such simplifications inevitably introduce errors to the predicted mechanical properties of composites, which may further influence the reliability of subsequent modeling and design efforts. Using a micromechanics-based failure modeling approach, this work investigates the effects of both TRS and microvoids on the mechanical properties of fiber-reinforced composites. The TRS is generated when composites are cooled down from the curing temperature. The microvoids are assumed to take realistically existing circular, triangular, square, and pentagonal shapes. Damage progression is systematically studied in six representative loading modes, five voids, and two TRS conditions. All results are statistically extracted to account for geometric uncertainties. The study unravels the interplay of TRS and microvoids in determining the mechanical properties of composites along with the corresponding failure mechanisms. This investigation provides high-fidelity predictions and theoretical insights to improve our understanding of TRS and microvoids in composites, mitigate their impacts, and guide future modeling and design efforts.

Experimental Investigation and Micromechanics-Based Analytical Modeling of Creep and Relaxation Behaviors of Beishan Granite

This paper investigates experimentally and numerically the short- and long-term strength and deformation behaviors of Beishan granite at room temperature. Single-stage creep, relaxation, and conventional triaxial compression tests were performed on cylindrical rock samples. Its typical brittle response is captured and the dependence of peak strength on confining pressure and time-dependent response on deviatoric stress are revealed. For constitutive modeling, a unified micromechanics-based plasticity-damage model is formulated based on the Mori–Tanaka method and the subcritical cracking theory postulate, with the focus on simulating both instantaneous strain and time-dependent deformation process over a broad range of time scales. Its unification is achieved by representing the evolution of damage, which is strongly coupled with plastic deformation induced by frictional sliding along closed cracks, as an internal variable that can be decomposed into instantaneous and time-dependent parts. The performance of the model with analytical predictions is well validated using the experimental results on Beishan granite.

Multi-level micromechanics-based homogenization for the prediction of damage behavior of multiscale fiber-reinforced composites

A multi-level micromechanics-based homogenization is proposed here to investigate the damage behavior of composites with multiscale fibers such as carbon nanotube (CNT) and carbon fiber. First, a molecular unit cell is constructed considering the interfacial characteristics between the CNT and a polymer matrix, after which molecular dynamics simulation and micromechanics are utilized to obtain the elastic properties of CNT-reinforced composites. A micromechanics-based progressive damage model is then adopted to predict the damage behavior of the CNT and carbon fiber-reinforced composites. Tensile tests are also conducted to investigate the stress–strain behaviors of the composites. To verify the applicability of the proposed model, the present predictions are compared with those obtained from the tensile test results. The proposed multi-level homogenization has shown to provide a close match to the experimental results. The proposed modeling scheme may facilitate a thorough investigation of the damage behavior of multiscale fiber-reinforced composites, proving the importance of each constituent at a different level.

Ductile fracture of high entropy alloys: From the design of an experimental campaign to the development of a micromechanics-based modeling framework

Cantor-type high entropy alloys form a new family of metallic alloys characterized by a combination of high strength and high fracture toughness. An experimental study on the CoCrNi alloy is first performed to determine the damage and fracture mechanisms under various stress states. A micromechanics-based ductile fracture model is identified and validated using these experimental data. The model corresponds to a hyperelastic finite strain multi-yield surface constitutive description coupled with multiple nonlocal variables. The yield surfaces consist of three distinct nonlocal solutions corresponding to three different modes of void expansion within an elastoplastic matrix: a void growth mode governed by a Gurson-based yield surface corrected for shear effects, an internal necking-driven coalescence mode governed by an extension of the Thomason yield surface based on the maximum principal stress, and a shear-driven coalescence mode governed by the maximum shear stress. This advanced formulation embedded in a large strain finite element setup captures the effects not only of the stress triaxiality but also of the Lode variable. In particular, the analysis shows that a failure model accounting for these two invariants of the stress tensor captures the fracture in high-entropy alloys over a wide range of conditions.

Micromechanical modeling of the viscoelastic–viscoplastic response of fiber-reinforced composites

This paper describes a newly proposed viscoelastic–viscoplastic constitutive model that is used to characterize the effective mechanical behaviors of fiber-reinforced composites based on micromechanical modeling. A homogenization approach is developed in which the effective stress of the fiber-reinforced composite is decomposed into an elastoplastic component and a viscous component. For the elastoplastic component, a bridge model is adopted to characterize the effective elastoplastic behaviors, while for the viscous component, homogenization theory applied to the time domain is utilized to describe the effective viscous responses. The overall stress for the composite can be obtained by superposing the stress contributions of the two components. The proposed micromechanics-based constitutive model has an explicit form, which contributes to the computational efficiency of the multiscale simulations for the composite structures. Unit cubes with 128 randomly distributed cylindrical fibers of equal size are created as the representative volume element models for numerical validation of the proposed constitutive model. The effects of fiber volume fraction, hardening law, loading condition, and strain rate are considered to comprehensively validate the constitutive model. Experimental results for IM7/8552 carbon fiber–reinforced composite were employed to validate the constitutive model. By comparing the model predictions to the experimental results and numerical observations, the constitutive model was found to provide acceptably good predictions of the viscoelastic–viscoplastic behaviors of the fiber-reinforced composites.

A micromechanics-based machine learning model for evaluating the microstructure-dependent rolling contact fatigue performance of a martensitic steel

We designed the prediction system for the rolling contact fatigue (RCF) performance of martensitic steel based on the machine learning (ML) algorithm and micro-mechanical simulations. The emphasis here is not only to propose a low-cost micromechanics-based ML prediction system, but also to establish the linkage between microstructure features and RCF responses. In this prediction system, the hierarchical microstructure modeling approach and size-dependent physics-based crystal plasticity (CP) framework were developed to capture the micromechanical response of the martensitic steel in RCF. The hierarchical microstructure geometry, crystallographic orientation, and the corresponding fatigue indicator parameter (FIP) obtained from CP simulations were selected for database construction. The data filtering method was adopted by considering the loading history of RCF. The random forest (RF) algorithm was trained using the CP simulations to link the microstructure features to RCF performance. After that, the confidence and limitation of the prediction system were explained and analyzed in detail. It is demonstrated that the prediction system is capable of precisely predicting the RCF performance and its relation to microstructure features in a physically sound way. Results give data-driven insights into the microstructure design for the desired mechanical and RCF performance of martensitic steel.

A micromechanics-based model for concrete-rock interface with similar triangular asperities

Direct shear tests on samples containing similar triangular asperities have been carried out under constant normal stiffness (CNS) conditions, and observations demonstrated that there exists local lift-off of shallower asperities across the interface, resulting in a redistribution of local stresses and further impacting the global shear behavior . This study further modifies the existing theoretical model based on multiple-asperity configurations, previously presented by the authors. The proposed method relates the normal and shear stresses on the individual asperity to interface strength and corresponding displacement in terms of the asperity inclination and contact areas. The emphasis is on quantifying the number of shallower asperities that would be lifted off when the closely contacted asperities are dislocated by an amount of interface dilation. In addition to the mechanism of local lift-off itself, the resultant redistribution of global shear stress on remaining asperities can be also taken into account. The proposed model is verified by predicting experimental observations published elsewhere, and the comparison appears to be satisfactory.

Comparison of Models to Predict Mechanical Properties of FR-AM Composites and a Fractographical Study

Continuous fiber-reinforced additive manufacturing (cFRAM) composites improve the mechanical properties of polymer components. Given the recent interest in their mechanical performance and failure mechanisms, this work aims to describe the principal failure mechanisms and compare the prediction capabilities for the mechanical properties, stiffness constants, and strength of cFRAM using two distinct predictive models. This work presents experimental tensile tests of continuous carbon fiber AM composites varying their reinforced fraction, printing direction, and fiber angle. In the first predictive model, a micromechanical-based model for stiffness and strength predicts their macroscopic response. In the second part, data-driven models using different machine learning algorithms for regression are trained to predict stiffness and strength based on critical parameters. Both models are assessed regarding their accuracy, ease of implementation, and generalization capabilities. Moreover, microstructural images are used for a qualitative evaluation of the parameters and their influence on the macroscopic response and failure surface topology. Finally, we conclude that although predicting the mechanical properties of cFRAM is a complex task, it can be carried on a Gaussian process regression and a micromechanical model, with good accuracy generalized onto different process parameters specimens.

Investigation of the Mechanical Properties for Polymer Reinforced by Nanoparticles with Considering Viscoelasticity of the Matrix

Investigation of the Mechanical Properties for Polymer Reinforced by Nanoparticles with Considering Viscoelasticity of the Matrix

Study on dispersion and wave velocity in 2D elliptic granular crystals by a micromechanics-based micromorphic model

This study considers two-dimensional elliptic granular crystals respectively with different aspect ratios. Using a micromechanics-based micromorphic model, macroscopic micromorphic constitutive modulus tensors of elliptic granular crystals are obtained. Two modes of Taylor expansion of relative displacements are used to establish contact relation between particles. This study obtains micromorphic transverse-rotational and longitudinal waves. Obvious dispersions of micromorphic waves are given in 2D elliptic granular crystals. With increase of aspect ratio, width of frequency band gap increases when wave propagates along [Formula: see text] direction but decreases when wave propagates along [Formula: see text] direction. Two modes of Taylor expansion of relative displacements only have influence on dispersions and frequency band gap of transverse-rotational waves. Velocities of longitudinal and transverse-rotational waves first decrease to zero, keep zero for a range of frequency and then increase to a larger wave velocity with increase of frequency for different aspect ratios. The situation with a larger aspect ratio leads to larger transverse-rotational and longitudinal velocities, and ratio between transverse-rotational and longitudinal velocities decreases from 0.7 to 0.59, when wave propagates along [Formula: see text] direction. However, it leads to smaller transverse-rotational and longitudinal velocities, and ratio between two velocities decreases from 0.88 to 0.56, when wave propagates along [Formula: see text] direction.

A micromechanics-based damage constitutive model considering microstructure for aluminum alloys

Aluminum alloys undergoing deformation exhibit complex multi-type-void damage evolution driven by microscale heterogeneous deformation; in return, the accumulated damage evolution would affect the microscale heterogeneous deformation. Meanwhile, the above interaction depends significantly on the microstructure characteristics and determines the macroscale flow and ductile fracture behaviors. These make it difficult to model the deformation response and ductile fracture of aluminum alloys with various microstructures. Aiming at this issue, a micromechanics-based damage constitutive model considering the mutual effects between microstructure, micro/macro-scale deformation, and damage and fracture was developed in this study for deformation of aluminum alloys under tension-dominated loading conditions. During the modeling, the damage was characterized in terms of the evolutions of coexisting multi-type voids. The multiple-type voids were modeled separately as functions of the local micro-strain/stress of their respective phases and microstructure characteristics according to the micromechanical mechanisms. Furthermore, a self-consistent method was employed to calculate the heterogeneous micro-strain/stress of phases and the overall macroscale flow behavior of the multiphase aggregate. In particular, the constitutive behavior of each phase in the self-consistent method was modeled by coupling the softening effect of void evolution and microstructure characteristics, thus the interaction between microscale heterogeneous deformation and damage evolution was captured. The model parameters were determined by matching the calculated and experimental evolutions of the multi-type voids measured via in-situ synchrotron radiation X-ray computed tomography and load-displacement curves during deformation. Applied to the 2219 aluminum alloy, this model accurately predicts the flow stress, damage evolution and fracture behavior under various microstructures and those of tailor-welded blanks with a gradient microstructure. Furthermore, the model clarifies the mutual effects between the microstructure, damage evolution and deformation behavior of aluminum alloys. The developed model can also be generalized to other multiphase metals containing a distribution of hard-brittle particles. And it is thus believed to be with a well general prediction for the deformation response and ductile fracture of this kind of multiphase metals with various microstructures or gradient microstructures, and further facilitates the understanding of their complex damage evolution and flow behavior.

Micromechanics-Based Low Cycle Fatigue Life Prediction Model of ECAPed Aluminum Alloy

Ultrafine-grained aluminum alloys (UFG AA) show great potential in the design of fatigue-resistant lightweight alloys, and the methodology to assess low-cycle fatigue (LCF) life remains to be studied. In this work, a micromechanics-based LCF life prediction model is presented by conducting crystal plasticity finite element simulation (CPFEM). The fatigue indicator parameter (FIP) of maximum accumulated equivalent plastic strain energy, modulated by triaxiality, is developed to assess the material damage in the microstructure. Particularly, a new multiaxial strain parameter is proposed by considering the combined influence of the mean strain and non-proportional cyclic additional hardening effect, and then directly embedding into the cyclic J-integral. Finally, the reformulated Manson-Coffin relationship is theoretically constructed by correlating the crack tip opening displacement to the crack propagation equation. The results show the scatter fatigue life of UFG AA6061 is not only related to the inhomogeneous evolution of plastic deformation but also to the local stress state. Since the proposed approach considers both the deformation mechanisms at the micro-scale and the corresponding macroscopic responses, it can predict the LCF life of UFG AA with reasonable accuracy.

Experimental investigation and micromechanics-based damage modeling of the stress relaxation mechanical properties in gray sandstone

The geomechanical behaviors of the gray sandstones under dry and fully saturated conditions are investigated by both of experimental and numerical studies in this paper. Conventional triaxial compression tests and single-stage stress relaxation tests are performed on cylindrical specimens under these two different states. The experimental results show that both peak strength and elastic modulus are reduced due to the presentence of the pore water which is contributed the weakening. While the typical incomplete attenuation characteristics of the two states are only having slight difference, the final stress relaxation extent under the statured condition is larger than the dry condition when the strain ratio is the same. Based on the pioneering work, a new micromechanical damage–friction coupling constitutive model with containing fewer parameters and each being physically meaningful for the stress relaxation is proposed here. Its chief novelty lies in considering both the instantaneous plastic internal variables and relaxation load to build the relationship between model’s parameter and experimental data. The single-stage relaxation tests of the sandstones are well-benchmarked with this model, which indicates that the proposed new model can capture the incomplete attenuation features of stress relaxation behavior of gray sandstones.

Micromechanics-based phase field fracture modelling of CNT composites

We present a novel micromechanics-based phase field approach to model crack initiation and propagation in carbon nanotube (CNT) based composites. The constitutive mechanical and fracture properties of the nanocomposites are first estimated by a mean-field homogenisation approach. Inhomogeneous dispersion of CNTs is accounted for by means of equivalent inclusions representing agglomerated CNTs. Detailed parametric analyses are presented to assess the effect of the main micromechanical properties upon the fracture behaviour of CNT-based composites. The second step of the proposed approach incorporates the previously estimated constitutive properties into a phase field fracture model to simulate crack initiation and growth in CNT-based composites. The modelling capabilities of the framework presented is demonstrated through three paradigmatic case studies involving mode I and mixed mode fracture conditions.