Multiscale Damage Model Research Articles

Multiscale damage analysis based on the variational effective model

AbstractIn the damage analysis of material with complex microstructures, a full‐scale direct numerical simulation (DNS) could produce huge computational costs. Alternatively, multiscale modeling is a more effective method by using less degrees of freedom to balance the calculation accuracy and cost. In this paper, a new multiscale damage modeling method is proposed based on the framework of the variational effective model originally presented by Jezdan et al. and the relaxation damage model presented by Junker et al. A variational statement for the free energy and the dissipation potential for a coarse scale model is constructed by relating the free energy and dissipation potential of the fine scale model. In this way, the coarse scale damage variable is defined instead of directly solving in the fine scale model; therefore, the computational efficiency can be increased. Besides, the relaxation damage model can effectively avoid ill‐posed boundary value problems in damage analysis without use of gradients or integration techniques. Two numerical examples are provided to demonstrate the effectiveness of the proposed method.

A Lennard-Jones potential based cohesive zone model and its application in multiscale damage simulation of graphene reinforced nanocomposites

A new mixed-mode cohesive zone model based on Lennard-Jones potential (LJCZM) is proposed to simulate the interface failure between graphene and epoxy matrix. The values of model parameters are obtained from a large number of molecular dynamics simulations, and a UMAT subroutine is programmed and validated to introduce this model into the ABAQUS platform. This process spans from the nanoscale to the microscale, which provides a new routine for the multiscale damage modeling of the graphene reinforced epoxy nanocomposite at microscale. In addition, the continuous damage phase-field model is used to simulate the matrix damage, and the values of model parameters are determined from the molecular dynamic simulations of the bulk epoxy at nanoscale. At last, the effects of parameters such as volume fraction, aspect ratio, orientation, and curvature of graphene nanoplatelets are investigated. The results indicate that the nanocomposite reinforced with high content and large aspect ratio graphene nanoplatelets presents the lower ultimate stress and fracture strain. In addition, the orientation and waviness of the graphene also significantly affect the mechanical properties of the nanocomposites. The nanocomposite reinforced with graphene platelets with greater waviness has higher stiffness and strength but lower toughness. The rationality and effectiveness of the model are verified through comparison with other existing results.

Multiscale modeling of diffuse damage and localized cracking in quasi-brittle materials under compression with a quadratic friction law

The diffuse damage and localized cracking of quasi-brittle materials (i.e., rocks and concretes) under compression can be delineated by a matrix-microcrack system, wherein a solid matrix phase is weakened by a large number of randomly oriented and distributed microcracks, and the macroscopic cracking is formed by a progressive evolution of microcracks. Several homogenization-based multiscale models have been proposed to describe this matrix-microcrack system, but most of them are based on a linear friction law on the microcrack surface, rendering a linear strength criterion. In this paper, we propose a new quadratic friction law within the local multiscale friction-damage (LMFD) model to capture the plastic distortion due to frictional sliding along the rough microcrack surface. Following that, a macroscopic Ottosen-type nonlinear strength criterion is rationally derived with up-scaling friction-damage coupling analysis. An enhanced semi-implicit return mapping (ESRM) algorithm with a substepping scheme is then developed to integrate the complex nonlinear constitutive model. The performance of LMFD model is evaluated compared to a wide range of experimental data on plain concretes, and the robustness of ESRM algorithm is assessed through a series of numerical tests. Subsequently, to effectively describe the localized cracking process, a regularization scheme is proposed by combining the phase-field model with the established LMFD model, and the discretization independent crack localization is numerically verified.

Computational analysis of the failure mechanisms of a laminated composite in double-edge notch compression configuration

This manuscript presents a combined experimental–computational investigation of the compression failure response of laminated composites in double-edge notch compression (DENC) configuration. Analysis of in-situ and post-test DENC experiment results indicates the presence of multiple failure mechanisms, including ply splitting, delamination, and compression kink bands. In order to characterize the onset, growth, and interplay of the critical and subcritical damage mechanisms, a multiscale progressive damage analysis approach is implemented. A nonlocal multiscale damage model explicitly tracks the intraply failure mechanisms that lead to the formation and propagation of kink bands in the specimen. A cohesive zone model is used to track initiation and progression of ply splitting in the specimen. The splitting model was implemented using implicit finite element simulations and deployed with a pre-crack insertion technique to reduce simulation time while preserving prediction accuracy. Model parameters are calibrated based on available calibration data and measurements. The effects of split location and growth characteristics on model predictions are studied. The computational model along with a suite of experiments were employed to study the formation, growth and interactions of damage mechanisms in the composite specimens subjected to compression loading. The onset of matrix damage is not clear from the experimental images but the model predicts early onset around the onset time of splits which greatly reduce the stress concentration at the notches. Analysis of acoustic emission energy experimental data indicate that observable compression failure mechanisms are not causing nonlinearity consistently exhibited in the experiment responses. Simulation results demonstrate the capability of the multiscale modeling approach to predict critical kink bands and sub-critical matrix cracking and splitting in the DENC specimens while reducing computational cost compared to a direct numerical simulation of fibers and matrix.

A novel multiscale prediction strategy for simulating the progressive damage behavior of plain-woven bamboo fabrics reinforced epoxy resin composites

This study proposed a novel multiscale prediction strategy, including mesoscale and macroscale damage evolution modeling, to investigate the effective properties and progressive damage failure behavior of plain-woven reinforced composites (PWRCs) under various external loads (tension, compression). A high-precision mesoscale representative volume element (RVE) that could accurately describe the local mechanical behavior of PWRCs was developed by combining experimental characterization (scanning electron microscope and X-ray computed tomography) and numerical simulation. To solve the problem of inaccurate prediction results caused by multiscale characteristics and complex stress changes in the damaged area of PWRCs, the strain-based 3D Hashin failure criterion and the multiscale damage models were used to predict the damage initiation and evolution of mesoscale reinforcement (bamboo fiber yarn bundle) and macroscale composites, respectively. Considering the damage evolution law of isotropic materials, a damage model based on the Von Mises criterion was used to characterize the damage initiation and evolution of mesoscale matrix epoxy resin (EP) under external loading. The effective properties and mechanical behavior of the PWRCs were transferred from mesoscale to macroscale through the progressive homogenization method. The bilinear constitutive relationship of the mixed-mode cohesive element was used to characterize the interlaminar failure of the PWRCs. Finally, the corresponding mechanical characterization (tension, compression) of the PWRCs was carried out. Moreover, the experimental results were highly consistent with the simulation results, verifying the reliability of the novel multiscale prediction strategy in investigating the mechanical response of the PWRCs at multiple scales and revealing the damage mechanism of the PWRCs.

Data-driven physics-constrained recurrent neural networks for multiscale damage modeling of metallic alloys with process-induced porosity

Data-driven physics-constrained recurrent neural networks for multiscale damage modeling of metallic alloys with process-induced porosity

Different effects of interfacial properties on the tensile and compressive damage mechanisms of 3D woven composites: Multiscale damage model and numerical comparative study

A multiscale damage model is proposed based on a micro-mesoscale bridging model and a multiscale kinking model, which can predict the damage development processes of 3D woven composites (3DWCs) under different loading conditions using only few material parameters. At the microscale, the various mesoscopic damage modes of yarns, including tensile fiber breakage, compressive fiber kinking and transverse inter-fiber crack, can be simply divided into matrix- and fiber-dominated damage. Using this multiscale damage model, a numerical comparative study is conducted to investigate the effect of interfacial properties on the mechanical performances and damage mechanism of 3DWCs. The numerical results indicate that the interfacial properties exhibit different effects on the tensile and compressive strengths and damage mechanisms of 3DWCs. The interaction of different damage modes controls the overall trend of the tensile strength of 3DWCs. There is an optimum point for the tensile strength of 3DWCs at different interfacial fracture toughness. Beyond the optimum point, the tensile strength of 3DWCs is negatively correlated with interfacial properties. Unlike the tensile loading case, the better the interfacial properties, the later fiber kinking occurs, resulting in higher compressive strength of 3DWCs.

Simulation of the dynamic cracking of brittle materials using a nonlocal damage model with an effective strain rate effect

In this study, a nonlocal multiscale damage model that considers the effect of a strain rate is presented. Moreover, this model is combined with the scaled boundary finite element method (SBFEM) and quadtree mesh for dynamic crack propagation in quasi-brittle materials. The scaling centre of each SBFEM subdomain was selected as the material point, and the bond connecting two material points was referred to as the material bond. Microscopic damage was quantified based on the stretch rate of the material bond, and macroscale topological damage was calculated by taking the weighted average of the microscopic damage over the bonds within the influence domain. The bell distribution function is utilised as the weight function in the calculation of the nonlocal weight function. To account for the impact of the strain rate during dynamic loading, an effective rate R is introduced to enhance multiscale damage by modifying the damage threshold and bond softening coefficient throughout the analysis process. By analysing the energetic degradation function of the phase field, which establishes a connection between the macroscale topological damage and energy-based damage, a nonlocal multiscale damage model was incorporated into the framework of the SBFEM. Quadtree mesh discretization was employed to achieve rapid and high-quality multilevel mesh generation by effectively utilising the hanging nodes. Three typical dynamic cracking examples were simulated using the proposed model, and the results were compared with the relevant experimental results and references. The results show that the method is suitable for accurate dynamic cracking simulation in quasi-brittle materials. Moreover, the results indicate that the proposed method can spontaneously simulate dynamic crack bifurcation without introducing additional crack bifurcation criteria. For a compact tensile test of concrete under different loading rates, the method proposed in this study can accurately simulate the corresponding failure modes. The results also show that without considering the effect of the strain rate, the damage develops rapidly in an unconstrained state, which is inconsistent with the actual case.

Investigation on the off-axis tensile failure behaviors of 3D woven composites through a coupled numerical-experimental approach

Computational models with high precision and efficiency are in urgent need for the damage analyses of 3D angle-interlock woven composites which are widely accepted in composites industry. A novel concurrent multi-scale damage evolution modeling scheme is established based on a meso-scale representative volume cell (RVC) model and the multiphase finite element method to characterize the off-axis tensile response of carbon/epoxy composites. Modified Puck criterion and maximum shear stress criterion are adopted for fiber yarns. Parabolic yield criterion is adopted for the matrix. The fiber breakage, the inter-fiber fracture and matrix cracking are considered at mesoscopic level. To validate the proposed multi-scale damage model, off-axis tensile test is conducted with the help of 3D Digital Image Correlation (DIC) method. A reasonably good agreement is achieved between numerical predictions and experimental observations. Furthermore, the validated damage model is used to predict the tensile response of the composites considering full range on-axis and off-axis angles.

Multi-scale damage modeling and out-of-plane shear behavior of carbon/carbon honeycomb structure

In response to the demand for the ultra-high stability and light-weight optical structure in high-resolution spacecraft, the present study proposes a novel carbon/carbon (C/C) honeycomb structure which integrates the superiorities of C/C composite and honeycomb structure. The C/C honeycomb was fabricated by chemical vapor infiltration (CVI) processing with continuous carbon fiber preform, and then the L- and W-direction shear experiments were conducted. A multi-scale damage model is established to describe the mechanical and damage behavior of the C/C honeycomb, which includes the damage model and constitutive model in both meso-scale and macro-scale. The effects of yarn orientation, side length, wall thickness and height of C/C honeycomb on L- and W-direction shear characteristics as well as damage modes of the novel C/C honeycomb are comprehensively researched. The results show that the C/C honeycomb has excellent shear properties when the yarn orientation is ±45° as well as the side length and wall thickness are about l=6mm and t=0.3mm, respectively. With the yarn orientation shifts from 0°/90° to ±45°, the damage region transforms from top and bottom surfaces of the C/C honeycomb structure to honeycomb walls. As the side length increases and the wall thickness decreases, the damage region is distributed obliquely along the honeycomb wall. This research contributes to the design and optimization of optical-mechanical structures in high-resolution spacecraft.

An anisotropic nonlinear multiscale damage model for mechanical behavior of a composite laminate with matrix cracks

An anisotropic nonlinear multiscale damage model for mechanical behavior of a composite laminate with matrix cracks

Multiscale modeling of particle-induced damage in AA7075 aluminum sheet at large plastic strains

Large plastic deformation and ductile damage in precipitation hardening aluminum alloy AA7075 is driven by plastic flow in the vicinity of particles as well as fracture and decohesion of second phase particles embedded in the matrix. The current work investigates the deformation and damage characteristics of Fe-rich intermetallic particles, and η and θ precipitates in AA7075-O sheet. A multiscale model simulation methodology is presented and applied to analyze large-scale plastic deformation and damage characteristics. The methodology utilizes nanoscale molecular dynamics simulation to obtain matrix-particle interface strength properties and Weibull statistics to capture experimental fracture characteristics of particles. The above sub-models are incorporated within a 2-D real particle microstructure-based finite element model to conduct a comparative study of the roles of decohesion and fracture in the development of plasticity and void damage in AA7075-O sheet. In addition, in-situ SEM uniaxial tensile tests are carried out to assess the effectiveness of the simulation methodology and to compare the experimental and numerical results. Post-test high resolution X-ray computed tomography (HR-XCT) was also carried out to qualitatively observe particle-induced voiding in the material. The numerical methodology is shown to capture well the experimental trends in damage evolution of the individual particles. It is observed that particle damage is a function of inherent particle properties, their morphological features, and matrix strain localization characteristics. Larger-size Fe-rich particles are observed to undergo damage at an earlier stage, and consequently, affect the strain localization characteristics the most. In contrast, η precipitates are found to be most resistant to particle damage, followed by θ precipitates. Higher stresses inside strain localization bands, caused increased void damage initiation and growth of η and θ precipitates. Overall, particle fracture is observed to be marginally higher compared to particle decohesion, irrespective of the particle type.

Hierarchical multi-scale analysis of the effect of varying fiber bundle geometric properties on the mechanical properties of 3D braided composites

A hierarchical multi-scale numerical model is developed to predict the effect of cross-sectional geometric properties on the mechanical response of three-dimensional (3D) braided composites. In this model, the effective properties are transferred from the fiber bundle scale to the mesoscale, and the finite element and analytical methods are used to predict the macroscopic mechanical properties. Damage evolution was evaluated, based on a continuous damage mechanics approach. A user-defined material subroutine (UMAT), in a nonlinear finite element analysis, has been developed to implement the proposed model and further determine the response and subsequent damage evolution in 3D braided composites subjected to quasi-static tension. The elastic properties of the composites are predicted using a hybrid multi-scale model. The agreement between the numerical simulations and the experimental results is good. It has been shown that the cross-sectional geometry of the fiber bundle properties has a significant influence on the tensile behavior of the composite, which is captured by the proposed multi-scale damage model. This research offers a theoretical analysis for selecting the optimized fiber bundle geometry for using in FE predictions of 3D braided composites.

A multi-scale damage model and mechanical behavior for novel light-weight C/C honeycomb sandwich structure

The high-resolution spacecraft poses an urgent need for opto-mechanical structure with ultra-high stability and light-weight. Owing to the advantages of both carbon fiber-reinforced carbon-based composites (C/C composites) and honeycomb sandwich structure, a novel C/C honeycomb sandwich structure strategy is proposed in this study. It was fabricated by using weaving fabrics and Chemical Vapor Infiltration (CVI) process, then was tested under out-of-plane compression. Taking the weave structure of honeycomb wall, anisotropy characteristics and damage mechanism of C/C composites, as well as the parameters of core size, a multi-scale damage model is established and validated to investigate mechanical behavior of the novel structure. The effects of influence factors (side length, thickness and height of core) on mechanical properties and damage mode of the novel sandwich structure are investigated. The results demonstrate that the optimal honeycomb core sizes for improving the light-weight and high load-bearing integration performance are l = 5 mm–7.5 mm and t = 0.3 mm–0.4 mm. The matrix damage occurs in the middle region of core, while fiber damage occurs at the end of core when its height reaches 15 mm. This study is helpful for design and optimization for opto-mechanical structure of high-resolution spacecraft.

Investigation on the effect of interface properties on compressive failure behavior of 3D woven composites through micromechanics-based multiscale damage model

In this paper, the effect of interface properties on the compressive failure behavior of 3D woven composites (3DWC) is investigated by incorporating a micromechanics-based multiscale damage model (MMDM). The correlation between the mesoscopic stress of yarns and microscopic stress of constituents is established by defining a stress amplification factor. With the microscopic stresses, the fiber breakage and matrix failure can be separately evaluated at the microscale, without assuming the yarns as transversely isotropic homogeneous materials. Especially, the interfacial debonding between yarns and matrix is also a dominant damage mode within 3DWC. Given that there is still a lack of studies on the influence of interfacial properties on the compressive failure behavior of 3DWC, it is meaningful to perform numerical parametric studies to reveal how the interface properties contribute to the damage mechanisms of 3DWC under compressions. The predicted results indicate that with the increase of interface strengths and fracture toughness, the compressive resistance of 3DWC can be significantly improved, resulting in higher strength and failure strain. Additionally, the studied 3DWCs with weak, medium and strong interfaces exhibit different damage development processes.

Multiscale damage modelling of notched and un-notched 3D woven composites with randomly distributed manufacturing defects

This work proposes a stochastic multiscale computational framework for damage modelling in 3D woven composite laminates, by considering the random distribution of manufacturing-induced imperfections. The proposed method is demonstrated to be accurate, while being simple to implement and requiring modest computational resources. In this approach, a limited number of cross-sectional views obtained from micro-computed tomography (µCT) are used to obtain the stochastic distribution of two key manufacturing-induced defects, namely waviness and voids. This distribution is fed into a multiscale progressive damage model to predict the damage response of three-dimensional (3D) orthogonal woven composites. The accuracy of the proposed model was demonstrated by performing a series of finite element simulations of the un-notched and notched tensile tests (having two different hole sizes) for resin-infused thermoplastic (Elium®) 3D woven composites. Excellent correlation was achieved between experiments and the stochastic finite element simulations. This demonstrates the effectiveness of the proposed stochastic multiscale model. The model successfully captured the stochastic nature of tensile responses (ultimate tensile strength and stiffness), damage modes (matrix damage and fibre failure), and initiation and propagation of transverse cracks in thermoplastic 3D woven composites, consistent with experimental observation. The stochastic computational framework presented in this paper can be used to guide the design and optimization of 3D textile composite structures.

Multiscale image-based modeling of progressive damage in 3D5D braided composites with yarn-reduction

The special-shape fiber-reinforced composites are improbable to be represented by the representative volume element (RVE). Hence, a multiscale image-based model is proposed to reveal the progressive damage in 3D5D braided composites with/without yarn-reduction. The microscale and mesoscale models of the materials are reconstructed by Micro-CT, considering the yarns’ twists, global compression, and yarns’ misalignment. Subsequently, the continuous damage method and the cohesive-zone model are proposed to characterize the damage behavior of the microscale and mesoscale constituents. These constitutive models are implemented by a user-defined subroutine UMAT in ABAQUS. Finally, based on the homogenization procedure and the multiscale analysis method, the effects of structures on microscale, mesoscale, and macroscale properties of 3D5D braided composites without/with yarn-reduction are analyzed sequentially. The results show that cross-section variations and twists in the yarns modify the damage initiation. The wedge-shaped stress migration phenomenon occurs near the yarn-reduction point. Besides, the macroscopic simulation of strain fields and the damage morphology agrees well with the DIC measurements and Micro-CT results. The established multiscale framework is expected to predict the progressive damage of 3D5D braided composites with/without yarn-reduction and provide the theoretical basis for the structure design.

A combined experimental and numerical approach to investigate the failure behaviors of 3D woven composites under biaxial tensile loading

The failure behaviors of 3D woven composites (3DWC) under biaxial tensile loadings are investigated through a combined experimental and numerical approach in this paper. Appropriate biaxial cruciform specimen of 3DWC is first designed according to the experimental requirements. The biaxial tensile experiments are conducted on a servo-hydraulic biaxial testing facility, and then the full-field strain distributions and crack morphologies of cruciform specimens are analyzed in detail. For the multiscale geometric reconstruction of 3DWC, a full-thickness mesoscopic RVC is first extracted from the periodic woven architecture, and then a novel full-scale geometric modeling method is developed to reconstruct the biaxial cruciform specimens of 3DWC. Particularly, in conjunction with the micromechanics of failure theory, a multiscale damage model is proposed to simulate the biaxial failure behaviors of 3DWC. With the stress amplification factor, a transfer relationship between mesoscopic and microscopic stresses is established, and then the damage states of matrix and fibers within yarns can be separately determined. By comparing the experimental and predicted results, the realistic damage mechanism of 3DWC under biaxial tensile loading can be elucidated.

Multiscale Modeling of Radiation Damage in Oxide Dispersed Strengthened Steel Alloys: A Perspective

Multiscale Modeling of Radiation Damage in Oxide Dispersed Strengthened Steel Alloys: A Perspective

New nonlocal multiscale damage model for modelling damage and cracking in quasi-brittle materials

A new method for the simulation of crack initiation and propagation in quasi-brittle materials is proposed that combines the scaled boundary finite element method and a nonlocal multiscale damage model. The scaling centre of the scaled boundary finite element subdomain is taken as the material point. Microscopic damage is defined in terms of the stretch rate of bonds of material points, and macroscale topologic damage is evaluated as the weighted average of microscale damage over bonds in the influence domain. Through the energetic degradation function of phase field analysis, which connects energy-based damage and macroscale topologic damage, the nonlocal multiscale damage model is inserted into the framework of the scaled boundary finite element method. The quadtree discrete mesh technique is used to rapidly obtain a high-quality multilevel mesh by taking full advantage of the hanging nodes that it allows. A detailed arc length method for solving nonlinear equations is also presented in this paper. Four typical examples, one Mode I and three mixed-mode cracking simulations, show that the proposed method can be used to simulate crack initiation and propagation in quasi-brittle materials and correctly describe crack propagation paths and load-deformation curves. Compared with other methods, the nonlocal multiscale damage model presented in this paper can provide a more accurate description of local cracking damage zones, and the results are more reasonable, with higher calculation accuracy and efficiency. The numerical examples also indicate that there is no mesh sensitivity problem when the mesh size of the damage process region is less than 1/5 of the radius of the influence domain.