Concurrent Multiscale Model Research Articles

An ANN-based concurrent multiscale damage evolution model for hierarchical fiber-reinforced composites

In this paper, an ANN-based concurrent multiscale damage evolution model is proposed, which is able to investigate the complex failure behaviors of hierarchical fiber-reinforced composites. In the framework of the proposed model, yarn damage evolution laws at the mesoscale are indirectly derived from the microscale representative volume element (RVE), using artificial neural networks (ANNs) as a surrogate model. A homogenized characterization method is proposed to derive the homogenized damage variables. The homogenized strain and damage variables of the microscale RVE are taken as inputs and outputs in ANNs, respectively. The dataset is generated by combining clustering with the finite element simulation. A typical kind of plain-woven composite is adopted as a benchmark material for numerical implementation and experimental verification. The numerical predictions, including the tensile properties and damage evolution, are consistent with the results from quasi-static tension experiments.

An efficient multi-scale method for failure mechanism analysis of SiCf/Ti composites with experimental validation

This study focuses on developing and validating a high-precision concurrent multi-scale finite element model considering the progressive damage model (PDM) and the cohesive zone model (CZM) for predicting the damage evolution of SiCf/Ti composites. At the macro-scale, a constitutive model describing the anisotropic damage criterion of SiCf/Ti composites was implemented by means of a user-defined subroutine (VUMAT). Meanwhile, based on the submodelling, a representative volume element (RVE) model was developed to systematically analyze the failure modes of the SiC fibers, the matrix, and the interface, respectively. Specifically, the crack initiation and propagation in the stress concentration zones were further discussed. Simultaneously, experimental methods were employed to verify the feasibility of the current model. During the uniaxial compression, the brittle fracture of the SiC fibers and ductile fracture of the matrix are the predominant failure modes of SiCf/Ti composites, with fiber fracture being the dominant factor. The crack initiates at the fibers, propagates rapidly to the fiber-matrix interface, and then extends into the matrix. Moreover, the fracture locations are suscepticle to stress concentrations, leading to the crack initiation and propagation. The predicted results show that the local damage has a significant effect on the failure mechanism of SiCf/Ti composites and this multi-scale model provides a scientific reference for the design and optimization of composites.

Multi-scale modelling of deformation heterogeneities in explosively welded layered sheets

A multi-scale numerical investigation of local heterogeneities in the strain and stress fields occurring during forming of explosively welded layered metallic sheets is the main goal of the research. Explosive welding is a complex process involving various phenomena occurring in materials during an impact at high velocities and pressures, especially at the interfaces of colliding metals. As a result, the interface of the layered metallic sheets is often highly heterogeneous at the microscale level, what directly affects the sheet behaviour under subsequent forming conditions. To investigate this issue, the mesh-free numerical model of the explosive welding process is used first to recreate the characteristic features of the interface morphology. Various detonation velocities are used to provide diversified morphological features at the interface. Obtained results are then used as input data to develop the concurrent multi-scale finite element model of material behaviour under deformation conditions. The multi-scale modelling concept with explicit representation of the interface region is used. The highly refined heterogeneous FE mesh was generated in the interface region to capture local heterogeneities occurring at the microscale. Particular attention is put on numerical investigation of an influence of interface morphology in the welding zone on the development of the stress localisation that may directly lead to fracture initiation during forming.

Self-consistent homogenization-based parametrically upscaled continuum damage mechanics model for composites subjected to high strain-rate loading

This paper develops a Parametrically Upscaled Continuum Damage Mechanics (PUCDM) model for carbon fiber/epoxy matrix composites subjected to high strain-rate loading. The PUCDM model for predicting high strain-rate induced deformation and damage evolution at the macroscopic scale, explicitly incorporates microstructural morphology and micro-inertia in its constitutive coefficients. It is developed using self-consistent homogenization that uses a concurrent multiscale model to account for the effect of micro-inertia and stress wave interaction with the microstructure. The concurrent model embeds a statistically equivalent representative volume element (SERVE) of the microstructure in an exterior domain, whose constitutive and damage response are described by the PUCDM model. Micromechanical modeling for the composite microstructure involves a unified cohesive zone enhanced phase-field damage model for fiber-matrix interface debonding, fiber breakage, and matrix cracking. The PUCDM model parameters for the upscaled domain are determined through micro-macro-scale energy equivalence, along with traction reciprocity and displacement continuity at the SERVE-exterior domain interface that are enforced using a Lagrange multiplier-based approach. Simulations using the concurrent model analyze stress wave propagation and damage evolution in composite microstructures with three different fiber volume fractions at multiple strain rates in the range of 102 − 105 s−1. The fiber volume fraction and spatial distributions affect the overall stiffness and damage evolution in the PUCDM model. Results of the analysis demonstrate the need for representation of micro-inertia, strain rates and microstructure morphology in the PUCDM-based stiffness and damage model parameters for high strain-rates above [Formula: see text].

A concurrent irradiation-mechanics multiscale coupling model

• A novel concurrent irradiation-mechanical multiscale coupling model is developed. • Models of irradiation defect kinetics and irradiation hardening are established. • The difference between post irradiation and concurrent irradiation-deformation tests are disclosed. • Dislocation channel formation is not always correlated with yield drop. The vast majority of our current knowledge regarding the basic mechanisms controlling irradiation effect on mechanical properties is based almost entirely on the results of post-irradiation experiments or theoretical models. However, the concurrent effects of irradiation, mechanical stress, and thermal damage on the failure phenomena of materials and components remain largely unexplored due to its internal multiscale-multiphysics coupling nature. We present here a concurrent irradiation-mechanics multiscale coupling model. The concurrent evolutions of nanoscale irradiation defect clusters, microscale dislocation configurations, and mechanical responses are well captured based on coupling cluster dynamics, discrete dislocation dynamics, and the finite element methods using an effective time marching scheme. Model predictions of defect densities and size are in general agreement with experimental observations. Irradiation hardening is shown to take place also in samples undergoing concurrent irradiation-mechanical loading, similar to samples tested post-irradiation. However, the occurrence of plastic flow localization and dislocation channel formation is not accompanied with apparent yield drop (softening) under concurrent irradiation-mechanical loading conditions, which is different from the post-irradiation case.

Concurrent multiscale modeling of in-plane micro-damage evaluation in Z-pinned composite laminates

Most of the unit cell models for Z-pinned composite laminates (ZCL) are mesoscopic in scale, where the fiber reinforced zone is modeled as homogeneous but without detailed characterization and failure analysis of the fibers and matrix. This paper proposes a new concurrent multiscale unit cell model to investigate the in-plane micro-damage evolution of ZCL. The novelty worth mentioning is the proposed element-based method to generate random microbuckling spatial fibers in the fiber reinforced zone, where the microbuckling is caused by fiber waviness and fiber crimp, and then the mesh of fiber, Z-pin, matrix, and the interface between Z-pin and matrix is regenerated. In-plane tensile tests (ASTM D3039) are conducted for verification. There is good agreement between experiment and simulation, only with deviations of −0.97% and 2.69% for tensile modulus and fracture initiation stress, respectively. The research indicates that in-plane micro-damage initiates from the interface between Z-pin and matrix. The stress concentration and higher local fiber volume fraction, caused by the microbuckling spatial fibers clustered near the Z-pin, play a major role in the evolution of interface damage, crack initiation and growth.

Data-driven Bayesian model-based prediction of fatigue crack nucleation in Ni-based superalloys

This paper develops a Bayesian inference-based probabilistic crack nucleation model for the Ni-based superalloy René 88DT under fatigue loading. A data-driven, machine learning approach is developed, identifying underlying mechanisms driving crack nucleation. An experimental set of fatigue-loaded microstructures is characterized near crack nucleation sites using scanning electron microscopy and electron backscatter diffraction images for correlating the grain morphology and crystallography to the location of crack nucleation sites. A concurrent multiscale model, embedding experimental polycrystalline microstructural representative volume elements (RVEs) in a homogenized material, is developed for fatigue simulations. The RVE domain is modeled by a crystal plasticity finite element model. An anisotropic continuum plasticity model, obtained by homogenization of the crystal plasticity model, is used for the exterior domain. A Bayesian classification method is introduced to optimally select informative state variable predictors of crack nucleation. From this principal set of state variables, a simple scalar crack nucleation indicator is formulated.

Development of the Concurrent Multiscale Discrete-Continuum Model and Its Application in Plasticity Size Effect

A concurrent multiscale model coupling discrete dislocation dynamics to the finite element method is developed to investigate the plastic mechanism of materials at micron/submicron length scales. In this model, the plastic strain is computed in discrete dislocation dynamics (DDD) and transferred to the finite element method (FEM) to participate in the constitutive law calculation, while the FEM solves the complex boundary problem for DDD simulation. The implementation of the whole coupling scheme takes advantage of user subroutines in the software ABAQUS. The data structures used for information transferring are introduced in detail. Moreover, a FE mesh-based regularization method is proposed to localize the discrete plastic strain to continuum material points. Uniaxial compression tests of single crystal micropillars are performed to validate the developed model. The results indicate the apparent dependence of yield stress on sample size, and its underlying mechanisms are also analyzed.

A self-consistent homogenization framework for dynamic mechanical behavior of fiber reinforced composites

This paper proposes a self-consistent homogenization framework for developing finite strain, elastic constitutive models of carbon fiber–epoxy composites for high strain-rate loading. The framework incorporates a concurrent multiscale model, in which an RVE is embedded in a homogenized exterior domain, is developed with self-consistent displacement compatibility and traction reciprocity constraints at the RVE-exterior domain interface. It overcomes limitations of periodic boundary conditions on the RVE for dynamic problems under high strain-rate conditions and allows for the evaluation of material constitutive relations accounting for micro-scale inertia. The proposed self-consistent formulation incorporates the effect of stress waves propagation in the microstructure, along with their interaction with heterogeneities resulting in reflection and transmission at the interfaces. The concurrent model is used to study dynamic composite behavior at strain-rates in the range of 102-105 s−1 for two RVEs, one containing a single fiber and another with 70 randomly distributed fibers. For strain-rates above 104 s−1, the dynamic part of the stress becomes significant and dominates over the static part of the stress. Results of the analysis show that for high strain-rate dynamic loading, constitutive models for the composites must account for micro-inertia, in addition to strain-rates and microstructural morphology.

A continuum–atomistic multi-scale analysis of temperature field problems and its application in phononic nano-structures

In this paper, a novel coupling technique is developed in continuum–atomistic multi-scale analysis of temperature field problems. In this manner, a new thermostat is introduced based on the single-atom sub-system, where its capability to control the temperature and produce the canonical ensemble is investigated. Moreover, the performance of proposed thermostat is verified by comparing the distribution of velocities to the Maxwell-Boltzmann distribution. The single-atom sub-system thermostat is then incorporated into the concurrent multi-scale model to relate the temperature field between the continuum and atomistic domains with complex lattice thermal fields. In order to illustrate the capability of proposed coupling continuum–atomistic model, the multi-scale analysis is performed through several numerical examples at various temperature fields and the results are compared with those obtained from the full atomistic model and finite element simulation. Finally, the continuum–atomistic multi-scale technique is applied in numerical simulation of the lattice heat conduction in two-dimensional phononic nano-structures. • A single-atom sub-system thermostat is developed that presents the canonical ensemble. • The performance of proposed thermostat is verified by comparing the velocities distribution to the Maxwell-Boltzmann distribution. • A concurrent multi-scale technique is presented based on the proposed single-atom thermostat. • The concurrent multi-scale technique is applied to model the lattice heat conduction in phononic nano-structures. • The behavior of thermal decay time is investigated for various model parameters in a phononic crystal.

A Data-Driven Bayesian Model for Predicting Fatigue Crack Nucleation in Polycrystalline Ni-Based Superalloys

This paper develops a Bayesian, probabilistic crack nucleation model in the Ni-based superalloy Ren\'e 88DT for fatigue loading. A data-driven, machine learning approach is developed to identify the underlying mechanics driving crack nucleation. An experimental set of fatigue-loaded microstructures is characterized near crack nucleation sites using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) images to correlate grain morphology and crystallography to the spatial location of crack nucleation sites. A concurrent multiscale model that embeds polycrystalline microstructures, created from the EBSD images, in a self-consistent homogenized material is developed for low cycle fatigue simulations needed to create a database of state variables. The polycrystalline domain is modeled by a crystal plasticity finite element model (CPFEM), while a homogenized anisotropic plasticity model is used for the exterior domain. A Bayesian classification method is introduced to optimally select the most informative state variable predictors of crack nucleation and constructs a near-Pareto frontier of models with varying complexity. From this principal set of state variables, a simplified scalar crack nucleation indicator is formulated which encompasses all of the relevant components derived from the main discriminators. This Bayesian approach allows the micromechanical state variables responsible for causing crack nucleation events to come out naturally from existing data. The final result is a model that predicts the probability of nucleating a crack at a microstructural location, given the mechanical state of the material.

A concurrent multiscale approach for modeling recycled aggregate concrete

The use of recycled concrete aggregates in new concrete is an alternative that can provide economical and environmental benefits. However, the influence of the inert particles on the mechanical behavior of concrete needs to be better understood. To provide a comprehensive simulator to predict the failure mechanism of this material taking into account its heterogeneity in mesoscale, a mesh fragmentation technique composed of interface solid finite elements equipped with a tensile damage model is employed. To minimize computational costs, a concurrent multiscale strategy based on the use of coupling finite elements to connect the macro and mesoscale regions is adopted. In mesoscale, the different phases of the recycled aggregate concrete (RAC) are explicitly represented, consisting of: (i) new mortar matrix; (ii) recycled aggregate composed of old matrix and crushed rock (natural aggregate); and (iii) interfacial transition zones in between all of them. For the regions where cracks are not expected, homogenized elastic parameters are assumed for the RAC. Three-point bending beams experimentally tested by Casuccio et al. [4] are numerically analyzed for concrete with compressive strength targets of 18, 37 and 48 MPa. These concrete beams were produced with coarse aggregates derived from natural crushed stone and another two coming from recycled concrete with high and normal strengths. The numerical results obtained show that the concurrent multiscale model is able to represent the tensile failure mechanism of the RAC, taking into account explicitly the effects of the recycled components on crack patterns and structural predictions.

Numerical investigation of matrix cracking propagation in cross‐ply laminated composites subjected to three‐point bending load using concurrent multiscale model

AbstractThe purpose of the present study is to analyze fiber‐matrix debonding and induced matrix cracking formation as two major micromechanical damage modes in cross‐ply composite laminates using a two‐dimensional numerical approach. To this aim, the cross‐ply laminates containing 90‐degree layers are modeled, where the fibers are arranged randomly in transverse plies. Damage modes in this numerical model are simulated by the cohesive surface method. The performed analyses reveal that in the laminates with 90‐degree layers located in the outer positions, the primary micro damage mode is micro matrix cracking which is initiated from the fiber‐matrix debonding damage mode and will be followed by matrix cracking. The main benefit of the present study in comparison to other numerical methods is proposing a virtual test method for damage analysis of different cross‐ply laminates in which, the matrix cracking formation will emerge physically in a random and antisymmetric pattern similar to the experimental observations.

3D concurrent multiscale model for crack propagation in concrete

A new approach for concurrent multiscale modeling of three-dimensional crack propagation in concrete is proposed. A macroscopic model with homogenized elastic parameters is adopted in the regions where the material behaves elastically. For regions where cracks are expected to occur, a mesoscopic model based on a mesh fragmentation technique is used to represent the concrete as a heterogeneous three-phase material composed of mortar matrix, coarse aggregates and interfacial transition zone. In this technique, standard finite elements with high aspect ratio are inserted in between all regular finite elements of the mortar matrix and in between the mortar matrix and aggregate elements in order to describe the crack initiation and propagation process by using an appropriate tensile damage constitutive model. Coarse aggregates with regular shapes are generated from a grading curve and placed into the mortar matrix randomly, using the “take-and-place” method. Coupling finite elements are used for connecting the non-matching meshes corresponding to the macro and mesoscale regions, without increasing the total number of degrees of freedom of the problem. Realistic predictions of crack formation and propagation were obtained for different tests, replicating accurately the observed experimental patterns.

A combined experimental/numerical investigation on hygrothermal aging of fiber-reinforced composites

This work investigates hygrothermal aging degradation of unidirectional glass/epoxy composite specimens through a combination of experiments and numerical modeling. Aging is performed through immersion in demineralized water. Interlaminar shear testes are performed after multiple conditioning times and after single immersion/redrying cycles. Degradation of the fiber-matrix interface is estimated using single-fiber fragmentation tests and reverse modeling combining analytical and numerical models. A fractographic analysis of specimens aged at 50°C and 65°C is performed through X-ray computed tomography. The aging process is modeled using a numerical framework combining a diffusion analysis with a concurrent multiscale model with embedded hyper-reduced micromodels. At the microscale, a pressure-dependent viscoelastic/viscoplastic model with damage is used for the resin and fiber-matrix debonding is modeled with a cohesive-zone model including friction. A comparison between numerical and experimental results is performed.

Updating of structural multi-scale monitoring model based on multi-objective optimisation

Structural safety assessments are implemented based on measured data, but the limited number of sensors restricts the comprehensive acquisition of response information in large complex structures. A concurrent multi-scale model utilises global and local simulation characteristics to expand the insufficient measured data. Thus, good global and local simulation capability is necessary for structural health monitoring-oriented multi-scale model, and the updating of this monitoring model needs to consider the multi-type responses that are obtained from different structural scales. However, the existing methods usually integrate multi-type responses into a single-objective function, which cannot ensure the acquisition of the optimal parameters. Moreover, in common parameter screening method, the perturbation and threshold are set artificially, which causes a strong subjectivity, and the common polynomial response surface fits poorly for highly non-linear problem. Therefore, an updating method of the structural multi-scale monitoring model based on multi-objective optimisation is proposed. For the proposed method, a variance analysis based on the orthogonal experimental design is used to screen the unique significant influence parameters. The Kriging spatial interpolation technique is used to establish the approximate surrogate model between the response and its corresponding influence parameters. Simultaneously, the responses obtained from the global and local structural scales are used to define the sub-objectives of the multi-objective function vector in order to avoid the introduction of weight coefficients. Then, the multi-objective optimisation algorithm NSGA-II is used to obtain the optimal parameter values and realise the comprehensive updating of the initial multi-scale monitoring model. Finally, based on the health monitoring system of the large shell structure of the Zhuhai Opera House, the initial multi-scale monitoring model is updated using the proposed method. The structural dynamic characteristics and local stress obtained from the initial model, updated model and the real structure are compared to validate the effectiveness of the proposed method.

Mixed-dimensional coupling method for box section member based on the optimal stress distribution pattern

Mixed-dimensional coupling is significant for the accurate performance analysis of a concurrent multi-scale model, while the stress distribution pattern is a key problem that influences the mixed-dimensional coupling method. With respect to existing coupling methods, the real stress pattern of the complicated section is replaced by the approximate formula, the uniform distribution pattern of shear stress is used along the sectional thickness direction, and the shear stress of the sectional corner is neglected. The aforementioned simplified assumptions of stress distribution pattern are the key reasons that cause a distortion of the local stress and reduce the reliability of the multi-scale model. In the study, the optimal stress distribution pattern is determined using the proposed method, in order to provide the optimal stress distribution for mixed-dimensional coupling, and improve the accuracy of the multi-scale model. First, a stress distribution calculation model based on the higher-dimensional element type and section size of member is established. Next, the stress distribution pattern is determined and optimized using the surface fitting technology and iterative calculation, in which the coefficient of determination R2 is selected as the optimization index. Third, under the specified local coordinate system, the multipoint constraint equations for mixed-dimensional coupling are determined based on the optimal stress distribution patterns and element shape functions. Finally, the optimal stress distribution patterns of box section, which consider the linear distribution along the thickness direction and stress contribution in the sectional corner, are determined. Furthermore, concurrent multi-scale models of a cantilever beam and warren truss structure with the box section are established, and are used to validate the effectiveness and applicability of the proposed method based on a comparison of the structural global responses, local responses, and dynamic characteristics.

An adaptive concurrent multiscale model for concrete based on coupling finite elements

A new adaptive concurrent multiscale approach for modeling concrete that contemplates two well separated scales (represented by two different meshes) is proposed in this paper. The macroscale stress distribution is used as an indicator to identify critical regions (where the material is prone to degrade) with the explicit aim to enrich these zones with detailed mesoscale material information comprising three basic phases: coarse aggregates, mortar matrix and interfacial transition zone. Thus, the concrete initially idealized as a homogeneous material is gradually replaced and enhanced by a heterogeneous multiphase one. This technique is particularly powerful to handle cases where the region with nonlinear behavior is not easy to anticipate. Furthermore, the proposed approach does not require the definition of a periodic cell (or a RVE), and the meshes from distinct scales are totally independent. The new adaptive mesh technique is based on the use of coupling finite elements to enforce the continuity of displacements between the non-matching meshes associated with the two different scales of analysis. Besides that, mesh fragmentation concepts are incorporated to simulate the crack formation and propagation at the mesoscopic scale, without the need of defining complex and CPU-time demanding crack-tracking algorithms. The strategy is developed integrally within the framework of continuum mechanics, which represents an advantage with respect to other approaches based on discrete traction/separation-law. Numerical examples with complex crack patterns are conducted to validate the proposed multiscale approach. Furthermore, the efficiency and accuracy of the novel technique are compared against full mesoscale and standard concurrent multiscale models, showing excellent results.

Elastic crack propagation model for crystalline solids using a self-consistent coupled atomistic–continuum framework

Deformation and failure processes of crystalline materials are governed by complex phenomena at multiple scales. It is necessary to couple these scales for physics-based modeling of these phenomena, while overcoming limitations of modeling at individual scales. To address this issue, this paper develops self-consistent elastic constitutive and crack propagation relations of crystalline materials containing atomic scale cracks, from observations made in a concurrent multi-scale simulation system coupling atomistic and continuum domain models. The concurrent multi-scale model incorporates a finite temperature atomistic region containing the crack, a continuum region represented by a self-consistent crystal elasticity constitutive model, and a handshaking interphase region. Atomistic modeling is done by the molecular dynamics code LAMMPS, while continuum modeling is conducted by the finite element method. For single crystal nickel a nonlinear and nonlocal crystal elasticity constitutive relation is derived, consistent with the atomic potential function. An efficient, staggered solution scheme with parallel implementation is designed for the coupled problem. The atomistic–continuum coupling is achieved by enforcing geometric compatibility and force equilibrium in the interphase region. Quantitative analyses of the crack propagation process focuses on size dependence, strain energy release rate, crack propagation rate and degradation of the local stiffness. The self-consistent constitutive and crack propagation relations, derived from the concurrent model simulation results are validated by comparing results from the concurrent and full FE models. Excellent accuracy and enhanced efficiency are observed in comparison with pure MD and concurrent model results.

Crack propagation with adaptive grid refinement in 2D peridynamics

The most common technique for the numerical implementation of peridynamic theory is based on a mesh-free approach, in which the whole body is discretized with a uniform grid and a constant horizon. As a consequence of that computational resources may not be used efficiently. The present work proposes adaptive refinement algorithms for 2D peridynamic grids. That is an essential component to generate a concurrent multiscale model within a unified approach. Adaptive grid refinement is here applied to the study of dynamic crack propagation in two dimensional brittle materials. Refinement is activated by using a new trigger concept based on the damage state of the material, coupled with the more traditional energy based trigger, already proposed in the literature. We present as well a method, to generate the nodes in the refined zone, which is suitable for an efficient numerical implementation. Moreover, strategies for the mitigation of spurious reflections and distortions of elastic waves due to the use of a non-uniform grid are presented. Finally several examples of crack propagation in planar problems are presented, they illustrate the potentialities of the proposed algorithms and the good agreement of the numerical results with experimental data.