Multiscale modeling of fracture of MgO: Sensitivity of interatomic potentials

Three different interatomic potentials, namely, B-G I Model, B-G II Model and L-C Model, are used in multiscale modeling and simulation of a center-cracked specimen made of magnesia subjected to monotonically increasing loading. The specimen is decomposed into a far field, a near field and a crack-tip region. The analytical solution in the far field from linear elastic fracture mechanics (LEFM) is utilized. The solution of the near field is based on a multiscale field theory. In the crack-tip region, molecular dynamics (MD) simulation is employed. These methodologies are integrated to simulate mixed mode fracture of magnesia (MgO). Three different interatomic potentials are examined and the interatomic potential and interatomic force between Mg-Mg, Mg-O and O-O are shown. The numerical results of crack propagation demonstrate that (1) crack closure is witnessed in B-G I Model but not in B-G II Model and L-C Model, (2) B-G II Model and L-C Model diverge in the early stage. The cause of instability and the remedy are also discussed.     

Multiscale constitutive modeling and numerical simulation of fabric material

A multiscale model for a fabric material is introduced. The model is based on the assumption that on the macroscale the fabric behaves as a continuum membrane, while on the microscale the properties of the microstructure are accounted for by a constitutive law derived by modeling a pair of overlapping crimped yarns as extensible elasticae. A two-scale finite element method is devised to solve selected boundary-value problems.     

Coarse-grained atomistic simulation of dislocations

This paper presents a new methodology for coarse-grained atomistic simulation of dislocation dynamics. The methodology combines an atomistic formulation of balance equations and a modified finite element method employing rhombohedral-shaped 3D solid elements suitable for fcc crystals. With significantly less degrees of freedom than that of a fully atomistic model and without additional constitutive rules to govern dislocation activities, this new coarse-graining (CG) method is shown to be able to reproduce key phenomena of dislocation dynamics for fcc crystals, including dislocation nucleation and migration, formation of stacking faults and Lomer-Cottrell locks, and splitting of stacking faults, all comparable with fully resolved molecular dynamics simulations. Using a uniform coarse mesh, the CG method is then applied to simulate an initially dislocation-free submicron-sized thin Cu sheet. The results show that the CG simulation has captured the nucleation and migration of large number of dislocations, formation of multiple stacking fault ribbons, and the occurrence of complex dislocation phenomena such as dislocation annihilation, cutting, and passing through the stacking faults. The distinctions of this method from existing coarse-graining or multiscale methods and its potential applications and limitations are also discussed.     

Multiscale modeling of the plasticity in an aluminum single crystal

This paper describes a numerical, hierarchical multiscale modeling methodology involving two distinct bridges over three different length scales that predicts the work hardening of face centered cubic crystals in the absence of physical experiments. This methodology builds a clear bridging approach connecting nano-, micro- and meso-scales. In this methodology, molecular dynamics simulations (nanoscale) are performed to generate mobilities for dislocations. A discrete dislocations numerical tool (microscale) then uses the mobility data obtained from the molecular dynamics simulations to determine the work hardening. The second bridge occurs as the material parameters in a slip system hardening law employed in crystal plasticity models (mesoscale) are determined by the dislocation dynamics simulation results. The material parameters are computed using a correlation procedure based on both the functional form of the hardening law and the internal elastic stress/plastic shear strain fields computed from discrete dislocations. This multiscale bridging methodology was validated by using a crystal plasticity model to predict the mechanical response of an aluminum single crystal deformed under uniaxial compressive loading along the [4 2 1] direction. The computed strain-stress response agrees well with the experimental data.     

Multiscale modeling of strain-hardening cementitious composites

This research involves the multiscale characterization of strain-hardening cementitious composites under tensile loading. The sensitivity of cracking behavior to fiber dispersion is studied using a special form of lattice model, in which each fiber is explicitly represented. It is shown that the nonlocal modeling of fiber bridging forces is essential for obtaining realistic patterns of crack development and strain-hardening behavior. Crack count and crack size are simulated for progressively larger levels of tensile strain. The influence of fiber dispersion is clearly evident: regions with significantly fewer fibers act as defects, reducing strength and strain capacity of the material.     

Multiscale modeling of irradiated polycrystalline FCC metals

We propose a set of models for the post-irradiation deformation response of polycrystalline FCC metals. First, a defect- and dislocation-density based evolution model is developed to capture the features of irradiation-induced hardening as well as intra-granular softening. The proposed hardening model is incorporated within a rate-independent single crystal plasticity model. The result is a non-homogeneous deformation model that accounts for defect absorption on the active slip planes during plastic loading. The macroscopic non-linear constitutive response of the polycrystalline aggregate of the single crystal grains is then obtained using a micro–macro transition scheme, which is realized within a Jacobian-free multiscale method (JFMM). The Jacobian-free approach circumvents explicit computation of the tangent matrix at the macroscale by using a Newton–Krylov process. This has a major advantage in terms of storage requirements and computational cost over existing approaches based on homogenized material coefficients in which explicit Jacobian computation is required at every Newton step. The mechanical response of neutron-irradiated single and polycrystalline OFHC copper is studied and it is shown to capture experimentally observed grain-level phenomena.     

Multiscale cohesive failure modeling of heterogeneous adhesives

A novel multiscale cohesive approach that enables prediction of the macroscopic properties of heterogeneous thin layers is presented. The proposed multiscale model relies on the Hill's energy equivalence lemma, implemented in the computational homogenization scheme, to couple the micro- and macro-scales and allows to relate the homogenized cohesive law used to model the failure of the adhesive layer at the macro-scale to the complex damage evolution taking place at the micro-scale. A simple isotropic damage model is used to describe the failure processes at the micro-scale. We establish the upper and lower bounds on the multiscale model and solve several examples to demonstrate the ability of the method to extract physically based macroscopic properties.     

Multiscale tow-phase flow modeling of sheet and cloud cavitation

A multiscale two-phase flow model based on a coupled Eulerian/Lagrangian approach is applied to capture the sheet cavitation formation, development, unsteady breakup, and bubble cloud shedding on a hydrofoil. No assumptions are needed on mass transfer. Instead natural free field nuclei and solid boundary nucleation are modelled and enable capture of the sheet and cloud dynamics. The multiscale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics, and a transition scheme to bridge the micro and macro scales. With this multiscale model small nuclei are seen to grow into large bubbles, which eventually merge to form a large scale sheet cavity. A reentrant jet forms under the sheet cavity, travels upstream, and breaks the cavity, resulting in the emission of high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The method is validated on a 2D NACA0015 foil and is shown to be in good agreement with published experimental measurements in terms of sheet cavity lengths and shedding frequencies. Sensitivity assessment of the model parameters and 3D effects on the predicted major cavity dynamics are also discussed.     

Efficient and robust constitutive integrators for single-crystal plasticity modeling

Small-scale deformation phenomena such as subgrain formation, development of texture, and grain boundary sliding require simulations with a high degree of spatial resolution. When we consider finite-element simulation of metal deformation, this equates to thousands or hundreds of thousands of finite elements. Simulations of the dynamic deformations of metal samples require elastic–plastic constitutive updates of the material behavior to be performed over a small time step between updates, as dictated by the Courant condition. Further, numerical integration of physically-based equations is inherently sensitive to the step in time taken; they return different predictions as the time step is reduced, eventually approaching a stationary solution. Depending on the deformation conditions, this converged time step becomes short (10⁻⁹ s or less). If an implicit constitutive update is applied to this class of simulation, the benefit of the implicit update (i.e., the ability to evaluate over a relatively large time step) is negated, and the integration is prohibitively slow. The present work recasts an implicit update algorithm into an explicit form, for which each update step is five to six times faster, and the compute time required for a plastic update approaches that needed for a fully-elastic update. For dynamic loading conditions, the explicit model is found to perform an entire simulation up to 50 times faster than the implicit model. The performance of the explicit model is enhanced by adding a subcycling algorithm to the explicit model, by which the maximum time step between constitutive updates is increased an order of magnitude. These model improvements do not significantly change the predictions of the model from the implicit form, and provide overall computation times significantly faster than the implicit form over finite-element meshes. These modifications are also applied to polycrystals via Taylor averaging, where we also see improved model performance.     

Multiscale simulation of viscoelastic free surface flows

A micro–macro approach based on combining the Brownian configuration fields (BCF) method [M.A. Hulsen, A.P.G. van Heel, B.H.A.A. van den Brule, Simulation of viscoelastic flow using Brownian configuration fields, J. Non-Newtonian Fluid Mech. 70 (1997) 79–101] with an Arbitrary Lagrangian–Eulerian (ALE) Galerkin finite element method, using elliptic mesh generation equations coupled with time-dependent conservation equations, is applied to study slot coating flows of polymer solutions. The polymer molecules are represented by dumbbells with both linear and non-linear springs; hydrodynamic interactions between beads are incorporated. Calculations with infinitely extensible (Hookean) and pre-averaged finitely extensible (FENE-P) dumbbell models are performed and compared with equivalent closed-form macroscopic models in a conformation tensor based formulation [M. Pasquali, L.E. Scriven, Free surface flows of polymer solutions with models based on the conformation tensor, J. Non-Newtonian Fluid Mech. 108 (2002) 363–409]. The BCF equation for linear dumbbell models is solved using a fully implicit time integration scheme which is found to be more stable than the explicit Euler scheme used previously to compute complex flows. We find excellent agreement between the results of the BCF based formulation and the macroscopic conformation tensor based formulation. The computations using the BCF approach are stable at much higher Weissenberg numbers, (where λ is the characteristic relaxation time of polymer, and is the characteristic rate of strain) compared to the purely macroscopic conformation tensor based approach, which fail beyond a maximum Wi. A novel computational algorithm is introduced to compute complex flows with non-linear microscopic constitutive models (i.e. non-linear FENE dumbbells and dumbbells with hydrodynamic interactions) for which no closed-form constitutive equations exist. This algorithm is fast and computationally efficient when compared to both an explicit scheme and a fully implicit scheme involving the solution of the non-linear equations with Newton’s method for each configuration field.     

基于显微CT图像的近场动力学建模与复合材料微结构破坏模拟

随着纤维增强复合材料应用领域的不断扩展且用量激增,亟需理清复合材料微观结构损伤对宏观力学性能影响的内在机制。因此,发展针对纤维增强复合材料微结构破坏过程的建模与高效模拟方法就显得十分重要。本文借助显微CT(Micro-computed Tomography)扫描技术,提出了一种基于显微CT图像中像素点离散的近场动力学建模与模拟方法。一方面,近场动力学作为一种由积分方程建模的非局部理论,便于采用基于空间点离散的数值计算方法,相比传统的连续介质力学能够更有效地模拟材料从连续变形到裂纹萌生与扩展(非连续变形)的全过程。另一方面,对显微CT图像使用像素点灰度阈值分割处理技术,能够快速建立含有复合材料原位微结构信息的空间点离散模型。该离散模型可以直接用于微结构破坏过程的近场动力学模拟,从而避免了传统的数值模拟技术需要依据像素点先建立光滑的几何模型、再划分成有限单元网格的复杂前处理过程,并且极大地保留了复合材料的原位组分分布信息。数值模拟结果表明,基于显微CT图像的近场动力学建模方法能够精确捕捉到复合材料微结构信息,并能准确模拟纤维增强复合材料的微结构破坏过程。     

Multiscale modeling of crack initiation and propagation at the nanoscale

Fracture occurs on multiple interacting length scales; atoms separate on the atomic scale while plasticity develops on the microscale. A dynamic multiscale approach (CADD: coupled atomistics and discrete dislocations) is employed to investigate an edge-cracked specimen of single-crystal nickel, Ni, (brittle failure) and aluminum, Al, (ductile failure) subjected to mode-I loading. The dynamic model couples continuum finite elements to a fully atomistic region, with key advantages such as the ability to accommodate discrete dislocations in the continuum region and an algorithm for automatically detecting dislocations as they move from the atomistic region to the continuum region and then correctly “converting” the atomistic dislocations into discrete dislocations, or vice-versa. An ad hoc computational technique is also applied to dissipate localized waves formed during crack advance in the atomistic zone, whereby an embedded damping zone at the atomistic/continuum interface effectively eliminates the spurious reflection of high-frequency phonons, while allowing low-frequency phonons to pass into the continuum region.The simulations accurately capture the essential physics of the crack propagation in a Ni specimen at different temperatures, including the formation of nano-voids and the sudden acceleration of the crack tip to a velocity close to the material Rayleigh wave speed. The nanoscale brittle fracture happens through the crack growth in the form of nano-void nucleation, growth and coalescence ahead of the crack tip, and as such resembles fracture at the microscale. When the crack tip behaves in a ductile manner, the crack does not advance rapidly after the pre-opening process but is blunted by dislocation generation from its tip. The effect of temperature on crack speed is found to be perceptible in both ductile and brittle specimens.     

Multiscale modeling of oriented thermoplastic elastomers with lamellar morphology

Thermoplastic elastomers (TPEs) are block copolymers made up of “hard” (glassy or crystalline) and “soft” (rubbery) blocks that self-organize into “domain” structures at a length scale of a few tens of nanometers. Under typical processing conditions, TPEs also develop a “polydomain” structure at the micron level that is similar to that of metal polycrystals. Therefore, from a continuum point of view, TPEs may be regarded as materials with heterogeneities at two different length scales. In this work, we propose a constitutive model for highly oriented, near-single-crystal TPEs with lamellar domain morphology. Based on small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) observations, we consider such materials to have a granular microstructure where the grains are made up of the same, perfect, lamellar structure (single crystal) with slightly different lamination directions (crystal orientations). Having identified the underlying morphology, the overall finite-deformation response of these materials is determined by means of a two-scale homogenization procedure. Interestingly, the model predictions indicate that the evolution of microstructure—especially the rotation of the layers—has a very significant, but subtle effect on the overall properties of near-single-crystal TPEs. In particular, for certain loading conditions—namely, for those with sufficiently large compressive deformations applied in the direction of the lamellae within the individual grains—the model becomes macroscopically unstable (i.e., it loses strong ellipticity). By keeping track of the evolution of the underlying microstructure, we find that such instabilities can be related to the development of “chevron” patterns.     

Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics

A computational method (CADD) is presented whereby a continuum region containing dislocation defects is coupled to a fully atomistic region. The model is related to previous hybrid models in which continuum finite elements are coupled to a fully atomistic region, with two key advantages: the ability to accomodate discrete dislocations in the continuum region and an algorithm for automatically detecting dislocations as they move from the atomistic region to the continuum region and then correctly “converting” the atomistic dislocations into discrete dislocations, or vice-versa. The resulting CADD model allows for the study of 2d problems involving large numbers of defects where the system size is too big for fully atomistic simulation, and improves upon existing discrete dislocation techniques by preserving accurate atomistic details of dislocation nucleation and other atomic scale phenomena. Applications to nanoindentation, atomic scale void growth under tensile stress, and fracture are used to validate and demonstrate the capabilities of the model.     

Lagrangian and Hamiltonian formalisms for coupled higher-order elements: theory,modeling, simulation

Nonlinear Dynamics - In this work, the definition of the constitutive relation of a classical higher-order two-terminal element from Chua’s table is extended to the coupled element. The way...     

Mesoscopic modeling of Acoustic Emission through an energetic approach

The aim of the present work is to present a simple model for damage progression and Acoustic Emission that correctly accounts for energy dissipation due to the formation of micro-cracks and the creation of surfaces in a material undergoing external loading, and thus to derive the scaling behaviour observed in experiments. To do this, energy balance considerations are included in a Fibre Bundle Model approach. The model predictions are first illustrated in a uniaxial test under quasistatic loading conditions. Numerical results are then compared to experimental data relative to tests on masonry elements of various sizes subjected compression. The scaling properties of Acoustic Emission under the chosen energy balance assumptions is analyzed and compared to previous numerical and experimental results in the literature. Power-law scaling behaviour is found with respect to specimen dimensions.     

Multiscale modeling of the dynamics of solids at finite temperature

We develop a general multiscale method for coupling atomistic and continuum simulations using the framework of the heterogeneous multiscale method (HMM). Both the atomistic and the continuum models are formulated in the form of conservation laws of mass, momentum and energy. A macroscale solver, here the finite volume scheme, is used everywhere on a macrogrid; whenever necessary the macroscale fluxes are computed using the microscale model, which is in turn constrained by the local macrostate of the system, e.g. the deformation gradient tensor, the mean velocity and the local temperature. We discuss how these constraints can be imposed in the form of boundary conditions. When isolated defects are present, we develop an additional strategy for defect tracking. This method naturally decouples the atomistic time scales from the continuum time scale. Applications to shock propagation, thermal expansion, phase boundary and twin boundary dynamics are presented.     

Non-smooth dynamic modeling and simulation of an unmannedbicycle on a curved pavement

The non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground.According to the Carvallo-Whipple configuration,the unmanned bicycle is reduced to four rigid bodies,namely,rear wheel,rear frame,front fork,and front wheel,which are connected by perfect revolute joints.The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point,and these forces are described by the Hunt-Crossley contact force model and the Lu Gre friction force model,respectively.According to the characteristics of flat and curved pavements,calculation methods for contact forces and their generalized forces are presented.The dynamics of the system is modeled by the Lagrange equations of the first kind,a numerical solution algorithm of the dynamic equations is presented,and the Baumgarte stabilization method is used to restrict the drift of the constraints.The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies.The feasibility of the proposed model is demonstrated by simulations under different motion states.     

Multiscale simulation of material removal processes at the nanoscale

A dynamic multiscale simulation method has been used to study the nanoscale material removal processes for single crystals. The model simultaneously captures the atomistic mechanisms during material removal from the free surface and the long-range mobility of dislocations and their interactions without the computational cost of full atomistic simulations. The method also permits the simulation of system sizes that are approaching experimentally accessibly systems, albeit in 2D. Simulations are performed on single crystal aluminum to study the atomistic details of material removal, chip formation, surface evolution, and generation and propagation of dislocations for a wide range of tool speeds (20-800 m/s) at room temperature. The results from these simulations demonstrate the power of the developed method in capturing both long-range dislocation plasticity and short-range atomistic phenomena during tool advance. In addition, we have investigated the effect of the scratching depth during the material removal process. Fluctuations of scratching tangential force are related to dislocation generation events during the material removal process. A transition from dislocation generation and glides at lower tool speeds to localized amorphization at high tool speeds is found to give rise to an optimal tool speed for low cutting forces.