Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks

Multiscale computational techniques play a major role in solving problems related to viscoelastic composites due to the complexities inherent to these materials. In this paper, a numerical procedure for multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks is proposed in which the (global scale) homogenized viscoelastic incremental constitutive equations have the same form as the local‐scale viscoelastic incremental constitutive equations, but the homogenized tangent constitutive tensor and the homogenized incremental history‐dependent stress tensor at the global scale depend on the amount of damage accumulated at the local scale. Furthermore, the developed technique allows the computation of the full anisotropic incremental constitutive tensor of viscoelastic solids containing evolving cracks (and other kinds of heterogeneities) by solving the micromechanical problem only once at each material point and each time step. The procedure is basically developed by relating the local‐scale displacement field to the global‐scale strain tensor and using first‐order homogenization techniques. The finite element formulation is developed and some example problems are presented in order to verify the approach and demonstrate the model capabilities. Copyright © 2009 John Wiley & Sons, Ltd.     

A two-way coupled multiscale model for predicting damage-associated performance of asphaltic roadways

This paper presents a quasi-static multiscale computational model with its verification and rational applications to mechanical behavior predictions of asphaltic roadways that are subject to viscoelastic deformation and fracture damage. The multiscale model is based on continuum thermo-mechanics and is implemented using a finite element formulation. Two length scales (global and local) are two-way coupled in the model framework by linking a homogenized global scale to a heterogeneous local scale representative volume element. With the unique multiscaling and the use of the finite element technique, it is possible to take into account the effect of material heterogeneity, viscoelasticity, and anisotropic damage accumulation in the small scale on the overall performance of larger scale structures. Along with the theoretical model formulation, two example problems are shown: one to verify the model and its computational benefits through comparisons with analytical solutions and single-scale simulation results, and the other to demonstrate the applicability of the approach to model general roadway structures where material viscoelasticity and cohesive zone fracture are involved.     

Computational model for predicting nonlinear viscoelastic damage evolution in materials subjected to dynamic loading

Many inelastic solids accumulate numerous cracks before failure due to impact loading, thus rendering any exact solution of the IBVP untenable. It is therefore useful to construct computational models that can accurately predict the evolution of damage during actual impact/dynamic events in order to develop design tools for assessing performance characteristics. This paper presents a computational model for predicting the evolution of cracking in structures subjected to dynamic loading. Fracture is modeled via a nonlinear viscoelastic cohesive zone model. Two example problems are shown: one for model validation through comparison with a one-dimensional analytical solution for dynamic viscoelastic debonding, and the other demonstrates the applicability of the approach to model dynamic fracture propagation in the double cantilever beam test with a viscoelastic cohesive zone.     

Multiscale Toughening Mechanisms in Biological Materials and Bioinspired Designs

Biological materials found in Nature such as nacre and bone are well recognized as light‐weight, strong, and tough structural materials. The remarkable toughness and damage tolerance of such biological materials are conferred through hierarchical assembly of their multiscale (i.e., atomic‐ to macroscale) architectures and components. Herein, the toughening mechanisms of different organisms at multilength scales are identified and summarized: macromolecular deformation, chemical bond breakage, and biomineral crystal imperfections at the atomic scale; biopolymer fibril reconfiguration/deformation and biomineral nanoparticle/nanoplatelet/nanorod translation, and crack reorientation at the nanoscale; crack deflection and twisting by characteristic features such as tubules and lamellae at the microscale; and structure and morphology optimization at the macroscale. In addition, the actual loading conditions of the natural organisms are different, leading to energy dissipation occurring at different time scales. These toughening mechanisms are further illustrated by comparing the experimental results with computational modeling. Modeling methods at different length and time scales are reviewed. Examples of biomimetic designs that realize the multiscale toughening mechanisms in engineering materials are introduced. Indeed, there is still plenty of room mimicking the strong and tough biological designs at the multilength and time scale in Nature.     

A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements

In this article, we develop a dynamic version of the variational multiscale (D‐VMS) stabilization for nearly/fully incompressible solid dynamics simulations of viscoelastic materials. The constitutive models considered here are based on Prony series expansions, which are rather common in the practice of finite element simulations, especially in industrial/commercial applications. Our method is based on a mixed formulation, in which the momentum equation is complemented by a pressure equation in rate form. The unknown pressure, displacement, and velocity are approximated with piecewise linear, continuous finite element functions. To prevent spurious oscillations, the pressure equation is augmented with a stabilization operator specifically designed for viscoelastic problems, in that it depends on the viscoelastic dissipation. We demonstrate the robustness, stability, and accuracy properties of the proposed method with extensive numerical tests in the case of linear and finite deformations.     

高三轴应力条件下粒子填充粘弹性材料的能量耗散

研究了微粒填充粘弹性材料在变形过程中的能量耗散。在高三轴度应力条件下,由于同时考虑了界面脱粘引起的损伤,故能量耗散主要可分为两部分1)由基体材料的粘性性质所引起的粘性耗散功;2)由界面全脱粘所引发的界面粘结能的耗散。结合微损伤演化的规律,在忽略惯性效应的前提下,导出了损伤耗散功的一般表达式。利用Mori-Tanaka平均应力场的概念,提出了一种方便地计算材料中的粘性耗散功的近似方法。在此基础上,计算了材料中的粘性耗散功和损伤耗散功,并讨论了加载速率、界面粘结能、基体材料的松弛时间、平均粒径和粒径分散度等对这两种耗散机制的影响。     

A multiscale model for predicting the viscoelastic properties of asphalt concrete

It is well known that the accurate prediction of long term performance of asphalt concrete pavement requires modeling to account for viscoelasticity within the mastic. However, accounting for viscoelasticity can be costly when the material properties are measured at the scale of asphalt concrete. This is due to the fact that the material testing protocols must be performed recursively for each mixture considered for use in the final design.In this paper, a four level multiscale computational micromechanics methodology is utilized to determine the accuracy of micromechanics versus directly measured viscoelastic properties of asphalt concrete pavement. This is accomplished by first measuring the viscoelastic dynamic modulus of asphalt binder, as well as the elastic properties of the constituents, and this comprised the first scale analysis. In the second scale analysis, the finite element method is utilized to predict the effect of mineral fillers on the dynamic modulus. In the third scale analysis, the finite element method is again utilized to predict the effect of fine aggregates on the dynamic modulus. In the fourth and final scale analysis, the finite element method is utilized to predict the effect of large aggregates on the dynamic modulus of asphalt concrete. This final predicted result is then compared to the experimentally measured dynamic modulus of two different asphalt concretes for various volume fractions of the constituents. Results reveal that the errors in predictions are on the order of 60 %, while the ranking of the mixtures was consistent with experimental results. It should be noted that differences between the “final predicted results” and the experimental results can provide fruitful ground for understanding the effect of interactions not considered in the multiscale approach, most importantly, chemical interactions.     

Locality constraints within multiscale model for non‐linear material behaviour

This paper presents a two‐scale approach for the mechanical and numerical modelling of materials with microstructure‐like concrete or fibre‐reinforced concrete in the non‐linear regime. It addresses applications, where the assumption of scale separation as the basis for classical homogenization methods does not hold. This occurs when the resolution of micro and macro scale does not differ ab initio or when evolving fluctuations in the macro‐fields are in the order of the micro scale during the loading progress. Typical examples are localization phenomena. The objective of the present study is to develop an efficient solution method exploiting the physically existing multiscale character of the problem. The proposed method belongs to the superposition‐based methods with local enrichment of the large‐scale solution ū by a small‐scale part u ′. The main focus of the present formulation is to allow for locality of the small‐scale solution within the large‐scale elements to achieve an efficient solution strategy. At the same time the small‐scale information exchange over the large‐scale element boundaries is facilitated while maintaining the accuracy of a refined complete solution. Thus, the emphasis lies on finding appropriate locality constraints for u ′. To illustrate the method the formulation is applied to a damage mechanics based material model for concrete‐like materials. Copyright © 2006 John Wiley & Sons, Ltd.     

Generalized self-consistent scheme for upscaling of viscoelastic properties of highly-filled matrix-inclusion composites – Application in the context of multiscale modeling of bituminous mixtures

In this paper, a multiscale material model for the prediction of viscous properties of bituminous mixtures is presented. The multiscale model is based on the mix design, i.e., volume fractions of different material phases and the intrinsic viscoelastic material behavior of the latter, making goal-oriented optimization of bituminous mixtures feasible. Previous developments for upscaling of viscoelastic properties of a bitumen/filler-composite (mastic) [Lackner, et al. J Mater Civil Eng 2005; 17 (5): 485–91] and of asphalt [Aigner, et al. J Mater Civil Eng 2009; 21: 771–80] are improved with regards to (i) the employed mode of upscaling, i.e., the way information is transferred from one scale of observation to the next higher scale of observation, and (ii) the underlying micromechanical concept. As regards the latter, the use of the so-called generalized self-consistent scheme, suitable for highly-filled matrix/inclusion-type morphologies, as is the case for asphalt, is proposed. The assessment of the proposed upscaling scheme with respective experimental results indicates the improved suitability of the generalized self-consistent scheme versus the commonly employed (at least for modeling of matrix-inclusion materials) Mori–Tanaka scheme, resulting in a sound representation of test data.     

Multiscale design of a rectangular sandwich plate with viscoelastic core and supported at extents by viscoelastic materials

This work presents a multiscale model of viscoelastic constrained layer damping treatments for vibrating plates/beams. The approach integrates a finite element (FE) model of macroscale vibrations and a micromechanical model to include effects of microscale structure and properties. The FE model captures the shear deformation of the viscoelastic core, rotary inertial effects of all layers, and viscoelastic boundaries of the plate. Comparison with analytical and FE results validates the proposed FE model. A self-consistent (SC) model makes the micro to macro scale transition to approximate the effective behavior a heterogeneous core. Modal damping resulting from the presence of voids and negative stiffness regions in the core material is modeled. Results show that negative stiffness regions in the viscoelastic core material, even at low volume fractions, yield superior macroscopic damping behavior. The coupled SC and FE models provide a powerful multiscale predictive design tool for sandwich beams and plates.     

Model reduction for nonlinear multiscale parabolic problems using dynamic mode decomposition

In this article, a model reduction technique is presented to solve nonlinear multiscale parabolic problems using dynamic mode decomposition. The multiple scales and nonlinearity bring great challenges for simulating the problems. To overcome this difficulty, we develop a model reduction method for the nonlinear multiscale dynamic problems by integrating constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with dynamic mode decomposition (DMD). CEM-GMsFEM has shown great efficiency to solve linear multiscale problems in a coarse space. However, using CEM-GMsFEM to directly solve multiscale nonlinear parabolic models involves dynamically computing the residual and the Jacobian on a fine grid. This may be very computationally expensive because the evaluation of the nonlinear term is implemented in a high-dimensional fine scale space. As a data-driven method, DMD can use observation data and give an explicit expression to accurately describe the underlying nonlinear dynamic system. To efficiently compute the multiscale nonlinear parabolic problems, we propose a CEM-DMD model reduction by combing CEM-GMsFEM and DMD. The CEM-DMD reduced model is a coarsen linear model, which avoids the nonlinear solver in the fine space. It is crucial to judiciously choose observation in DMD. Only proper observation can render an accurate DMD model. In the context of CEM-DMD, we introduce two different observations: fine scale observation and coarse scale observation. In the construction of DMD model, the coarse scale observation requires much less computation than the fine scale observation. The CEM-DMD model using the coarse scale observation gives a complete coarse model for the nonlinear multiscale dynamic systems and significantly improves the computation efficiency. To show the performance of the CEM-DMD using the different observations, we present a few numerical results for the nonlinear multiscale parabolic problems in heterogeneous porous media.     

Micromechanical modelling of bituminous materials’ complex modulus at different length scales

The aim of this work is to establish a multi-scale modelling technique usable in the study of the complex viscoelastic properties of asphalt mixes. This technique is based on a biphasic approach. At each scale, the heterogeneous media is considered as a two-phase material composed of granular inclusions with linear elastic properties and a matrix of bituminous materials exhibiting linear viscoelastic behaviour at small strain values. In this approach, the homogeneous equivalent properties of biphasic composites are transferred from one scale of observation to the next, higher scale of observation. The viscoelastic properties of the matrix and the elastic properties of the aggregates serve as the input parameters for the numerical models. The generalised Maxwell rheological model is used to describe the viscoelastic behaviour of the matrix. Thanks to the rheological properties of bitumen and the elastic properties of the aggregates, the viscoelastic properties of mastic, mortar and hot mix asphalt (HMA) as bituminous composites can be, respectively, estimated using a micromechanical finite element model. Random inclusions of varying sizes and shapes are generated in order to construct the granular skeleton. A cyclic loading was imposed on the top layer of the digital model. The dynamic modulus of the pre-cited bituminous composites, obtained from the presented multi-scale modelling process while passing from the bitumen to the HMA scale, is validated by comparison with experimental measurements when possible. Concerning our results, we have found that at low temperature (?10 °C), the predicted dynamic modulus is satisfactorily comparable to the experimental measurements. On the other hand, an acceptable gap between predicted numerical results and experimental data takes place when the temperature increases.     

Stochastic fracture analysis of cracked structures with random field property using the scaled boundary finite element method

Fracture is one of the most prominent concerns for large scale applications of graphene. In this paper, we review some of the recent progresses in experimental and theoretical studies on the fracture behaviors of graphene, with discussions touching theoretical strength, mode I fracture toughness, mixed mode fracture, chemical fracture, irradiation fracture, dynamic fracture, impact fracture, and sonication fracture. In spite of rapid developments in experiments and simulations, there are still significant yet unresolved issues related to the fracture of graphene, examples including: (1) Can one enhance the toughness of graphene with designed topological defects? (2) How does grain size affect the strength of polycrystalline graphene? (3) How do the out-of-plane effects (e.g., wrinkle caused by external loading or curvature induced by topological defects) influence the fracture of graphene? (4) Can one develop a continuum model with the ability to capture graphene fracture with complicated modes, such as shear fracture coupled with wrinkling deformation and tear fracture? (5) How does fracture occur when tearing a polycrystalline graphene sheet? (6) Can one control the fracture behavior of graphene by combing the chemical, irradiation and stress effect? (7) How fast can cracks propagate in graphene? (8) What is the behavior of interfacial cracks in graphene, i.e., cracks along the grain boundaries or interfaces of heterogeneous structures? (9) How does a multilayer graphene membrane break under high speed impact and why such structures can absorb a large amount of kinetic energy? (10) Can one tailor/design the graphene structures with controlled fracture? The intention here is not to provide complete answers to such questions, but to draw attention from the mechanics community to them as potential research topics.     

Comparing the mechanical performance of synthetic and natural cellular materials

This work compares the mechanical performance of agglomerated cork against synthetic materials typically used as impact energy absorbers. Particularly, the study will focus on the expanded polystyrene (EPS) and expanded polypropylene (EPP).Firstly, quasi-static compression tests are performed in order to assess the energy storage capacity and to characterize the stress–strain behavior cellular materials under study. Secondly, guided drop tests are performed to study the response of these materials when subjected to multiple dynamic loading (two impacts). Thirdly, finite element analysis (FEA) is carried out in order to simulate the compressive behavior of the studied materials under dynamic loading.Results show that agglomerated cork is an excellent alternative to the synthetic materials. Not only for being a natural and sustainable material but also for withstanding considerable impact energies. In addition, its capacity to keep some of its initial properties after loading (regarding mechanical properties and dimensions) makes this material highly desirable for multiple-impact applications.     

Damage evolution and localization in heterogeneous materials under dynamical loading: stochastic modelling

A mathematical model of damage evolution in heterogeneous materials, which takes into account the random nature of local failure, is developed on the basis of the theory of stochastic equations. A damage evolution law, which allows for the energy dissipation due to the new surface formation as well as the influence of local (thermic) fluctuations is obtained. The kinetic differential equation for time-dependent probability distribution of a damage parameter is derived theoretically. Damage evolution and damage localization under dynamical loading are investigated numerically on the basis of the model developed.     

多尺度材料模型研究及应用

在分别介绍宏观,介观,微观,原子和电子尺度材料模型研究的基础上,论述了多尺度材料模型（MMM）这一新兴的跨学科的前沿研究领域产生的前提,概念主其在材料科学,特别是在宏观形变及新断裂过程研究中的重要作用,综合分析了多种跨尺度关联方法的原理,技术方案及其应用,并探讨了当前多尺度研究的热点及进一步发展的方向。     

Generalized viscoelastic designer functionally graded auxetic materials engineered/tailored for specific task performances

For arbitrary linear Kelvin model viscoelastic constitutive relations, generalized analyses based on collocation, least squares, Lagrangean multipliers, calculus of variation and inverse formulations are presented for determining viscoelastic designer material properties tailored and engineered to be best suited for specific boundary and loading conditions and their time histories. Optimum 3-D anisotropic designer materials, including auxetic viscoelastic functionally graded ones, are studied to minimize thermal stresses, creep buckling, creep rates, deflections, aero- and hydro- dynamic noise and static and dynamic aero-viscoelastic effects while concurrently lowering failure probabilities and extending structural survival times and maximizing or minimizing energy dissipation and its rate. The analyses are formulated for single structural elements as well as the entire structure. Extensions to the entire vehicle that incorporate aerodynamics, stability and control are discussed and the dimensions of computational requirements are estimated.     

Study on crack curving and branching mechanism in quasi-brittle materials under dynamic biaxial loading

Attempts are made to analyze the temporal and spatial effect and the complex mechanical behaviors of microcracks and the macro crack at mesoscopic scale based on the damage evolution principle. The mechanism of crack curving and branching in quasi-brittle materials under dynamic biaxial loading is investigated. The effects of different ratios between the load in the horizontal and vertical directions (for convenience, the loading ratio is denoted by B in this paper), crack dip angles and material homogeneity on crack curving and branching are considered. The results indicate that: Crack curving is mainly controlled by the loading ratio, while initiation and propagation of branch microcracks are related to the stress level. The initial dip angle of crack can vary the stress configuration at the crack tip zone. If the loading ratio remains constant, the crack tends to propagate toward the vertical direction with increasing crack dip angle. It is also found that heterogeneity due to defects in the material play an important role in the distribution of tiny voids and cracks in the material and the crack propagation mode. The results in this study are not only in good agreement with the physical test results, but also can provide some valuable reference for studies on the tensile properties and failure modes of heterogeneous quasi-brittle materials with internal defects.