Local homogenization in modeling of heterogeneous materials (original) (raw)

Two-step homogenization of asphalt mixtures

High Performance Structures and Materials IV, 2008

A novel approach to the prediction of nonlinear macroscopic response of asphalt mixtures is presented. It combines well established first order homogenization method and a concept of so called statistically equivalent periodic unit cell. Such a unit cell allows us to take into account a real microstructure of asphalt mixture when searching for the estimates of nonlinear macroscopic response. To that end the Fast Fourier Transform methods is examined. To enhance feasibility of the solution of the underlying nonlinear problem a two-step homogenization procedure is proposed. Several numerical examples are presented to show applicability of the proposed approach.

Importance of Heterogeneity in Asphalt Pavement Modeling

Common practice overlooks the highly heterogeneous nature of asphalt concrete (AC). Doing so equates to disregarding the effect of material properties' spatial variability on the field behavior of AC mixtures. This paper presents an alternative computational approach to assess the effect of AC heterogeneity on the performance of a pavement structure. Using finite elements, a three-dimensional, flexible pavement structure is subjected to a moving load. Each time the structure is modeled, a unique internal distribution of mechanical properties is assigned to the AC layer. Thus, several simulations of the pavement structure are prepared, modeling a different AC layer each time. Two sets of pavement structures were simulated, considering mechanical properties of the AC layer as having two levels of variability (intermediate and high). The results present qualitative and quantitative estimates of the actual effect of material spatial variability (i.e., the heterogeneity of material properties) on the performance of a flexible pavement structure via strain analyses. The results also highlight the importance of consistency and quality in AC compaction.

Computational Microstructure Modeling of Asphalt Mixtures

2011

Computational microstructure models have been actively pursued by the pavement mechanics community as a promising and advantageous alternative to limited analytical and semi-empirical modeling approaches. The primary goal of this research is to develop a ...

Macroscopic Constitutive Law for Mastic Asphalt Mixtures from Multiscale Modeling

International Journal for Multiscale Computational Engineering, 2010

A well established framework of an uncoupled hierarchical modeling approach is adopted here for the prediction of macroscopic material parameters of the Generalized Leonov (GL) constitutive model intended for the analysis of flexible pavements at both moderate and elevated temperature regimes. To that end, a recently introduced concept of a statistically equivalent periodic unit cell (SEPUC) is addressed to reflect a real microstructure of Mastic Asphalt mixtures (MAm). While mastic properties are derived from an extensive experimental program, the macroscopic properties of MAm are fitted to virtual numerical experiments performed on the basis of first order homogenization scheme. To enhance feasibility of the solution of the underlying nonlinear problem a two-step homogenization procedure is proposed. Here, the effective material properties are first found for a mortar phase, a composite consisting of a mastic matrix and a fraction of small aggregates. These properties are then introduced in place of the matrix in actual unit cells to give estimates of the model parameters on macroscale. Comparison with the Mori-Tanaka predictions is also provided suggesting limitations of classical micromechanical models.

A material model of asphalt mixtures based on Monte Carlo simulations

Nucleation and Atmospheric Aerosols, 2019

The paper aims to numerically reflect mineral-asphalt mixture structure by a standard FEM software. Laboratory test results are presented due to bending tests of circular notched elements. The result scatter is relatively high. An attempt was made to form a random aggregate distribution in order to obtain various results corresponding to laboratory tests. The material structure calibration, its homogenization and finite element dimensioning are the issues decisive for the objective mixture description. The representative volume element (RVE) is investigated here, while it does not precisely reflect the material structure it displays relevant global material parameters. The simulation procedure applied here makes it possible to introduce the name of Monte Carlo simulation-based constitutive model.

Modelling of Pavement Materials –Numerical and Experimental Aspects

Results of an extensive experimental and numerical research project on the response of Asphalt Concrete (AC) are presented. In the projects a material model for AC is being developed and implemented in the Finite Elements package CAPA-3D. Also, the test set-ups, instrumentation and test procedures necessary to characterise the material and determine the model parameters were developed. In an early stage of the project it was recognised that failure in tension and compression followed a different mechanism and needed to be described separately in order to capture the response to alternating loads. From the results of uniaxial tension tests it became apparent that also in tension a pronounced non-linearity occurred prior to the peak load. The adaptations necessary to incorporate this in the model are presented in this paper. The response predicted by the model relations is compared to that observed in laboratory tests to validate the model relations and it can be seen that the observed behaviour is described quite well by the model.

Microstructural Simulation of Asphalt Materials: Modeling and Experimental Studies

Journal of Materials in Civil Engineering, 2004

Asphalt concrete is a heterogeneous material composed of aggregates, binder cement, and air voids, and may be described as a cemented particulate system. The load carrying behavior of such a material is strongly related to the local load transfer between aggregate particles, and this is taken as the microstructural response. Simulation of this material behavior was accomplished using a finite element technique, which was constructed to simulate the micromechanical response of the aggregate/binder system. The model incorporated a network of special frame elements with a stiffness matrix developed to predict the load transfer between cemented particles. The stiffness matrix was created from an approximate elasticity solution of the stress and displacement field in a cementation layer between particle pairs. A damage mechanics approach was then incorporated with this solution, and this lead to the construction of a softening model capable of predicting typical global inelastic behaviors found in asphalt materials. This theory was then implemented within the ABAQUS finite element analysis code to conduct simulations of particular laboratory specimens. Experimental verification of the elastic response has included tests on specially prepared cemented particulate systems, which allowed detailed measurement of aggregate displacements and rotations using video imaging and computer analysis. Model simulations compared favorably with these experimental results. Additional simulations including inelastic behavior of laboratory indirect tension tests have been conducted, and while preliminary in nature these results also compared well with experimental data.

Computational microstructure modeling of asphalt mixtures subjected to rate-dependent fracture

2015

Computational microstructure models have been actively pursued by the pavement mechanics community as a promising and advantageous alternative to limited analytical and semi-empirical modeling approaches. The primary goal of this research is to develop a computational microstructure modeling framework that will eventually allow researchers and practitioners of the pavement mechanics community to evaluate the effects of constituents and mix design characteristics (some of the key factors directly affecting the quality of the pavement structures) on the mechanical responses of asphalt mixtures. To that end, the mixtures are modeled as heterogeneous materials with inelastic mechanical behavior. To account for the complex

Three-Dimensional Discrete Element Models for Asphalt Mixtures

The main objective of this paper is to develop three-dimensional ͑3D͒ microstructure-based discrete element models of asphalt mixtures to study the dynamic modulus from the stress-strain response under compressive loads. The 3D microstructure of the asphalt mixture was obtained from a number of two-dimensional ͑2D͒ images. In the 2D discrete element model, the aggregate and mastic were simulated with the captured aggregate and mastic images. The 3D models were reconstructed with a number of 2D models. This stress-strain response of the 3D model was computed under the loading cycles. The stress-strain response was used to predict the asphalt mixture's stiffness ͑modulus͒ by using the aggregate and mastic stiffness. The moduli of the 3D models were compared with the experimental measurements. It was found that the 3D discrete element models were able to predict the mixture moduli across a range of temperatures and loading frequencies. The 3D model prediction was found to be better than that of the 2D model. In addition, the effects of different air void percentages and aggregate moduli to the mixture moduli were investigated and discussed.