Simulated Micromechanical Models Using Artificial Neural Networks

A new method, termed simulated micromechanical models using artificial neural networks (MMANN), is proposed to generate micromechanical material models for nonlinear and damage behavior of heterogeneous materials. Artificial neural networks (ANN) are trained with results from detailed nonlinear finite-element (FE) analyses of a repeating unit cell (UC), with and without induced damage, e.g., voids or cracks between the fiber and matrix phases. The FE simulations are used to form the effective stress-strain response for a unit cell with different geometry and damage parameters. The FE analyses are performed for a relatively small number of applied strain paths and damage parameters. It is shown that MMANN material models of this type exhibit many interesting features, including different tension and compression response, that are usually difficult to model by conventional micromechanical approaches. MMANN material models can be easily applied in a displacement-based FE for nonlinear analysis of composite structures. Application examples are shown where micromodels are generated to represent the homogenized nonlinear multiaxial response of a unidirectional composite with and without damage. In the case of analysis with damage growth, thermodynamics with irreversible processes (TIP) is used to derive the response of an equivalent homogenized damage medium with evolution equations for damage. The proposed damage formulation incorporates the generalizations generated by the MMANN method for stresses and other possible responses from analysis results of unit cells with fixed levels of damage.     

Prediction of Damage Behaviors in Asphalt Materials Using a Micromechanical Finite-Element Model and Image Analysis

A study of the micromechanical damage behavior of asphalt concrete is presented. Asphalt concrete is composed of aggregates, mastic cement, and air voids, and its load carrying behavior is strongly related to the local microstructural load transfer between aggregate particles. Numerical simulation of this micromechanical behavior was accomplished by using a finite-element model that incorporated the mechanical load-carrying response between aggregates. The finite-element scheme used a network of special frame elements each with a stiffness matrix developed from an approximate elasticity solution of the stress and displacement field in a cementation layer between particle pairs. Continuum damage mechanics was then incorporated within this solution, leading to the construction of a microdamage model capable of predicting typical global inelastic behavior found in asphalt materials. Using image processing and aggregate fitting techniques, simulation models of indirect tension, and compression samples were generated from surface photographic data of actual laboratory specimens. Model simulation results of the overall sample behavior and evolving microfailure/fracture patterns compared favorably with experimental data collected on these samples.     

Viscoelastic Modeling and Field Validation of Flexible Pavements

The objective of this study was to characterize hot-mix asphalt (HMA) viscoelastic properties at intermediate and high temperatures and to incorporate laboratory-determined parameters into a three-dimensional finite element (FE) model to accurately simulate pavement responses to vehicular loading at different temperatures and speeds. Results of the developed FE model were compared against field-measured pavement responses from the Virginia Smart Road. Results of this analysis indicated that the elastic theory grossly underpredicts pavement responses to vehicular loading at intermediate and high temperatures. In addition, the elastic FE model could not simulate permanent deformation or delayed recovery, a known characteristic of HMA materials. In contrast, results of the FE viscoelastic model were in better agreement with field measurements. In this case, the average error in the prediction was less than 15%. The FE model successfully simulated retardation of the response in the transverse direction and rapid relaxation of HMA in the longitudinal direction. Moreover, the developed model allowed predicting primary rutting damage at the surface and its partial recovery after load application.     

Prediction of Creep Stiffness of Asphalt Mixture with Micromechanical Finite-Element and Discrete-Element Models

This study presents micromechanical finite-element (FE) and discrete-element (DE) models for the prediction of viscoelastic creep stiffness of asphalt mixture. Asphalt mixture is composed of graded aggregates bound with mastic (asphalt mixed with fines and fine aggregates) and air voids. The two-dimensional (2D) microstructure of asphalt mixture was obtained by optically scanning the smoothly sawn surface of superpave gyratory compacted asphalt mixture specimens. For the FE method, the micromechanical model of asphalt mixture uses an equivalent lattice network structure whereby interparticle load transfer is simulated through an effective asphalt mastic zone. The ABAQUS FE model integrates a user material subroutine that combines continuum elements with viscoelastic properties for the effective asphalt mastic and rigid body elements for each aggregate. An incremental FE algorithm was employed in an ABAQUS user material model for the asphalt mastic to predict global viscoelastic behavior of asphalt mixture. In regard to the DE model, the outlines of aggregates were converted into polygons based on a 2D scanned mixture microstructure. The polygons were then mapped onto a sheet of uniformly sized disks, and the intrinsic and interface properties of the aggregates and mastic were assigned for the simulation. An experimental program was developed to measure the properties of sand mastic for simulation inputs. The laboratory measurements of the mixture creep stiffness were compared with FE and DE model predictions over a reduced time. The results indicated both methods were applicable for mixture creep stiffness prediction.     

3D FE Analysis of Thermal Behavior of Billet in Rod and Wire Hot Continuous Rolling Process

 An FE model was developed to study thermal behavior during the rod and wire hot continuous rolling process. The FE code MSCMarc was used in the simulation using implicit static arithmetic. The whole rolling process of 30 passes was separated and simulated with several continuous 3D elastic plastic FE models. A rigid pushing body and a data transfer technique were introduced into this model. The on line experiments were conducted on 304 stainless steel and GCr15 steel hot continuous rolling process to prove the results of simulation by implicit static FEM. The results show that the temperature results of finite element simulations are in good agreement with experiments, which indicate that the FE model developed in this study is effective and efficient.     

Unified DSC Constitutive Model for Pavement Materials with Numerical Implementation

Need for unified and mechanistic constitutive models for pavement materials for evaluation of various distresses has been recognized; however, such models are not yet available. There have been efforts to develop unified models; however, they have been based usually on ad hoc combinations of models for special properties such as elastic, plastic, creep and fracture, often without appropriate connections to various coupled responses of bound and unbound materials, they may result and in a large number of parameters, often without physical meanings. The disturbed state concept (DSC) provides a modeling approach that includes various responses such as elastic, plastic, creep, microcracking and fracture, softening and healing under mechanical and environmental (thermal, moisture, etc.) within a single unified and coupled framework. A brief review is presented to identify the advantages of the DSC compared to other available models. The DSC has been validated and applied to a wide range of materials: geologic, asphalt, concrete, ceramic, metal alloys, and silicon. It allows for evaluation of various distresses such as permanent deformations (rutting), microcracking and fracture, reflection cracking, thermal cracking, and healing. The DSC is implemented in two- and three-dimensional finite-element (FE) procedures, which allow static, repetitive, and dynamic loads including elastic, plastic, creep, microcracking leading to fracture and failure. A number of examples are solved for various distresses considering flexible (asphalt) pavements; however, the DSC model is applicable to rigid (concrete) pavements also. It is felt that the DSC and the FE computer programs provide unique and novel approaches for pavement engineering. It is desirable to perform further research and applications including validation with respect to simulated and field behavior of pavements.     

Viscoelastic Model for Discrete Element Simulation of Asphalt Mixtures

This paper presents a viscoelastic model of asphalt mixtures with the discrete element method, where the viscoelastic behaviors of asphalt mastics (fine aggregates, fines, and asphalt binder) are represented by a Burger’s model. Aggregates are simulated with irregular shape particles consisting of balls bonded together by elastic contact models, and the interplaces between aggregates are filled with balls bonded with viscoelastic Burger’s model to represent asphalt mastic. Digital samples were prepared with the image analysis technique. The micromechanical model was developed with four constitutive laws to represent the interactions at contacts of discrete elements (balls) within an aggregate, within mastic, between an aggregate and mastic, and between two adjacent aggregates. Each of these constitutive laws consists of three parts: a stiffness model, a slip model, and a bonding model in order to provide a relationship between the contact force and relative displacement and also in order to describe slipping and tensile strength at a particular contact. The relationship between the microscale model input and macroscale material properties was derived, and an iterative procedure was developed to fit the dynamic modulus test data of asphalt mastic with Burger’s model. The favorable agreement between the discrete element prediction and the lab results on dynamic moduli and phase angles indicates that the viscoelastic discrete element model developed in this study is very capable of simulating constitutive behavior of asphalt mixtures.     

Suitability of Micromechanical Model for Elastic Analysis of Masonry

A micromechanical model is proposed for determining the overall linear elastic mechanical properties of simple-texture brick masonry. The model, originally developed for long-fiber composites, relies on the exact solution due to Eshelby and describes brickwork as a mortar matrix with insertions of elliptical cylinder-shaped bricks. Macroscopic elastic constants are derived from the mechanical properties of the constituent materials and phase volume ratios. Conformity of the suggested model to real brickwork behavior has been verified by performing uniaxial compression tests on masonry panels composed of fired bricks and mud mortar. Composite masonry panels of varying phase percentages were then constructed and tested by replacing several of the fired bricks with mud bricks. Comparison of experimental results with theoretical predictions demonstrates that the model is suitable even in the presence of strongly differentiated phases, and is moreover able to predict different behavior as a function of phase concentration. The model fits experimental results more closely than the micromechanical models previously reported in the literature.     

Explicit Finite-Element Analysis of 2024-T3/T351 Aluminum Material under Impact Loading for Airplane Engine Containment and Fragment Shielding

Uncontained aircraft engine failure can cause catastrophic damaging effects to aircraft systems if not addressed in the aircraft design. Mitigating the damaging effects of uncontained engine failure and improving the numerical modeling capability of these uncontained engine events are crucial. In this paper, high strain rate material behavior of one of the most extensively used materials in the aircraft industry is simulated and the results are compared against ballistic impact tests. Ballistic limits are evaluated by utilizing explicit finite-element (FE) simulations based on the corresponding ballistic impact experiments performed at different material thicknesses. LS-DYNA is used as a nonlinear explicit dynamics FE code for the simulations. A Johnson–Cook material model with different sets of parameters is employed as a thermo-viscoplastic material model coupled with a nonlinear equation of state and an accumulated damage evaluation algorithm for the numerical simulations. Predictive performance of the numerical models is discussed in terms of material characterization efforts, material model parameters, mesh sensitivities, and effects of stress triaxiality. It is shown that mesh refinement does not necessarily provide better results for ballistic limit simulations without considering and calibrating these interrelated factors. Moreover, it is shown that current models that can only fit a specific function for damage evaluation as a function of stress triaxiality are not always successful in predicting failure, especially if the state of stress changes significantly.     

Computational Constitutive Model for Predicting Nonlinear Viscoelastic Damage and Fracture Failure of Asphalt Concrete Mixtures

A computational constitutive model was developed to predict damage and fracture failure of asphalt concrete mixtures. Complex heterogeneity and inelastic mechanical behavior are addressed by the model by using finite-element methods and elastic–viscoelastic constitutive relations. Damage evolution due to progressive cracking is represented by randomly oriented interface fracture, which is governed by a newly developed nonlinear viscoelastic cohesive zone model. Computational simulations demonstrate that damage evolution and failure of asphalt concrete mixtures is dependent on the mechanical properties of the mixture. This approach is suitable for the relative evaluation of asphalt concrete mixtures by simply employing material properties and fracture properties of mixture components rather than by performing expensive laboratory tests recursively, which are typically required for continuum damage mechanics modeling.     

Comparative Study on Failure Prediction in Warm Forming Processes of Mg Alloy Sheet by the FEM and Ductile Fracture Criteria

An important concern in metal forming is whether the desired deformation can be accomplished without any failure of the material, even at elevated temperatures. This paper describes the utilization of ductile fracture criteria in conjunction with the finite element (FE) method for predicting the onset of fracture in warm metal working processes of magnesium alloy sheets. The uniaxial tensile tests of AZ31 alloy sheets with a thickness of 3 mm and FE simulations were performed to calculate the critical damage values for three kinds of ductile fracture criteria. The critical damage values for each criterion were expressed as the function of strain rate at various temperatures. In order to find out the best criterion for failure prediction, Erichsen cupping tests under isothermal conditions were carried out at various temperatures and punch velocities. Based on the plastic deformation histories obtained from FE analysis of the Erichsen cupping tests and the critical damage value curves, the initiation time and location of fracture were predicted under bi-axial tensile conditions. As a result, Cockcroft–Latham’s criterion showed good agreement with the experiments.     

A Study of Nonlinear Tire Contact Pressure Effects on HMA Rutting

The Indiana Department of Transportation/Purdue University accelerated pavement testing (APT) facility has been utilized in a number of studies of hot mix asphalt (HMA) rutting performance. The benefit of using APT is that rutting performance can be established in a few days of testing. Finite element (FE) models have been developed for relating APT to in‐service pavement performance. Factors addressed in the models include pavement geometry, boundary conditions, materials, loads, test conditions, and construction variables. Determining the effects of these factors provides a means for better interpreting APT test results and HMA rutting performance. A detailed analysis using 3D and 2D FE has been made of tire/pavement contact pressure effects on rutting. The analyses include tread pattern and constant and varying contact pressure. A creep model is used to represent the HMA time‐dependent material behavior. Based on test data, the material constants in the creep model were back calculated. Results of the FE studies show that the creep model can successfully characterize pavement material behavior through a reasonable approximation of loading and other factors.     

Modelling a Skin-Pass Rolling Process by Means of Data Mining Techniques and Finite Element Method

 An experience is presented using the finite element method (FEM) and data mining (DM) techniques to develop models that can be used to optimize the skin-pass rolling process based on its operating conditions. A FE model based on a real skin-pass process is built and validated. Based on this model, a group of FE models is simulated with different adjustment parameters and with different materials for the sheet; both variables are chosen from pre-set ranges. From all FE model simulations, a database is generated; this database is made up of the above mentioned adjustment parameters, sheet properties and the variables of the process arising from the simulation of the model. Various types of data mining algorithms are used to develop predictive models for each of the variables of the process. The best predictive models can be used to predict experimentally hard-to-measure variables (internal stresses, internal strains, etc) which are useful in the optimal design of the process or to be applied in real time control systems of a skin-pass process in-plant.     

Directionally Constrained Viscoplasticity for Metal Matrix Composites

A theoretical framework along with an experimental comparison and numerical simulation is presented, for the modeling of the viscoplastic behavior of metal matrix composites (MMCs). MMCs are finding increasing applications in aerospace structures. MMCs have strong directional properties that directly influence the evolution of the internal variables, namely, the backstress and viscoplastic strain. The model is developed within a micromechanical framework for MMCs using the equilibrium surface approach. The directional properties of MMCs are incorporated by proposing a constrained equilibrium surface, which is based on the constrained stress terms proposed. The micromechanical framework combines the viscoplastic properties of the matrix with the elastic properties of the fiber. Model-generated experimental comparisons and simulations are also presented.     

Damage Modeling of Saturated Rocks in Drained and Undrained Conditions

A new anisotropic damage model is proposed to describe the mechanical and poromechanical behavior of brittle rocks in drained and undrained conditions. Although phenomenological, the model is based on physical grounds of micromechanical analysis. Induced damage is represented by a second rank tensor, which is related to the density and orientation of microcracks. Damage evolution is related to propagation of the microcracks. The effective elastic compliance of the damaged material is obtained from a specific form of the Gibbs free enthalpy function. Irreversible damage-related strain due to residual opening of microcracks after unloading is also captured. The originality of our approach is that a poromechanical model of a saturated medium is constructed by extension of the mechanical model for dry material using micromechanical relationships. All the model parameters are determined from triaxial compression tests performed on dry material. The proposed model is applied to coupled poromechanical tests performed on typical brittle rock in saturated conditions. Comparison between test data and numerical simulations shows overall good agreement. The model proposed is able to describe the main features of poromechanical behavior related to microcracks induced in brittle geomaterials.     

Damage Theory Based on Composite Mechanics

A new theory of composite damage mechanics is developed. A material with damage is considered as a composite comprised of two different phases (called matrix and inclusion). Both phases are linearly elastic isotropic materials. The matrix is considered as the intact material, and the inclusion is the damaged material. Three different composite models, Voigt (parallel), Reuss (serial), and generalized self-consistent (spherical), are introduced for three types of damage distributions. These composite models are usually used for initial tangential modulus of a composite material, here we use them for secant modulus of a distressed material. Since the parallel and the serial models represent the upper and lower bounds for stiffness of materials, the composite damage theory obtains the upper and lower bounds for postpeak stress and the level of damage for the material beyond the elastic limit. The spherical model is in between the two bounds. Depending on the “elastic limit” of the inclusion, the theory can be used to describe elastic perfectly plastic behavior, strain hardening, and strain softening. Two different degradations, the linear and exponential degradations of the stress–strain response curve are introduced. The two degradation models are used in two different failure surfaces, i.e., Tresca and Mohr–Coulomb failure surfaces, to predict the postpeak behavior of distressed material.     

Structural Integrity Assessment by Models of Ductile Crack Extension in Sheet Metal

Methods for analytical and numerical simulation of ductile crack extension are used for the prediction of tolerable loads and residual strength of a structure. They cover a wide range from relatively modest phenomenological approaches which allow quick and inexpensive analyses to elaborate micromechanical models, in particular an analytical flaw assessment model, a finite element model which uses the crack tip opening angle as controlling parameter, a cohesive zone model and a ductile damage model. The various phenomenological and micro‐mechanical models constitute elements of an overall concept of damage analysis designated as Structural Integrity Assessment Method (SIAM). The contribution gives an overview over the respective concepts and equations and explains the application of these models by examples of numerical simulations of crack extension in metal sheets. The models are compared with respect to their capabilities, advantages, limitations and drawbacks.