Anisotropic Constitutive Model Research Articles

Anisotropic UH model for soils based on a simple transformed stress method

SummaryA simple method called anisotropic transformed stress (ATS) method is proposed to develop failure criteria and constitutive models for anisotropic soils. In this method, stress components in different directions are modified differently in order to reflect the effect of anisotropy. It includes two steps of mapping of stress. First, a modified stress tensor is introduced, which is a symmetric multiplication of stress tensor and fabric tensor. In the modified stress space, anisotropic soils can be treated to be isotropic. Second, a TS tensor is derived from the modified stress tensor for the convenience of developing anisotropic constitutive models to account for the effect of intermediate principal stress. By replacing the ordinary stress tensor with the TS tensor directly, the unified hardening model is extended to model the anisotropic deformation of soils. Anisotropic Lade's criterion is adopted for shear yield and shear failure in the model. The form of the original model formulations remains unchanged, and the model parameters are independent of the loading direction. Good agreement between the experimental results and predictions of the anisotropic unified hardening model is observed. Copyright © 2016 John Wiley & Sons, Ltd.

Anisotropic constitutive model incorporating multiple damage mechanisms for multiscale simulation of dental enamel

An anisotropic constitutive model is proposed in the framework of finite deformation to capture several damage mechanisms occurring in the microstructure of dental enamel, a hierarchical bio-composite. It provides the basis for a homogenization approach for an efficient multiscale (in this case: multiple hierarchy levels) investigation of the deformation and damage behavior. The influence of tension–compression asymmetry and fiber–matrix interaction on the nonlinear deformation behavior of dental enamel is studied by 3D micromechanical simulations under different loading conditions and fiber lengths. The complex deformation behavior and the characteristics and interaction of three damage mechanisms in the damage process of enamel are well captured. The proposed constitutive model incorporating anisotropic damage is applied to the first hierarchical level of dental enamel and validated by experimental results. The effect of the fiber orientation on the damage behavior and compressive strength is studied by comparing micro-pillar experiments of dental enamel at the first hierarchical level in multiple directions of fiber orientation. A very good agreement between computational and experimental results is found for the damage evolution process of dental enamel.

Constitutive behaviors and mechanical characterizations of fabric reinforced rubber composites

In this paper, the constitutive behaviors and mechanical performance of the reticulated fiber fabric reinforced rubber composites are investigated. Based on the theory of continuum mechanics, the anisotropic constitutive model is proposed to characterize the mechanical properties of the reticulated fabric reinforced rubber composites; then the influences of the reticulated fiber fabric on the mechanical behaviors of the rubber composites and the tubular fabric rubber seals are studied by experiments. Further, both the macroscopic and the microscopic finite element model are built to simulate their mechanical properties, which show a good agreement with the experimental results. The study will provide a theoretical basis and scientific guidance for the optimal design and the properties evaluation of fabric rubber seals.

A phase-field approach to model fracture of arterial walls: Theory and finite element analysis

This study uses a recently developed phase-field approach to model fracture of arterial walls with an emphasis on aortic tissues. We start by deriving the regularized crack surface to overcome complexities inherent in sharp crack discontinuities, thereby relaxing the acute crack surface topology into a diffusive one. In fact, the regularized crack surface possesses the property of Gamma-Convergence, i.e. the sharp crack topology is restored with a vanishing length-scale parameter. Next, we deal with the continuous formulation of the variational principle for the multi-field problem manifested through the deformation map and the crack phase-field at finite strains which leads to the Euler–Lagrange equations of the coupled problem. In particular, the coupled balance equations derived render the evolution of the crack phase-field and the balance of linear momentum. As an important aspect of the continuum formulation we consider an invariant-based anisotropic constitutive model which is additively decomposed into an isotropic part for the ground matrix and an exponential anisotropic part for the two families of collagen fibers embedded in the ground matrix. In addition we propose a novel energy-based anisotropic failure criterion which regulates the evolution of the crack phase-field. The coupled problem is solved using a one-pass operator-splitting algorithm composed of a mechanical predictor step (solved for the frozen crack phase-field parameter) and a crack evolution step (solved for the frozen deformation map); a history field governed by the failure criterion is successively updated. Subsequently, a conventional Galerkin procedure leads to the weak forms of the governing differential equations for the physical problem. Accordingly, we provide the discrete residual vectors and a corresponding linearization yields the element matrices for the two sub-problems. Finally, we demonstrate the numerical performance of the crack phase-field model by simulating uniaxial extension and simple shear fracture tests performed on specimens obtained from a human aneurysmatic thoracic aorta. Model parameters are obtained by fitting the set of novel experimental data to the predicted model response; the finite element results agree favorably with the experimental findings.

Simultaneously Coupled Mechanical-Electrochemical-Thermal Simulation of Lithium-Ion Cells

Understanding the combined electrochemical-thermal and mechanical response of a system has a variety of applications. For instance, such behavior is characterized routinely in reactor design to understand structural failure of components from electrochemical fatigue. In energy storage, the potential induced changes to properties of materials (e.g., swelling or surface oxidation induced fracture) have often been categorized as reliability concerns. For lithium ion batteries, there is the added concern over safety of the system in the event of mechanical failure of the cell components. In this work, we study different mechanical test conditions and examine the interaction between mechanical failure and electrochemical-thermal responses, by developing a simultaneously coupled model. We begin with a model system to demonstrate the steps involved in building the coupling framework and proceed to model a pouch-format cell with explicit representations for each individual component such as the active material, current collector, separator, etc. Anisotropic constitutive material models are presented to describe the mechanical properties of active materials and separator. Some initial results are shown in Figure 1. The model predicts accurately the force-strain response and fracture of battery structure, simulates the local failure of separator layer, and captures the onset of short circuit for lithium-ion battery cell under different test conditions. The difference in the electrochemical response and the implications for follow on chemical reactions under these test conditions are discussed. Acknowledgement This study was supported by Computer Aided Engineering for Batteries (CAEBAT) project of the Vehicle Technologies Office, Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy. The research was performed using computational resources sponsored by the Department of Energy's Office of Energy Efficiency and Renewable Energy, located at the National Renewable Energy Laboratory. Figure 1

A numerical study of isotropic and anisotropic constitutive models with relevance to healthy and unhealthy cerebral arterial tissues

This paper presents an analysis of hyperelastic constitutive models for continuous bodies both from a modeling and numerical point of view. Contributions are made within the context of finite element numerical simulations. Numerical results with relevance to flows in the cardiovascular system are outlined in the case of a sophisticated fluid–structure interaction problem, in specific complex geometries of anatomically accurate cerebral arteries in diseased state. In this regard, the work carefully outlines the numerical validation of constitutive models for healthy and unhealthy cerebral arterial tissues by means of simulations of static inflation tests on an idealized specimen of anterior cerebral artery (ACA). The healthy tissue is described by means of isotropic and anisotropic models that, are fitted with respect to experimental data describing the mechanical behavior of the ACA; the numerical results are presented highlighting the most important numerical aspects influencing the correct and efficient simulation of the mechanics of continuous bodies such as, for instance, the arterial wall. We further consider numerical simulations of unhealthy conditions of the tissue by taking into account different levels of weakening of its mechanical properties. Taking the cerebral cardiovascular system as a challenging test problem, we focus on the study of the effects of the imposed mechanical levels of degradation on kinematic quantities of interest by simulating static inflation tests for the different models. This work does not aim to propose a new mathematical model for the mechanical damage occurring at the onset of cardiovascular diseases such as cerebral aneurysms. The modeling and numerical techniques presented may be applied to a wide range of problems, equally challenging to that of the cardiovascular system with complex structural models and fluid–structure coupling.

Modelling and simulation of the mechanical response of a Dacron graft in the pressurization test and an end-to-end anastomosis

This work presents the modeling and simulation of the mechanical response of a Dacron graft in the pressurization test and its clinical application in the analysis of an end-to-end anastomosis. Both problems are studied via an anisotropic constitutive model that was calibrated by means of previously reported uniaxial tensile tests. First, the simulation of the pressurization test allows the validation of the experimental material characterization that included tests carried out for different levels of axial stretching. Then, the analysis of an end-to-end anastomosis under an idealized geometry is proposed. This case consists in evaluating the mechanical performance of the graft together with the stresses and deformations in the neighborhood of the Dacron with the artery. This research contributes important data to understand the functioning of the graft and the possibility of extending the analysis to complex numerical cases like its insertion in the aortic arch.

Mechanical characterisation of Dacron graft: Experiments and numerical simulation

Experimental and numerical analyses focused on the mechanical characterisation of a woven Dacron vascular graft are presented. To that end, uniaxial tensile tests under different orientations have been performed to study the anisotropic behaviour of the material. These tests have been used to adjust the parameters of a hyperelastic anisotropic constitutive model which is applied to predict through numerical simulation the mechanical response of this material in the ring tensile test. The obtained results show that the model used is capable of representing adequately the nonlinear elastic region and, in particular, it captures the progressive increase of the rigidity and the anisotropy due to the stretching of the Dacron. The importance of this research lies in the possibility of predicting the graft׳s mechanical response under generalized loading such as those that occur under physiological conditions after surgical procedures.

Material modeling of cardiac valve tissue: Experiments, constitutive analysis and numerical investigation

A key element of the cardiac cycle of the human heart is the opening and closing of the four valves. However, the material properties of the leaflet tissues, which fundamentally contribute to determine the mechanical response of the valves, are still an open field of research. The main contribution of the present study is to provide a complete experimental data set for porcine heart valve samples spanning all valve and leaflet types under tensile loading. The tests show a fair degree of reproducibility and are clearly indicative of a number of fundamental tissue properties, including a progressively stiffening response with increasing elongation. We then propose a simple anisotropic constitutive model, which is fitted to the experimental data set, showing a reasonable interspecimen variability. Furthermore, we present a dynamic finite element analysis of the aortic valve to show the direct usability of the obtained material parameters in computational simulations.

A representative-sandwich model for simultaneously coupled mechanical-electrical-thermal simulation of a lithium-ion cell under quasi-static indentation tests

The safety behavior of lithium-ion batteries under external mechanical crush is a critical concern, especially during large-scale deployment. We previously presented a sequentially coupled mechanical-electrical-thermal modeling approach for studying mechanical-abuse-induced short circuit. In this work, we study different mechanical test conditions and examine the interaction between mechanical failure and electrical-thermal responses, by developing a simultaneously coupled mechanical-electrical-thermal model. The present work utilizes a single representative-sandwich (RS) to model the full pouch cell with explicit representations for each individual component such as the active material, current collector, separator, etc. Anisotropic constitutive material models are presented to describe the mechanical properties of active materials and separator. The model predicts accurately the force-strain response and fracture of battery structure, simulates the local failure of separator layer, and captures the onset of short circuit for lithium-ion battery cells under sphere indentation tests with three different diameters. Electrical-thermal responses to the three different indentation tests are elaborated and discussed. Numerical studies are presented to show the potential impact of test conditions on the electrical-thermal behavior of the cell after the occurrence of short circuit.

A first-principles study of cementite (Fe3C) and its alloyed counterparts: Elastic constants, elastic anisotropies, and isotropic elastic moduli

A comprehensive computational study of elastic properties of cementite (Fe3C) and its alloyed counterparts (M3C (M = Al, Co, Cr, Cu, Fe, Hf, Mn, Mo, Nb, Ni, Si, Ta, Ti, V, W, Zr, Cr2FeC and CrFe2C) having the crystal structure of Fe3C is carried out employing electronic density-functional theory (DFT), all-electron PAW pseudopotentials and the generalized gradient approximation for the exchange-correlation energy (GGA). Specifically, as a part of our systematic study of cohesive properties of solids and in the spirit of materials genome, following properties are calculated: (i) single-crystal elastic constants, Cij, of above M3Cs; (ii) anisotropies of bulk, Young’s and shear moduli, and Poisson’s ratio based on calculated Cijs, demonstrating their extreme anisotropies; (iii) isotropic (polycrystalline) elastic moduli (bulk, shear, Young’s moduli and Poisson’s ratio) of M3Cs by homogenization of calculated Cijs; and (iv) acoustic Debye temperature, θD, of M3Cs based on calculated Cijs. We provide a critical appraisal of available data of polycrystalline elastic properties of alloyed cementite. Calculated single crystal properties may be incorporated in anisotropic constitutive models to develop and test microstructure-processing-property-performance links in multi-phase materials where cementite is a constituent phase.

Generalized Lorentz-Lorenz homogenization formulas for binary lattice metamaterials

Generalized Lorentz-Lorenz formulas are developed for the effective parameters of binary lattice metamaterials composed of a periodic arrangement of electric and/or magnetic inclusions. The proposed homogenization approach is based on a dual dipole approximation for the induced currents. The obtained formulas for the metamaterial effective electric and magnetic characteristics duly consider both electric and magnetic polarizabilities of the inclusions and completely describe the effects of frequency and spatial dispersion. Several numerical examples are provided to demonstrate the general applicability of the proposed formulas to different types of binary lattices and inclusions. It is shown that the proposed effective parameters have the capability of providing a physically sound and accurate description of wave propagation in the metamaterials in an extended range of frequencies in contrast to the equivalent parameters that can be defined in the absence of impressed sources and assuming a local anisotropic constitutive model, which hides inherent spatial dispersion effects and nonphysical features. To gain further insight into the metamaterial response and the physical meaningfulness of calculated effective parameters, the power flow of metamaterial supported modes is analyzed and its homogenized representation is compared to the complete description. A correspondence between the power flow due to the microscopic field and the effect of spatial dispersion in the homogenized parameters is established.

Study on Yield Function and Plastic Potential Under Non‐Associated Flow for Accurate Earing Prediction in Cup Drawing

Prediction of more than four ears in a cup drawing process can be successfully achieved by considering r‐value and stress directionalities. Yld2004‐18p based on associated flow rule and Yld2000‐2D based on non‐associated flow rule are the examples. The former, however, is more costly in terms of computational efficiency than the latter. In this work, an anisotropic constitutive model based on non‐associated flow rule which combines two different functions, Hill (1948) and Yld2000‐2d, is implemented to a user defined material model. The accuracy of the anisotropic directionalities (yield stresses and plastic strain ratios) is evaluated. Simulation of a mini‐die cup drawing with a body stock alloy predicted eight ears, in good agreement with the experimental results. The use of Hill (1948) model for the yield function and Yld2000‐2d for plastic potential under the framework of non‐associated flow rule led to accurate prediction of up to eight ears at the lower computational cost.

Constitutive modeling of human saphenous veins at overloading pressures

In the present study, inflation tests with free axial extension of 15 human vena saphena magna were conducted ex vivo to obtain data suitable for multi-axial constitutive modeling at overloading conditions (pressures up to approximately 15kPa). Subsequently the data were fitted with a hyperelastic, nonlinear and anisotropic constitutive model based on the theory of the closed thick-walled tube. It was observed that initial highly deformable behavior (up to approximately 2.5kPa) in the pressure–circumferential stretch response is followed by progressive large strain stiffening. Contrary to that, samples were much stiffer in longitudinal direction, where the observed stretches were in the range 0.98–1.03 during the entire pressurization in most cases. The effect of possible residual stress was evaluated in a simulation of the intramural stress distribution with the opening angle prescribed to 0°, 10°, 20°, 30°, 40°, and 50°. The result suggests that the optimal opening angle making the stress distribution through the wall thickness uniform is about 40°. The material parameters presented here are suitable for use in mechanobiological simulations describing the adaptation of the autologous vein wall after bypass surgery.

Anisotropic Constitutive Model for Predictive Analysis of Composite Laminates

An anisotropic plastic constitutive model for fiber-reinforced composite material, is developed, which is simple and efficient to be implemented into computer program for a predictive analysis procedure of composite laminates. An anisotropic initial yield criterion, as well as work-hardening model and subsequent yield surface are established that includes the effects of different yield strengths in each material direction, and between tension and compression. The current model is implemented into a computer code, which is Predictive Analysis for Composite Structures (PACS). The accuracy and efficiency of the anisotropic plastic constitutive model and the computer program PACS are verified by solving a number of various fiber-reinforced composite laminates. The comparisons of the numerical results to the experimental and other numerical results available in the literature indicate the validity and efficiency of the developed model. Keywords: Anisotropic Plasticity, Fiber Composite, Predictive Finite Element Analysis

Simplified Anisotropic Plasticity Model for Analyzing the Postyield Behavior of Cold-Formed Sheet-Metal Shear Panel Structures

AbstractA simplified anisotropic constitutive model for orthotropic metal sheets is developed herein to analyze the off-axial stress-strain response of cold-formed metal sheets, where the material plastic anisotropy is induced by work hardening during the forming process. Hill’s 1948 anisotropic yield criterion is used to determine the material initial yielding, and the strain hardening is modeled using a mixed kinematic-isotropic hardening law along with constantly changing material principal directions as a result of the off-axial plastic loading. The isotropic hardening parameters were expressed using Fourier series and are functions of the loading directions. The expression of hardening parameters using Fourier series allows the model to be adaptively calibrated to the current state of stress using as few as three sets of off-axial stress-strain data. The proposed model is able to predict the direction-dependent strain hardening behavior of orthotropic metal sheets, as well as account for the progress...

A New Model for the Cross Anisotropic Nonlinear Elastic Behavior of Unbounded Soils for Road Pavements

This study presents a new generalized small strain nonlinear anisotropic constitutive model for use in the elastic analysis of unbounded soils for road pavements. The model rests on a method to determine the cross anisotropic moduli of unbounded soils based on the classic repeated-load triaxial compression test. The model incorporates nonlinear small-strain behavior in a triaxial stress space by considering the inter-dependency of the bulk K*, shear G* and cross anisotropic modulus, J. In agreement with the laboratory test results the moduli, at a given water content, are dependent on the initial state of stress in p–q space. The model is derived by considering pure isothermal elastic behavior and by letting the net elastic work per unit volume along a closed stress path equal to zero. An approximate stress–strain curve, using solely the non linear constitutive model, is obtained using a linear analysis that simulates a typical triaxial test. Finally a non linear finite element analysis, which incorporates the non linear constitutive model, is carried out to provide a more elaborate assessment of model performance.

Experimental Study of Isotropic and Anisotropic Constitutive Models

AbstractThis paper analyzes the validity of the yield surface and flow rule of several isotropic and anisotropic constitutive models. These aspects are studied based on drained triaxial tests, with a number of different stress paths in a computer-controlled stress path cell. The Cam clay, modified Cam clay, and p-q-θ models are used to study the isotropic behavior, whereas the anisotropic conditions are analyzed using the Melanie, MIT-E3, and S-CLAY1 models. Both under the isotropic and anisotropic conditions, the results indicate that the surface described by the undrained effective stress path is suitable for simulating the yield and plastic potential surfaces. In terms of isotropic behavior, the p-q-θ model is the most suitable for predicting the yield, whereas the plastic potential function is closely simulated by the yield function of the modified Cam clay model. For the anisotropic models studied, the MIT-E3 model provides a better approximation of the anisotropic behavior of the Santa Clara clay.

Biaxial mechanical properties of the human thoracic and abdominal aorta, common carotid, subclavian, renal and common iliac arteries

The biomechanics of large- and medium-sized arteries influence the pathophysiology of arterial disease and the response to therapeutic interventions. However, a comprehensive comparative analysis of human arterial biaxial mechanical properties has not yet been reported. Planar biaxial extension was used to establish the passive mechanical properties of human thoracic (TA, [Formula: see text]) and abdominal (AA, [Formula: see text]) aorta, common carotid (CCA, [Formula: see text]), subclavian (SA, [Formula: see text]), renal (RA, [Formula: see text]) and common iliac (CIA, [Formula: see text]) arteries from 11 deceased subjects ([Formula: see text]years old). Histological evaluation determined the structure of each specimen. Experimental data were used to determine constitutive parameters for a structurally motivated nonlinear anisotropic constitutive model. All arteries demonstrated appreciable anisotropy and large nonlinear deformations. Most CCA, SA, TA, AA and CIA specimens were stiffer longitudinally, while most RAs were stiffer circumferentially. A switch in anisotropy was occasionally demonstrated for all arteries. The CCA was the most compliant, least anisotropic and least frequently diseased of all arteries, while the CIA and AA were the stiffest and the most diseased. The severity of atherosclerosis correlated with age, but was not affected by laterality. Elastin fibers in the aorta, SA and CCA were uniformly and mostly circumferentially distributed throughout the media, while in the RA and CIA, elastin was primarily axially aligned and concentrated in the external elastic lamina. Constitutive modeling provided good fits to the experimental data for most arteries. Biomechanical and architectural features of major arteries differ depending on location and functional environment. A better understanding of localized arterial mechanical properties may support the development of site-specific treatment modalities for arterial disease.

Anisotropic Life Prediction for Single Crystal Nickel-Base Flat Plate with a Hole

The material properties of single crystal (SC) superalloys are orientation-dependent. To fully exploit the material capacity, the life modeling needs to consider the anisotropy. In the present study the life modeling of SC nickel-base superalloys is considered by employing the modified Mücker's anisotropic theory in which a Hill type function is utilized for describing the anisotropic failure. Strain-controlled low cycle fatigue (LCF) experiments of SC nickel-base superalloys at different crystallographic orientations (i.e. [00, [01 and [11) under high temperatures (i.e. 760°C) are carried out to verify the modeling availability for the modified Mücker's anisotropic theory. Further, based on the stress-strain field obtained by the anisotropic elastoplastic constitutive model coupled with the finite element method (FEM), the modified Mücker's anisotropic theory is employed to predict the fatigue life for SC flat plate with a hole.