Anisotropic Material Model Research Articles

Numerical implementation of the radial vector hysteresis model

This paper discusses the numerical implementation of a new vector hysteresis model, the radial vector model, introduced as general hysteresis vector model for both isotropic and anisotropic magnetic materials. The present implementation is a 2-D one that uses ellipses as critical surfaces. The results computed by the model, applied to some basic vector hysteresis configurations, are in agreement with experimental behavior

Dynamic pre-processing software for the hyperviscoelastic modeling of complex anisotropic biological tissue materials

Soft biological tissues are complex structures with intricate microstructure, which is usually highly anisotropic. These tissues are typically composed of multiple fiber bundles, which may have a unique orientation, defined for each single element in a large finite element mesh for modeling complex structures such as the human heart. These complex orientations can be difficult to define in an ABAQUS input deck using existing methods. In general, each change in fiber orientation requires a “new material” to be defined. Using the conventional method of defining material properties in ABAQUS is time consuming and, as a result of the large number of input constants required, is prone to errors. It is therefore deemed desirable to create a new means of material property input. The ∗∗CC Cards method presented partitions the material property data for a time-dependent, anisotropic, material response into discrete card images, and thus eliminates much of the redundant data input required by ABAQUS. This strategy is also more efficient, both computationally and from the viewpoint of user time required.

Application of integration algorithems for elasto-plasticity constitutive model for anisotropic sheet materials

Two algorithms of computing stress increment by using the elasto-plasticity constitutive model are firstly formulated, which are the Euler integration method and the radial return method. Hill'48 anisotropic yield criterion is used. The Euler integration method can not obtain more accurate computation of the stress increment as the radial return method unless enough subintervals are taken, by which the Euler integration method will take excessive computing time. Without decreasing any accuracy, the radial return method can save much time. Finally, a square cup deep drawing from NUMISHEET'93 benchmarks is simulated with a self-developed code SheetForm in order to investigate the accuracy and efficiency of the radial return method.

Forming of aluminum alloys at elevated temperatures – Part 1: Material characterization

A temperature-dependent anisotropic material model for use in a coupled thermo-mechanical finite element analysis of the forming of aluminum sheets was developed. The anisotropic properties of the aluminum alloy sheet AA3003-H111 were characterized for a range of temperatures 25–260 °C (77–500 °F) and for different strain rates. Material hardening parameters (flow rule) and plastic anisotropy parameters ( R 0, R 45 and R 90) were calculated using standard ASTM uniaxial tensile tests. From this experimental data, the anisotropy coefficients for the Barlat YLD96 yield function [Barlat, F., Maeda, Y., Chung, K., Yanagawa, M., Brem, J.C., Hayashida, Y., Lege, D.J., Matsui, K., Murtha, S.J., Hattori, S., Becker, R.C., Makosey, S., 1997a. Yield function development for aluminum alloy sheets. J. Mech. Phys. Solids 45 (11/12), 1727–1763] in the plane stress condition were calculated for several elevated temperatures. Curve fitting was used to calculate the anisotropy coefficients of Barlat’s YLD96 model and the hardening parameters as a function of temperature. An analytical study of the accuracy and usability of this curve fitting technique is presented through the calculation of plastic anisotropy R-parameters and yield function plots at different temperatures.

An effective reluctivity model for nonlinear and anisotropic materials in time-harmonic finite element computations

In time-harmonic finite element analysis, the nonlinear behavior of soft-magnetic materials is often modeled by effective reluctivity curves, to account for the time-dependence of the reluctivity during one cycle of the applied sinusoidal signal. In this paper, the effective reluctivity concept is generalized in such a way, that nonlinear and anisotropic materials can be modeled as well. The model is used to simulate the flux line distribution and the loss distribution in a three-phase transformer under no-load operation.

Nonlinear viscoelastic behavior of paper fiber composites

Anisotropic material model for composites made from phenol–formaldehyde impregnated paper is developed starting from Schapery’s nonlinear viscoelastic and nonlinear viscoplastic constitutive law derived from thermodynamics. Methodology for determination of the included stress-dependent functions has been developed and used to determine properties of two composites in two directions related to material symmetry. Creep with following strain recovery tests have been performed at several levels of stress. Data reduction is based on two-step load application methodology to include effect of finite time of load increase to the plateau value and its removal. No stiffness reducing micro damage was detected and the plastic deformations were considered negligible or accounted for in a simplified manner. The material model was used to simulate a constant stress rate loading and unloading test. Model is validated comparing simulations with results from test.

An anisotropic fibre-matrix material model at finite elastic-plastic strains

In this paper a constitutive model for anisotropic finite strain plasticity, which considers the major effects of the macroscopic behaviour of matrix-fibre materials, is presented. As essential feature matrix and fibres are treated separately, which allows as many bundles of fibres as desired. The free energy function is additively split into a part related to the matrix and in parts corresponding to the fibres. Usually the free energy function is defined by the integrity basis of the main variable and structural tensors, which leads to complicated numerical schemes. Here, the continuum is considered as superimposed of the isotropic matrix and further one-dimensional continua each of them represents one bundle of fibres. The deformation gradient applies to all continua introducing a constraint, which links the different continua. One of the most striking features of the model is its suitability for a numerical treatment.

Anisotropic moisture depending viscoelastic material model for wood

AbstractA moisture depending anisotropic viscoelastic material model is presented in this paper. The necessity of consideration cylindrical anisotropy is caused by the growing process. Wood exhibits different creep characteristics depending on the state of stress. Therefore, the consideration of anisotropic viscoelasticity is required. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping

Indentation tests are at present frequently employed for the identification of parameters contained in constitutive models of materials at different scales. The indentation curves (namely, the relationship between applied force and penetration depth) provide experimental data for the calibration of mechanical models through traditional semi-empirical formulae or, in recent times, through simulation of the test and inverse analysis. The main material parameters estimated in these ways are Young modulus and yield stress. A recently proposed technique combines the traditional indentation test with the mapping of the residual deformations (imprint), thus providing experimental data apt to identify isotropic material parameters in more accurate fashion and in larger number, including Poisson’s ratio, hardening coefficients, friction between the specimen and the indentation tool. In this paper, such new methodology is employed for the calibration of anisotropic material models. Axial-symmetric indenters are referred to. The mapped imprint (which, clearly, does not exhibit axial symmetry because of the specimen anisotropy) provides meaningful experimental data, additional to those deduced from the indentation curves. These curves are almost insensitive to differences of material properties along different directions. On the contrary, residual displacements reflect constitutive anisotropy and turn out to be crucial for the success of the parameter identification procedure. The classical Hill’s model for anisotropic perfect elasto-plasticity is adopted herein to describe material behavior. Three-dimensional finite element simulations are performed in finite strain regime by a commercial code. Inverse analysis is carried out by a batch, deterministic approach, using conventional optimization algorithms for the minimization of the discrepancy function. Sensitivity indices are computed in order to assess the identifiability of the parameters and to provide a basis for the design of the experiments. Numerical examples are discussed apt to test the performance of the proposed methodology in terms of result accuracy and computing effort in view of industrial applications.

Experimental and numerical study of stamp hydroforming of sheet metals

The objectives of this research was to experimentally and numerically study the stamp hydroforming process as a means for shaping aluminum alloy sheets. In stamp hydroforming, one or both surfaces of the sheet metal are supported with a pressurized viscous fluid to assist with the stamping of the part thereby eliminating the need for a female die. The pressurized fluid serves several purposes: (1) supports the sheet metal from the start to the end of the forming process, thus yielding a better formed part, (2) delays the onset of material failure and (3) reduces wrinkle formation. This paper focuses on the experimental and numerical results of the stamp hydroforming process utilizing a fluid pressure applied to one surface of the sheet metal. The effects of applying a constant, varying and localized pressure to the surface of 3003-H14-aluminum sheet alloy were evaluated. Experiments demonstrated draw depths improvements up to 31% before the material failed. A failure prediction analysis by Hsu was also carried out to predict an optimal fluid pressure path for the varying fluid pressure case. The commercial finite element analysis code Ls-Dyna3D was used to numerically simulate the stamp hydroforming process. Both isotropic and anisotropic material models were used and their predictions compared against the experimental results. The numerical simulations utilizing Barlat's anisotropic yield function accurately predicted the location of the material failure and the wrinkling characteristics of the aluminum sheet.

Capillary condensation monitored in birefringent porous silicon layers

We performed studies on the capillary condensation of various substances in optically anisotropic porous silicon layers. Their strong in-plane form birefringence has been utilized to analyze the polarization state of the transmitted light when molecules penetrate into the pores. The polarization state of the transmitted light is correlated with the filling fraction of the pores by an effective-medium model for anisotropic porous materials. The experimentally obtained adsorption/desorption isotherms show hysteresis typical for capillary condensation in porous materials. We discuss the shape of the hysteresis loops in the framework of the morphology of the layers. Pore-size distributions derived from adsorption/desorption isotherms are presented.

A constitutive model for anisotropic materials based on Neuber’s rule

Phenomenological approaches to fatigue damage prediction often rely on the assessment of local stress–strain concentrations in structural components. To avoid complex plastic analysis in fatigue assessment, approximate constitutive models have been developed to evaluate the local inelastic response of the material and which allow for an adequate lifetime prediction in a competitive time. One of these approximate methods is the Neuber rule, which has originally been elaborated for the uniaxial loading state of isotropic materials. This paper addresses an approximate method for multiaxial loading of anisotropic materials. The proposed approach is based on a tensorial formulation of the Ramberg–Osgood equation and a generalization of the uniaxial Neuber hypothesis by assuming the equivalence of the deviatoric strain energy density for the elastic and inelastic solution in the notch region. After a decomposition of the stress tensor into a normalized direction tensor and a stress invariant, a nonlinear expression is obtained which can be iterated for the unknown inelastic stress state. It is shown that the proposed anisotropic Neuber rule includes the multiaxial isotropic and the classical uniaxial formulation as special cases. Furthermore, aspects of parameter identification are discussed for directionally solidified Nickel-based superalloys with transverse isotropic properties and single crystal materials with cubic anisotropy. Two numerical examples demonstrate the applicability of the proposed approach.

Numerical modelling of stainless steel plates in compression

The paper describes the development of numerical models for analysing stainless steel plates in compression. Material tests on coupons cut in the longitudinal, transverse and diagonal directions are included as are the results of tests on stainless steel plates. Detailed comparisons are made between the experimental and numerical ultimate loads, load–displacement curves and load–strain curves. It is shown that excellent agreement with tests can be achieved by using the compressive stress–strain curve pertaining to the longitudinal direction. The effect of anisotropy is investigated using elastic–perfectly-plastic material models, where the anisotropic material model is based on Hill’s theory. The models indicate that the effect of anisotropy is small and that it may not be required to account for anisotropy in the modelling of stainless steel plates in compression.

Unified constitutive modeling of anisotropic hyperelastic materials at large strains

In the present contribution we propose a generalized hyperelastic model for fiber-reinforced structures. Along with the earlier generalized orthotropic hyperelastic formulation [1] this constitutive model forms a reliable basis for the adequate numerical simulation of various anisotropic materials at large elastic strains.

Finite Element and Distress Models for Geosynthetic-reinforced Pavements

A finite element (FE) response model has been developed to describe stress and strain response parameters for geosynthetic-reinforced flexible pavement systems where the geosynthetic is placed at the bottom of the unbound aggregate layer. The model contains membrane elements and an anisotropic linear-elastic material model for the geosynthetic inclusion. Elasto-plastic models are used for the asphalt concrete, base aggregate and subgrade layers. Principal response parameters extracted from the FE model include vertical strain in the top of the subgrade and bulk stress in the unbound base aggregate layer. These response parameters are used in empirical damage models for the prediction of long-term pavement performance and the definition of reinforcement benefit. Reinforcement benefit is defined in terms of an extension of service life of the pavement, a reduction in aggregate thickness for equivalent service life, or a combination of the two. The damage models are calibrated from reinforced and unreinforced pavement test sections. The model is shown to provide general descriptions of reinforcement mechanisms that are consistent with those previously observed in instrumented pavement test sections. A companion paper (S.W., Perkins and M.Q., Edens (2003) A Design Model for Geosynthetic-Reinforced Pavements, International Journal of Pavement Engineering) describes the use of the response and damage models in a parametric study from which a design model for geosynthetic-reinforced pavements is developed.

Development of a one point quadrature shell element for nonlinear applications with contact and anisotropy

A general purpose shell element for nonlinear applications including sheet metal forming simulation is developed based on reduced integration with one point quadrature. The developed shell element has five degrees of freedom and four nodes. It covers flexible warping behavior without artificial warping correction. A physical stabilization scheme with the assumed natural strain method is employed to derive a strain field that can be decomposed into the sum of a constant and a linear term with respect to the natural coordinates. The rigid body projection is introduced to treat rigid body rotations effectively. The shell element incorporates elasto-plastic planar anisotropic material models based on the incremental deformation theory. Linear and nonlinear patch tests are performed and the results are compared with analytical or previously reported results. Simulations that include impact and deformable body contact are performed to show the robustness of the contact algorithm. Finally, to demonstrate the capability of handling anisotropic materials, the developed shell element is used for the circular cup drawing process simulation in order to predict the earing profile of Al 2008-T4 alloy sheet.

Three-dimensional simulation of hemming with the explicit FE-method

This paper is dedicated to three-dimensional simulation of hemming of an automotive hood. The results from the simulations are compared with measurements on hoods manufactured in the production line, both with and without adhesives, in order to check the validity of the FE-model. Both the ordinary serial version as well as the massively parallel processing (MPP)-version of the code LS-DYNA have been applied in the simulations, in order to verify that the two versions are giving the same results, and thereby ensuring that the MPP-version can be used for this type of simulations. Four different types of under-integrated shell elements, three of them based on the Mindlin shell theory and one based on a degenerated solid element, have been used in order to determine which of them is showing the best agreement with test results. Furthermore, results from a transversely anisotropic material model are compared to results from a model with full anisotropy in order to study if anisotropy is a crucial issue in these simulations. One simulation was performed of the case with adhesives between the parts. The effects on the roll-in of the adhesives were in this simulation modelled as a smaller friction coefficient in the contacts between the two parts. Finally, the effect on roll-in from the preceding stamping is studied in an FE-model with pre-strained outer and inner parts.

An analysis of stretch forming of thermoplastic composites

AbstractThermoplastic composite sheet materials have found an increasing number of applications through the use of matched‐die compression molding. The combination of high strength, low weight and moderate manufacturing costs makes the material an attractive alternative to sheet metal stampings in a number of applications. However, a significant range of conventional sheet forming techniques may also prove suitable for these materials, provided the effects of strain rate and temperature can be properly understood and exploited, leading to a further reduction of manufacturing costs and an increasing number of potential applications. In this work, limiting strains in biaxial stretch forming were explored using the hemispherical stretch forming test. The materials tested contain 20, 35, and 40 percent by weight of randomly oriented glass fiber in a polypropylene matrix. The forming tests were performed at temperatures ranging from 75°C to 150°C and at punch speeds of 0.01cm/sec, 0.1cm/sec, and 1cm/sec. A rotationally symmetric, anisotropic material model with rate sensitivity was developed and incorporated into an axisymmetric finite element model of the stretch‐forming process. The model parameters were temperature‐dependent, though the temperature distribution in the formed part was assumed to be uniform. Strain distributions in the formed parts are compared to finite element method results, and the results are good up to the point when localized necking begins to dominate the strain distribution. These forming limit strains are compared with predictions based on Marciniak's imperfection theory, with good results.

“Forbidden” planes for Rayleigh waves

Existence of forbidden planes, on which Rayleigh waves cannot propagate, is discussed. A mathematical model for anisotropic materials possessing forbidden planes is constructed. An example of transversely isotropic material having forbidden planes is presented.

Anisotropic creep modeling based on elastic projection operators

The paper presents a unified approach for creep modeling of anisotropic materials, and is specified in more detail to the cases of isotropy, cubic symmetry and transversal isotropy. Thereby an additive decomposition of the elastic and inelastic strain tensors into dilational and isochoric Kelvin modes is assumed. Each of these modes is obtained from fourth order projection operators, resulting from solution of the eigenvalue problem for the fourth order anisotropic elasticity tensor. For simplicity the amount of strain rate for each mode is determined with a Norton type ansatz in terms of an equivalent stress, and the experimental phenomenon of primary creep is taken into account by a back stress tensor of Armstrong-Frederick type, which is also decompose into Kelvin modes. Two numerical creep simulations investigate the crystal orientation for a compact tension specimen made out of CMSX-4 superalloy.