Constitutive models for computational solid mechanics codes are in LAME--the Library of Advanced Materials for Engineering. These models describe complex material behavior and are used in our finite deformation solid mechanics codes. To ensure the correct implementation of these models, regression tests have been created for constitutive models in LAME. A selection of these tests is documented here. Constitutive models are an important part of any solid mechanics code. If an analysis code is meant to provide accurate results, the constitutive models that describe the material behavior need to be implemented correctly. Ensuring the correct implementation of constitutive models is the goal of a testing procedure that is used with the Library of Advanced Materials for Engineering (LAME) (see [1] and [2]). A test suite for constitutive models can serve three purposes. First, the test problems provide the constitutive model developer a means to test the model implementation. This is an activity that is always done by any responsible constitutive model developer. Retaining the test problem in a repository where the problem can be run periodically is an excellent means of ensuring that the model continues to behave correctly. A second purpose of a test suite for constitutive models is that it gives application code developers confidence that the constitutive models work correctly. This is extremely important since any analyst that uses an application code for an engineering analysis will associate a constitutive model in LAME with the application code, not LAME. Therefore, ensuring the correct implementation of constitutive models is essential for application code teams. A third purpose of a constitutive model test suite is that it provides analysts with example problems that they can look at to understand the behavior of a specific model. Since the choice of a constitutive model, and the properties that are used in that model, have an enormous effect on the results of an analysis, providing problems that highlight the behavior of various constitutive models to the engineer can be of great benefit. LAME is currently implemented in the Sierra based solid mechanics codes Adagio [3] and Presto [4]. The constitutive models in LAME are available in both codes. Due to the nature of a transient dynamics code--e.g. Presto--it is difficult to test a constitutive model due to inertia effects that show up in the solution. Therefore the testing of constitutive models is primarily done in Adagio. All of the test problems detailed in this report are run in Adagio. It is the goal of the constitutive model test suite to provide a useful service for the constitutive model developer, application code developer and engineer that uses the application code. Due to the conflicting needs and tight time constraints on solid mechanics code development, no requirements exist for implementing test problems for constitutive models. Model developers are strongly encouraged to provide test problems and document those problems, but given the choice of having a model without a test problem or no model at all, certain requirements must be kept loose. A flexible code development environment, especially with regards to research and development in constitutive modeling, is essential to the success of such an environment. This report provides documentation of a number of tests for the constitutive models in LAME. Each section documents a separate test with a brief description of the model, the test problem and the results. This report is meant to be updated periodically as more test problems are created and put into the test suite.
The Library of Advanced Materials for Engineering (LAME) provides a common repository for constitutive models that can be used in computational solid mechanics codes. A number of models including both hypoelastic (rate) and hyperelastic (total strain) constitutive forms have been implemented in LAME. The structure and testing of LAME is described in Scherzinger and Hammerand ([3] and [4]). The purpose of the present report is to describe the material models which have already been implemented into LAME. The descriptions are designed to give useful information to both analysts and code developers. Thus far, 33 non-ITAR/non-CRADA protected material models have been incorporated. These include everything from the simple isotropic linear elastic models to a number of elastic-plastic models for metals to models for honeycomb, foams, potting epoxies and rubber. A complete description of each model is outside the scope of the current report. Rather, the aim here is to delineate the properties, state variables, functions, and methods for each model. However, a brief description of some of the constitutive details is provided for a number of the material models. Where appropriate, the SAND reports available for each model have been cited. Many models have state variable aliases for some or all of their state variables. These alias names can be used for outputting desired quantities. The state variable aliases available for results output have been listed in this report. However, not all models use these aliases. For those models, no state variable names are listed. Nevertheless, the number of state variables employed by each model is always given. Currently, there are four possible functions for a material model. This report lists which of these four methods are employed in each material model. As far as analysts are concerned, this information is included only for the awareness purposes. The analyst can take confidence in the fact that model has been properly implemented and the methods necessary for achieving accurate and efficient solutions have been incorporated. The most important method is the getStress function where the actual material model evaluation takes place. Obviously, all material models incorporate this function. The initialize function is included in most material models. The initialize function is called once at the beginning of an analysis and its primary purpose is to initialize the material state variables associated with the model. Many times, there is some information which can be set once per load step. For instance, we may have temperature dependent material properties in an analysis where temperature is prescribed. Instead of setting those parameters at each iteration in a time step, it is much more efficient to set them once per time step at the beginning of the step. These types of load step initializations are performed in the loadStepInit method. The final function used by many models is the pcElasticModuli method which changes the moduli that are to be used by the elastic preconditioner in Adagio. The moduli for the elastic preconditioner are set during the initialization of Adagio. Sometimes, better convergence can be achieved by changing these moduli for the elastic preconditioner. For instance, it typically helps to modify the preconditioner when the material model has temperature dependent moduli. For many material models, it is not necessary to change the values of the moduli that are set initially in the code. Hence, those models do not have pcElasticModuli functions. All four of these methods receive information from the matParams structure as described by Scherzinger and Hammerand.
Constitutive modeling is an important aspect of computational solid mechanics. Sandia National Laboratories has always had a considerable effort in the development of constitutive models for complex material behavior. However, for this development to be of use the models need to be implemented in our solid mechanics application codes. In support of this important role, the Library of Advanced Materials for Engineering (LAME) has been developed in Engineering Sciences. The library allows for simple implementation of constitutive models by model developers and access to these models by application codes. The library is written in C++ and has a very simple object oriented programming structure. This report summarizes the current status of LAME.
This research focuses on the development of a constitutive model for carbon nanotube polymer composites incorporating nanoscale attributes of the interface between the nanotube and polymer. Carbon nanotube polymer composites exhibit promising properties, as structural materials and the current work will motivate improvement in their load transfer capabilities. Since separation events occur at different length and time scales, the current work also addresses the challenge of multiscale modeling in interpreting inputs at different length and time scales. The nanoscale phase separation phenomena are investigated using molecular dynamics (MD) simulations. The simulations based on MD provide grounds for developing a cohesive zone model for the interface based on laws of thermodynamics.
Effective elastic properties for carbon nanotube reinforced composites are obtained through a variety of micromechanics techniques. Using the in-plane elastic properties of graphene, the effective properties of carbon nanotubes are calculated utilizing a composite cylinders micromechanics technique as a first step in a two-step process. These effective properties are then used in the self-consistent and Mori-Tanaka methods to obtain effective elastic properties of composites consisting of aligned single or multi-walled carbon nanotubes embedded in a polymer matrix. Effective composite properties from these averaging methods are compared to a direct composite cylinders approach extended from the work of Hashin and Rosen (1964) and Christensen and Lo (1979). Comparisons with finite element simulations are also performed. The effects of an interphase layer between the nanotubes and the polymer matrix as result of functionalization is also investigated using a multi-layer composite cylinders approach. Finally, the modeling of the clustering of nanotubes into bundles due to interatomic forces is accomplished herein using a tessellation method in conjunction with a multi-phase Mori-Tanaka technique. In addition to aligned nanotube composites, modeling of the effective elastic properties of randomly dispersed nanotubes into a matrix is performed using the Mori-Tanaka method, and comparisons with experimental data are made. Computational micromechanical analysis of high-stiffness hollow fiber nanocomposites is performed using the finite element method. The high-stiffness hollow fibers are modeled either directly as isotropic hollow tubes or equivalent transversely isotropic effective solid cylinders with properties computed using a micromechanics based composite cylinders method. Using a representative volume element for clustered high-stiffness hollow fibers embedded in a compliant matrix with the appropriate periodic boundary conditions, the effective elastic properties are obtained from the finite element results. These effective elastic properties are compared to approximate analytical results found using micromechanics methods. The effects of an interphase layer between the high-stiffness hollow fibers and matrix to simulate imperfect load transfer and/or functionalization of the hollow fibers is also investigated and compared to a multi-layer composite cylinders approach. Finally the combined effects of clustering with fiber-matrix interphase regions are studied. The parametric studies performed herein were motivated by and used properties for single-walled carbon nanotubes embedded in an epoxy matrix, and as such are intended to serve as a guide for continuum level representations of such nanocomposites in a multi-scale modeling approach.
Polymers and fiber-reinforced polymer matrix composites play an important role in many Defense Program applications. Recently an advanced nonlinear viscoelastic model for polymers has been developed and incorporated into ADAGIO, Sandia's SIERRA-based quasi-static analysis code. Standard linear elastic shell and continuum models for fiber-reinforced polymer-matrix composites have also been added to ADAGIO. This report details the use of these models for advanced adhesive joint and composites simulations carried out as part of an Advanced Simulation and Computing Advanced Deployment (ASC AD) project. More specifically, the thermo-mechanical response of an adhesive joint when loaded during repeated thermal cycling is simulated, the response of some composite rings under internal pressurization is calculated, and the performance of a composite container subjected to internal pressurization, thermal loading, and distributed mechanical loading is determined. Finally, general comparisons between the continuum and shell element approaches for modeling composites using ADAGIO are given.
The critical time step needed for explicit time integration of laminated shell finite element models is presented. Each layer is restricted to be orthotropic when viewed from a properly oriented material coordinate system. Mindlin shell theory is used in determining the laminated response that includes the effects of transverse shear. The effects of the membrane-bending coupling matrix from the laminate material model are included. Such a coupling matrix arises even in the case of non-symmetric lay-ups of differing isotropic layers. Single point integration is assumed to be used in determining a uniform strain response from the element. Using a technique based upon one from the literature, reduced eigenvalue problems are established to determine the remaining non-zero frequencies. It is shown that the eigenvalue problem arising from the inplane normal and shear stresses is decoupled from that arising from the transverse shear stresses. A verification example is presented where the exact and approximate results are compared.
A linear elastic constitutive equation for modeling fiber-reinforced laminated composites via shell elements is specified. The effects of transverse shear are included using first-order shear deformation theory. The proposed model is written in a rate form for numerical evaluation in the Sandia quasi-statics code ADAGIO and explicit dynamics code PRESTO. The equation for the critical time step needed for explicit dynamics is listed assuming that a flat bilinear Mindlin shell element is used in the finite element representation. Details of the finite element implementation and usage are given. Finally, some of the verification examples that have been included in the ADAGIO regression test suite are presented.
A triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented. Hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log timescale, in addition to the usual hygrothermal loads. Recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads. The nonlinear deformation process is computed using an incremental/iterative approach with the Newton-Raphson method used to find the incremental displacements in each time step. The presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation-independent mechanical loads, deformation-dependent pressure loads, and thermal loads. Unlike elastic structures that have a single critical load value associated with a given snapping or buckling instability phenomenon, viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times. Both creep buckling and snap through examples are presented here. In some cases, viscoelastic results are also obtained using the quasi-elastic method in which load-history effects are ignored, and time-varying viscoelastic properties are simply used in a series of elastic problems. The presented numerical examples demonstrate the capability and accuracy of the formulation.