A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.
The numerical integration of constitutive models in computational solid mechanics codes allows for the solution of boundary value problems involving complex material behavior. Metal plasticity models, in particular, have been instrumental in the development of these codes. Most plasticity models implemented in computational codes use an isotropic von Mises yield surface. The von Mises, or J2, model uses a predictor–corrector algorithm–the radial return algorithm–to integrate the model. For non-quadratic yield surfaces, including anisotropic yield surfaces, no simple algorithm exists. This paper presents and analyzes a line search algorithm for the return mapping problem that shows excellent improvement over a Newton–Raphson model. Two non-quadratic yield surfaces–one isotropic and one anisotropic–are studied in this paper. The line search algorithm used for integrating the models is shown to be reliable and robust. The theory and implementation of the models, the details of the return mapping algorithm, and results that show the effectiveness of the method are presented. Lastly, a few simple boundary value problems verify the implementation and show the impact of the models. For the internal pressurization of a cylinder, the importance of modeling anisotropy correctly is shown.
Experiments were performed to characterize the mechanical response of several different rigid polyurethane foams to large deformation. In these experiments, the effects of load path, loading rate, and temperature were investigated. Results from these experiments indicated that rigid polyurethane foams exhibit significant damage, volumetric and deviatoric plasticity when they are compressed. Rigid polyurethane foams were also found to be extremely strain-rate and temperature dependent. These foams are also rather brittle and crack when loaded to small strains in tension or to larger strains in compression. Thus, a phenomenological Unified Creep Plasticity Damage (UCPD) model was developed to describe the mechanical response of these foams to large deformation at a variety of temperatures and strain rates. This paper includes a description of recent experiments and experimental findings. Next, development of a UCPD model for rigid, polyurethane foams is described. Finite element simulations with the new UCPD model are compared with experimental results to show behavior that can be captured with this model.
Experiments were performed to characterize the mechanical response of several different rigid polyurethane foams to large deformation. In these experiments, the effects of load path, loading rate, and temperature were investigated. Results from these experiments indicated that rigid polyurethane foams exhibit significant damage, volumetric and deviatoric plasticity when they are compressed. Rigid polyurethane foams were also found to be extremely strain-rate and temperature dependent. These foams are also rather brittle and crack when loaded to small strains in tension or to larger strains in compression. Thus, a phenomenological Unified Creep Plasticity Damage (UCPD) model was developed to describe the mechanical response of these foams to large deformation at a variety of temperatures and strain rates. This paper includes a description of recent experiments and experimental findings. Next, development of a UCPD model for rigid, polyurethane foams is described. Finite element simulations with the new UCPD model are compared with experimental results to show behavior that can be captured with this model.
This memo derives a particular use of a rate-dependent, perfectly plastic Von Mises Plasticity constitutive model that represents a Newtonian (or Bingham) fluid. Only two parameters are needed: the viscosity and bulk modulus to complete the model parameterization. Under certain deformations, the model exactly represents a Newtonian fluid. Under others, the model shear thins. A Newtonian fluid representation may be used in confined flow applications in which a fluid-solid interaction is desired but code coupling is not.
The Virtual Fields Method (VFM) is an inverse method for constitutive model parameter identication that relies on full-eld experimental measurements of displacements. VFM is an alternative to standard approaches that require several experiments of simple geometries to calibrate a constitutive model. VFM is one of several techniques that use full-eld exper- imental data, including Finite Element Method Updating (FEMU) techniques, but VFM is computationally fast, not requiring iterative FEM analyses. This report describes the im- plementation and evaluation of VFM primarily for nite-deformation plasticity constitutive models. VFM was successfully implemented in MATLAB and evaluated using simulated FEM data that included representative experimental noise found in the Digital Image Cor- relation (DIC) optical technique that provides full-eld displacement measurements. VFM was able to identify constitutive model parameters for the BCJ plasticity model even in the presence of simulated DIC noise, demonstrating VFM as a viable alternative inverse method. Further research is required before VFM can be adopted as a standard method for constitu- tive model parameter identication, but this study is a foundation for ongoing research at Sandia for improving constitutive model calibration.
Instrumented, fully coupled thermal-mechanical experiments were conducted to provide validation data for finite element simulations of failure in pressurized, high temperature systems. The design and implementation of the experimental methodology is described in another paper of this conference. Experimental coupling was accomplished on tubular 304L stainless steel specimens by mechanical loading imparted by internal pressurization and thermal loading by side radiant heating. Experimental parameters, including temperature and pressurization ramp rates, maximum temperature and pressure, phasing of the thermal and mechanical loading and specimen geometry details were studied. Experiments were conducted to increasing degrees of deformation, up to and including failure. Mechanical characterization experiments of the 304L stainless steel tube material was also completed for development of a thermal elastic-plastic material constitutive model used in the finite element simulations of the validation experiments. The material was characterized in tension at a strain rate of 0.001/s from room temperature to 800 C. The tensile behavior of the tube material was found to differ substantially from 304L bar stock material, with the plasticity characteristics and strain to failure differing at every test temperature.