The Johnson Cook (JC) material model is often used for modeling hypervelocity impacts (HVI) because it is capable of capturing high rate deformation and temperature effects. Within the JC model, material damage leading to fracture is aggregated using a path dependent damage parameter. Contributions to the damage parameter are calculated at each cycle as the quotient of incremental effective plastic strain over the effective failure strain. The effective failure strain is a function of the stress state, strain rate, and temperature which changes locally throughout the simulation. Solid bodies often demonstrate variability in resilience resulting from material inclusions and defects. Therefore, in addition to the deterministic, state-based variability in the effective failure strain inherent to the JC model, efforts are often made to capture the effect of general material non-uniformity. Although other approaches may be available, the Weibull probability distribution is often employed within failure analyses to allow simulations to diverge from a completely uniform solution.In this paper, we investigate several methods of augmenting the JC damage model with Weibull variability. The implementation of each method provides a means for measured material uncertainty to enter the calculation. We focus on a standard three-parameter Weibull probability density function (pdf) although the methods proposed can be used with any probability distribution. Characteristics of the pdf are preserved within a solid body at its initial state but differ in the effect the JC effective failure strain has on these characteristics as the material state changes. The Weibull pdf under various loading conditions is discussed, and simulation results incorporating these methods are compared with those employing only the JC damage model or Weibull variability. Model formulationsCapturing variability of material behavior is an important component of modeling HVI events. Most materials will have some inhomogeneity due to imperfections within the crystalline structure, such as dislocations, grain boundaries, or other defects [1]. These non-uniformities introduce randomness in the material response, especially with regard to material failure and fracture at high strain rates. An approach is needed to model this variability in continuum mechanics based tools.The best method for incorporating material variability in the Johnson-Cook (JC) damage model has not yet been established, yet with some assumptions data describing both can be gleaned from the same test [2]. The unknown factor allowing multiple approaches is the effect pressure, temperature and strain rate have on the distribution of failure strain values. In this section, the JC model and the three-parameter Weibull probability distribution function (pdf) are described and methods for combining the two are introduced. These methods primarily differ in the way in which the characteristics of the pdf change with the state of the material, which will be shown to have a significant effect on simul...
Optical methods using digital image correlation (DIC) are utilized in developing rubber constitutive tests. Two and three dimensional DIC systems are employed to measure strains on rubber specimens subjected to uniaxial, planar, and biaxial stress states. A special membrane inflation test was developed and is described for providing the biaxial constitutive data. Deformation-induced material property changes for the three modes of testing are quantified using a concept based on energy dissipation. The constitutive test strain ranges for each of the three modes are separately selected to equalize the material states. The methodology is applied to filled rubber compounds in order to characterize them in terms of hyperelastic behavior. Evaluation and comparison of several common hyperelastic models are given, and application to finite element modeling of a structural rubber specimen is described.
In this paper, we investigate the Symmetric-SPH (S-SPH) method. S-SPH restores n-order consistency to the SPH formulation while remaining fully conservative by using a Taylor expansion of field variables to fit the kernel function. It has potential for HVI problems because it enables the ability to perform accurate stress and state calculations. We implement S-SPH in the Velodyne hydro-structural solver and evaluate its performance over a series of numerical examples including flyer impact, fragment penetration, and Taylor Rod impact. Idealized contact algorithms are employed to eliminate uncertainty in the flyer and Taylor impact problems while an advanced Lagrange multiplier algorithm is used for the fragment penetration test. We use the CTH hydrocode to provide a baseline response for each of the examples due to its ability to effectively handle penetration, hydrodynamic deformation, and shock propagation. Direct numerical comparisons are used to eliminate uncertainty from material characterizations, equation of state (EOS) models, and mesh resolution. We identify strengths and shortcomings of the S-SPH method and evaluate its utility for classes of HVI problems. We also compare the performance against SPH to compare relative accuracy, computational cost, and stability.
In this paper we develop methods based primarily on the work of Kuropatenko and Wilkins to improve the application of artificial viscosity in 3D finite element method (FEM) codes. The primary goal is to obtain better shock predictions for hypervelocity impacts (HVI) and reduce the need for user calibration. We focus on examining factors such as geometric variability with respect to shock direction, dynamic adaptation to changes in compressibility in the shock front, and anisotropic compression in multi-dimensional formulations. We implement the methods in the Velodyne hydro-structural code and investigate the effects on shock propagation using a series of simple flyer impact test cases which cover a range of system responses including strong and weak shocks. Various initial mesh geometries are utilized to examine mesh effects. Energetic materials using the Ignition and Growth Reactive Burn (IGRB) equation of state (EOS) are also examined due to the rapid change in compressibility and energy density which occurs due to reaction. These rapid changes can lead to insufficient damping in artificial viscosity calculations and thus provide an effective test case. We employ the CTH hydrocode to evaluate baseline shock behavior. The regular, ordered mesh of CTH allows for a consistent and precise application of the artificial viscosity. Direct numerical comparisons are used rather than experimental data to eliminate uncertainty due to factors such as material characterizations, EOS models, and mesh resolution. We compare the CTH results against various FEM artificial viscosity implementations to evaluate performance. It is demonstrated that shock response in FEM codes can be significantly improved by using updated artificial viscosity methods.
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