Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity

The aim of this paper is to compare a hyperelastic with a hypoelastic model describing the Eulerian dynamics of solids in the context of non-linear elastoplastic deformations. Specifically, we consider the well-known hypoelastic Wilkins model, which is compared against a hyperelastic model based on the work of Godunov and Romenski. First, we discuss some general conceptual differences between the two approaches. Second, a detailed study of both models is proposed, where differences are made evident at the aid of deriving a hypoelastic-type model corresponding to the hyperelastic model and a particular equation of state used in this paper. Third, using the same high order ADER Finite Volume and Discontinuous Galerkin methods on fixed and moving unstructured meshes for both models, a wide range of numerical benchmark test problems has been solved. The numerical solutions obtained for the two different models are directly compared with each other. For small elastic deformations, the two models produce very similar solutions that are close to each other. However, if large elastic or elastoplastic deformations occur, the solutions present larger differences.Comment: 14 figure

Design and Analysis of Air-Stiffened Vacuum Lighter-Than-Air Structures

Lighter-than-air (LTA) systems have been developed for numerous applications and have taken several forms. Airships, aerostats, blimps, and balloons are all part of this family of systems, which uses Archimedes principle to achieve neutral and positive buoyancy in air by replacing an air volume with LTA gases. These lifting gases stiffen the otherwise compliant envelope structures, allowing them to sustain the pressure difference brought by the displaced air. The compliance of these structures is a byproduct of the weight requirement, materials and geometrical arrangement of which these structures are built from, typically resulting in dimensionalities that exhibit low or virtually non-existent in-plane bending stiffness. The former has constrained the development of LTA structures that utilize an internal partial vacuum, rather than a lifting gas, to achieve positive buoyancy, where the structure would be subjected to a pressure differential near atmospheric pressure. Given the above limitation, this research presents the development trajectory and structural characterization of air stiffened designs, which utilize air to shape and serve as the core of a set of enclosing envelopes. The development trajectory established a simulation framework that enables the structural characterization of air-stiffened designs under a variety of geometric and loading conditions. Such framework allowed for the development of finite element solutions that included geometric, fluid-structure and contact nonlinearities, with capacity for further generalization. Given the developed framework, the structural characterization of the Helical Sphere and Icoron air-stiffened designs demonstrated a reduction of material modulus and strength requirements compared to membrane-over-frame designs, and showed the capability of air-stiffened designs to be tailored for specific material strength limits

An exponential time-differencing method for monotonic relaxation systems

We present first and second-order accurate exponential time differencing methods for a special class of stiff ODEs, denoted as monotonic relaxation ODEs. Some desirable accuracy and robustness properties of our methods are established. In particular, we prove a strong form of stability denoted as monotonic asymptotic stability, guaranteeing that no overshoots of the equilibrium value are possible. This is motivated by the desire to avoid spurious unphysical values that could crash a large simulation. We present a simple numerical example, demonstrating the potential for increased accuracy and robustness compared to established Runge-Kutta and exponential methods. Through operator splitting, an application to granular-gas flow is provided.acceptedVersio

Index to NASA Tech Briefs, 1975

This index contains abstracts and four indexes--subject, personal author, originating Center, and Tech Brief number--for 1975 Tech Briefs

Combining Discrete Equations Method and upwind downwind-controlled splitting for non-reacting and reacting two-fluid computations

International audienceA reactive Riemann solver is inserted into the Reactive Discrete Equations Method (RDEM) to compute high speed combustion waves. The anti-diffusive approach developed by Despres and Lagoutiere is also coupled with RDEM to accurately simulate reacting shocks. Increased robustness and efficiency when computing both multiphase interfaces and reacting flows are achieved thanks to an original upwind downwind-controlled splitting method (UDCS)

The Explicit Simplified Interface Method for compressible multicomponent flows

This paper concerns the numerical approximation of the Euler equations for multicomponent flows. A numerical method is proposed to reduce spurious oscillations that classically occur around material interfaces. It is based on the "Explicit Simplified Interface Method" (ESIM), previously developed in the linear case of acoustics with stationary interfaces (2001, J. Comput. Phys. 168, pp.~227-248). This technique amounts to a higher order extension of the "Ghost Fluid Method" introduced in Euler multicomponent flows (1999, J. Comput. Phys. 152, pp. 457-492). The ESIM is coupled to sophisticated shock-capturing schemes for time-marching, and to level-sets for tracking material interfaces. Jump conditions satisfied by the exact solution and by its spatial derivative are incorporated in numerical schemes, ensuring a subcell resolution of material interfaces inside the meshing. Numerical experiments show the efficiency of the method for rich-structured flows.Comment: to be published in SIAM Journal of Scientific Computing (2005

Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications (hybrid meeting)

This small collaborative workshop brought together experts from the Sino-German project working in the field of advanced numerical methods for hyperbolic balance laws. These are particularly important for compressible fluid flows and related systems of equations. The investigated numerical methods were finite volume/finite difference, discontinuous Galerkin methods, and kinetic-type schemes. We have discussed challenging open mathematical research problems in this field, such as multidimensional shock waves, interfaces with different phases or efficient and problem suited adaptive algorithms. Consequently, our main objective was to discuss novel high-order accurate schemes that reliably approximate underlying physical models and preserve important physically relevant properties. Theoretical questions concerning the convergence of numerical methods and proper solution concepts were addressed as well