14 Dec 94. Hydrocode Micro-Model Concept for Multi-Component Flow in Sediments Hans U. Mair

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1 Hydrocode Micro-Model Concept for Multi-Component Flow in Sediments Hans U. Mair Background Hydrocodes are Computational Mechanics tools that simulate the compressible dynamics (i.e., shock physics) of multiple solids and fluids. They are usually employed to simulate material responses on the macroscopic scale; however, it is possible to model the propagation of shocks through mixtures of materials (e.g., sediments) on the microscopic scale using hydrocode models in which the individual components are discretized. Though such microscopic models are often not directly applicable to the macroscopic problems, they can provide insight into the development of macroscopic constitutive models. Macroscopic constitutive models of crushable materials have long been employed (e.g., P- α and Effective Stress models), but microscopic models of such materials can provide valuable insight into the microscopic dynamics that drive the macroscopic response. An example is the relative flow or multi-component flow behavior of a mixture; macroscopic simulations of shock propagation through mixtures typically lump together all constituents in order to compute dynamic properties (velocity, pressure, etc.) at each point in space, even though relative motions (slip between constituents) can exist in fluid/solid mixtures like sediments. The U.S. Navy is attempting to enhance its sediment modeling capabilities. One enhancement under consideration is the development of a Multi-Component Effective Stress Model (MCESM), in which relative flow of the constituents is allowed within the framework of an Effective Stress model (a macroscopic constitutive model). In support of such a development, a microscopic model concept, previously proposed, 1 is described here in detail. Potential advantages and disadvantages of this model are also outlined. Concept The micro-model concept focuses on the development and application of hydrocode model of a gaseous sediment mixture, in which the fluid medium, as well as individual particles of the sediment solids, are discretized. Critical features of the model include simulation of the collapse and re-expansion of entrapped gas bubbles, crushing (fracture) of sediment grains, and slip between the fluid and solid components (including boundary layers, if necessary). 1 Chen, H.T, Barsoum, R., Goertner, J.A., Hinckley, W., Johnson, E.P., Mair, H.U., McDonald, E. and Valent, P., Shock Wave Propagation Initiative, April of 5

2 SPH Water "Particles" SPH Gas "Particles" Sediment Grain "Continuum Elements" Figure 1. Portion of SPH Sediment Micro-Model Though various forms of hydrocodes exist, this application seems best suited for Lagrangian hydrocodes that have incorporated Smoothed Particle Hydrodynamics (SPH) capability. In SPH, a continuum is discretized into a field of interacting Lagrangian particles (i.e., particles translate as the material distorts), much as billiard balls interact on a pool table. In the hydrocode micro-model, the water and gas are each modeled as many Lagrangian (SPH) "particles" that interact with standard Finite ("continuum") Element discretized sediment grains, as illustrated in Figure 1. Two hydrocodes have demonstrated such capabilities: PRONTO 2 and EPIC. 3,4 Several advantages are presented by this 2 Attaway, S.W., Heinstein, M.W. and Swegle, J.W., Coupling of Smooth Particle Hydrodynamics with the Finite Element Method, Nuclear Engineering and Design 150 (1994), pp Johnson, G.R., Petersen, E.H. and Stryk, R.A., Incorporation of an SPH Option into the EPIC Code for a Range of High Velocity Impact Computations, presented at the 1992 High Velocity Impact Symposium. 2 of 5

3 methodology. The sediment grains are modeled within a Lagrangian Finite Element frame, which is preferred for the dynamics of solids in which history variables like damage accumulation are present (e.g., fracture of sediment grains). The fluid constituents (water and gas) must be modeled within a frame that admits large material distortions and separations, since the fluids flow past surfaces of fracturing grains. The fixed-connectivity meshes of Lagrangian and Arbitrary Lagrangian/Eulerian hydrocodes, are probably not suitable for such applications. The traditional Eulerian frame for the dynamics of fluids may also not be suitable for the fluids in this micro-model; this would entail a Coupled Eulerian/Lagrangian approach for which algorithms for fracturing interfaces (e.g. fracture of Lagrangian sediment grains) are lacking. A single Eulerian frame for the entire micromodel, in which both the solids and fluids are Eulerian, is also likely not suitable; many Eulerian cells would contain a mixture of solid and fluid materials, whose properties and interactions become numerically smeared, resulting in numerical drag. The SPH method was chosen for consideration for the micro-model fluids since connectivity between particles is not fixed, and the particles can slip past the fracturing Lagrangian interfaces. Applicability The hydrocode micro-model will allow the analyst to track the histories of the individual materials, either at discrete points in the flow (microscopic properties) or as material averages (macroscopic properties), the latter being directly applicable to the development of the MCESM. Another advantage of the proposed micro-model is that it is readily altered to reflect mixed or non-uniform sediment properties such as grain size and roughness, gas content, and sediment materials. The model can be extended to include an interface with water. This is as simple as setting aside a portion of the domain in which only SPH particles interact (no Lagrangian grains), as illustrated in Figure 2. The water region can include gas particles; in fact, the propagation of shocks through bubbly liquids can be studied with such a model. 4 Johnson, G.R., Linking of Lagrangian Particle Methods to Standard Finite Element Methods for High Velocity Impact Computations, presented at Post-SMIRT Impact IV Seminar, Berlin, Germany, August of 5

4 Sediment Region Water Region Figure 2. Portion of Sediment/Water Interaction Micro-Model The interaction of multi-component sediments with thin plates (e.g., buried mines) can also be studied with a variant of the micro-model: a thick (on the scale of the model) plate of Lagrangian Finite Element material can be inserted as a boundary condition on the soil/water/gas mixture, with void or gas behind the plate, as illustrated in Figure 3. The micro-model can further assist in the development of experimental gages for use in saturated sediments, since the validated model will be able to "gage" the pressure at a point in space much smaller than is possible with state-of-the-art gages. Employed in this sense, the model will function as a tool to bridge the gap between, and enhance the combined value of, experimental and computational analyses. Difficulties Foreseen An obstacle expected to be encountered is the application of boundary conditions. For this and other reasons, a 2D, plane strain, model as illustrated in the attached figure must be developed. A disadvantage of the 2D model is the unphysical relationship between the "infinite" length sand grains and surrounding fluids. The interconnections of 4 of 5

5 Sediment Region Structure Region Void Figure 3. Portion of Sediment/Plate Interaction Micro-Model the sand grains and the interconnections of the fluid regions cannot both be modeled in 2D; physically meaningful results will therefore only be obtained by a 3D model. The 2D model is, however, a logical step toward the goal of a hydrocode micro-model; it will provide very useful information for gaging the feasibility of a 3D model, including mesh density requirements. The fracture modeling of the solid particles is a critical issue; however, this is a problem generic to hydrocodes and constitutive modeling. Potential approaches include deleting failed elements, transferring failed element material to SPH particles, and/or disconnecting adjacent elements. Sub-scale (relative to the length/time scales in the model) phenomena like boundary layers and surface tension 5 may figure prominently in the overall effects. 5 Wilson, W., Naval Surface Warfare Center, White Oak, MD, personal conversation, 8 Dec of 5