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Register a new userNumerical solution of shock and ramp compression for general material properties
حل رقمي لضغط الصدمة والصعود لخصائص المواد العامة
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Damian C. Swift
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صُمِمَتْ صيغة عامة لتمثيل الأنماط المادية للتطبيقات في التحميل الديناميكي. تم تصميم أساليب رقمية لحساب الاستجابة للصدمة والضغط المدرج والإفراز المدرج، تشمل الحلول السابقة لمعادلات الدولة المكعبة. وقد وجد أن الأساليب الرقمية كانت مرنة وثابتة، وتطابقت النتائج التحليلية بدقة عالية. تم ربط الحلول الأساسية للضغط المدرج والصدمة لحل المسارات الإجهاد المركب، مثل الأثر الصدمي المسبب والتفاعل الصدمي مع واجهة مستوية بين مواد مختلفة. هذه الحسابات تصحح الكثير من الفيزياء التي تشهدها التجارب الديناميكية المادية دون الحاجة إلى تحليلات محددة الموقع. تم إجراء حسابات بالأمثلة لتاريخ التحميل في المعادن، والتي توضح تأثير العمل البلاستيكي على الحرارات الناتجة في التجارب القريبة من الإحتسابية والإفراز الصدمي، وتأثير الانتقال المرحلي.
A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scalar equations of state. The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a planar interface between different materials. These calculations capture much of the physics of typical material dynamics experiments, without requiring spatially-resolving simulations. Example calculations were made of loading histories in metals, illustrating the effects of plastic work on the temperatures induced in quasi-isentropic and shock-release experiments, and the effect of a phase transition.
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We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long duration ramps are desired.
Here, we provide a theoretical framework revealing that a steady compression ramp flow must have the minimal dissipation of kinetic energy, and can be demonstrated using the least action principle. For a given inflow Mach number $M_{0}$ and ramp angle $alpha$, the separation angle $theta_{s}$ manifesting flow system states can be determined based on this theory. Thus, both the shapes of shock wave configurations and pressure peak $p_{peak}$ behind reattachment shock waves are predictable. These theoretical predictions agree excellently with both experimental data and numerical simulations, covering a wide range of $M_{0}$ and $alpha$. In addition, for a large separation, the theory indicates that $theta_{s}$ only depends on $M_{0}$ and $alpha$, but is independent of the Reynolds number $Re$ and wall temperature $T_{w}$. These facts suggest that the proposed theoretical framework can be applied to other flow systems dominated by shock waves, which are ubiquitous in aerospace engineering.
Direct modeling of porous materials under shock is a complex issue. We investigate such a system via the newly developed material-point method. The effects of shock strength and porosity size are the main concerns. For the same porosity, the effects of mean-void-size are checked. It is found that, local turbulence mixing and volume dissipation are two important mechanisms for transformation of kinetic energy to heat. When the porosity is very small, the shocked portion may arrive at a dynamical steady state; the voids in the downstream portion reflect back rarefactive waves and result in slight oscillations of mean density and pressure; for the same value of porosity, a larger mean-void-size makes a higher mean temperature. When the porosity becomes large, hydrodynamic quantities vary with time during the whole shock-loading procedure: after the initial stage, the mean density and pressure decrease, but the temperature increases with a higher rate. The distributions of local density, pressure, temperature and particle-velocity are generally non-Gaussian and vary with time. The changing rates depend on the porosity value, mean-void-size and shock strength. The stronger the loaded shock, the stronger the porosity effects. This work provides a supplement to experiments for the very quick procedures and reveals more fundamental mechanisms in energy and momentum transportation.
The collapse of cavities under shock is a key problem in various fields ranging from erosion of material, ignition of explosive, to sonoluminescence, etc. We study such processes using the material-point-method developed recently in the field of solid physics. The main points of the research include the relations between symmetry of collapsing and the strength of shock, other coexisting interfaces, as well as hydrodynamic and thermal-dynamic behaviors ignored by the pure fluid models. In the case with strong shock, we study the procedure of jet creation in the cavity; in the case with weak shock, we found that the cavity can not be collapsed completely by the shock and the cavity may collapse in a nearly isotropic way. The history of collapsing significantly influences the distribution of hot spots in the shocked material. The change in symmetry of collapsing is investigated. Since we use the Mie-Gr% {u}neisen equation of state and the effects of strain rate are not taken into account, the behavior is the same if one magnifies the spatial and temporal scales in the same way.
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