×

zbMATH — the first resource for mathematics

Numerical modelling of shocks in solids with elastic-plastic conditions. (English) Zbl 0782.73023
The problems of one- and two-dimensional shock waves under elastic- plastic conditions together with stiffened-gas equation of state are considered using flux-corrected transport technique. Both operator-split and non-operator-split results are used to demonstrate certain features of the solution. The elastic-plastic conditions highlight some differences between operator-split and non-operator split solutions. A comparison with hydrodynamic models in made. The errors due to initial conditions appear in the form of spikes when large pressure and energy ratio is considered. In other studies one would use an artificial heat conduction or viscocity term to eliminate these spikes. No such attempt is made here in order to avoid loss of high resolution of shock fronts.

MSC:
74J10 Bulk waves in solid mechanics
74J99 Waves in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
Software:
SHASTA
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Asay JR, Kerley GI (1987) The response of materials to dynamic loading. Int J Impact Engng 5:69
[2] Baer MR, Benner RE, Gross RJ, Nunziato JW (1986) Modeling and computation of deflagration-to-detonation transition (DDT) in reactive Granular materials. In: Ludford GSS (ed) Reacting flow: combustion and chemical reactors, part 2, Lectures in Applied Mathematics 24:479
[3] Book DL, Boris JP, Hain K (1975) Flux-corrected transport. II. Generalizations of the method. J Comput Phys 18:248 · Zbl 0306.76004
[4] Boris JP, Book DL (1973) Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works. J Comput Phys 11:38 · Zbl 0251.76004
[5] Boris JP, Book DL (1976) Flux-corrected transport. III. Minimal-error FCT algorithms. J Comput Phys 20:397 · Zbl 0325.76037
[6] DaSilva L, Ng A, Parfeniuk D (1985) Simulations of temperature measurements of shock-heated solids. J Appl Phys 58:3634
[7] Dietachmayer GS (1987) On the numerical simulation of small scale intense atmospheric vortices. PhD thesis, Monash University, Australia
[8] Harlow FH, Amsden AA (1971) Fluid dynamics. Report LA-4700, Los Alamos Scientific Laboratory (Reprinted 1980)
[9] Noh WF (1987) Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux. J Comput Phys 72:78 · Zbl 0619.76091
[10] Oran ES, Boris JP (1987) Numerical simulation of reactive flow. Elsevier Science Publishing Co., New York · Zbl 0875.76678
[11] Pongracic H (1988) Numerical modelling of large body impacts. PhD thesis, Monash University, Australia
[12] Sod GA (1978) A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J Comp Phys 27:1 · Zbl 0387.76063
[13] Steinberg DJ (1987) Constitutive model used in computer simulation of time-resolved, shock-wave data. Int J Impact Engng 5:603
[14] Tyndall MB (1991) Numerical modelling of shock waves in solid materials. PhD thesis, Monash University, Australia
[15] Tyndall MB (1992) Using flux-corrected transport (FCT) to model simple plate impact problems. Submitted to Int J Impact Engng
[16] Wilkins ML (1964) Calculation of elastic-plastic flow. In: Adler B, Fernbach S, Rotenberg M (eds) Methods in Computational Physics 3:211
[17] Woodward P, Colella P (1984) The numerical simulation of two-dimensional fluid flow with strong shocks. J Comput Phys 54:115 · Zbl 0573.76057
[18] Zalesak ST (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31:335 · Zbl 0416.76002
[19] Zel’dovich YB, Raizer YP (1967) Physics of shock waves and high-temperature hydrodynamic phenomena, Vol I, II. Academic Press
[20] Zukas JA (1990) High velocity impact dynamics. Wiley
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.