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Deformation and fracture model for a multicomponent elastoplastic porous medium with continuous variation of physicomechanical characteristics

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Strength of Materials Aims and scope

Abstract

A mathematical model and a procedure of solving problems for the development of functionally gradient porous materials ensuring the desired distribution of stress-strain state parameters over the volume of the structure under explosion and impact loadings are proposed. The choice of the model is based on general theoretical concepts and is validated by comparison of the calculated results with experimental data.

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Abbreviations

v i :

velocity-vector components

S ij :

stress-deviator components

E :

specific internal energy

ɛ ij :

strain-rate-deviator components

σ ij :

stress-tensor components

δ ij :

Kronecker delta

D/Dt :

Jaumann derivative

e ij :

strain-rate-tensor components

μ:

shear modulus

σ:

yield stress

f :

porosity parameter

d s , η:

material constants

V s :

specific volume of a matrix

V p ,V :

specific volume of pores and a porous medium, respectively

P s :

pressure in a matrix

σ s , μ s :

yield stress and shear modulus of a matrix

Φ:

porosity

ɛ p ij :

plastic-strain-tensor components

x :

relative volume (compressibility)

ɛp :

equivalent plastic strain

α1,n 1,b, h :

material constants

T m ,T m0 :

melting temperature under loading and under normal conditions, respectively

ρ0 :

initial density

V 0 :

initial specific volume of an alloy

α n :

weight fraction of thenth component

V 0n :

specific volume of thenth component

γ 0 :

Grüneisen function

K s :

isothermal modulus in compression

β:

thermal-expansion coefficient

C v :

thermal capacity at constant volume

ρ1 :

density atT=0 K

m :

parameter of interatomic interaction

E 0 :

initial specific energy of thermal vibrations

f * :

limiting value off

ɛ p * :

limiting value of ɛp

W 0 :

impact velocity

ɛ0 :

specific internal energy atT=0 K

References

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Authors
  1. A. V. Gerasimov
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  2. R. A. Krektuleva
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Additional information

Research Institute of Applied Mathematics and Mechanics, Tomsk University, Tomsk, Russia. Translated from Problemy Prochnosti, No. 2, pp. 139–150, March–April, 1999.

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Gerasimov, A.V., Krektuleva, R.A. Deformation and fracture model for a multicomponent elastoplastic porous medium with continuous variation of physicomechanical characteristics. Strength Mater 31, 210–218 (1999). https://doi.org/10.1007/BF02511111

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  • DOI: https://doi.org/10.1007/BF02511111

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