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Based on the standard linear solid model, the solutions in Laplace domain, such as particle velocity v, particle displacement u, radial stress σr, tangential stress σθ, radial strain εr, tangential strain εθ, reduced velocity potential γ (RVP), and reduced displacement potential ψ (RDP), are derived from the spherical wave equations. The propagating characteristics of these physical quantities, as mentioned above, are calculated by using Crump algorithm for inverse Laplace transformation. The numerical inversion results reveal that the initial response to strong discontinuity spherical stress wave in viscoelastic material is purely elastic response. The strong discontinuities, such as σr, σθ, εr, εθ and v, contain geometrical attenuation and viscoelastic damping in the process of wave propagation. The variables, such as σr, σθ, εr, εθ,u and ψ, converge to steady values as time approaches to infinity. The peak values of RVP γ and RDP ψ, which are constant in a purely elastic material, are steadily reduced with the spreading distance increasing in viscoelastic material. The steady values of ψ are in inverse relation to the static shear modulus Ga, and directly proportional to the steady cavity pressure and the cube of the cavity radius r.
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Keywords:
- mechanics of explosion /
- spherical stress waves /
- standard linear solid model /
- Laplace inversion transform
[1] Garg S K 1968 J. Appl. Math. Phys. 19 243
[2] Garg S K 1968 J. Appl. Math. Phys. 19 778
[3] Li X L 2000 Explosion and Shock Waves 20 186 (in Chinese) [李孝兰 2000 爆炸与冲击 20 186]
[4] Li X L 2000 Explosion and Shock Waves 20 283 (in Chinese) [李孝兰 2000 爆炸与冲击 20 283]
[5] Perzyna P 1963 J. Appl. Math. Phys. 14 241
[6] Zabinski M P, Phillips A 1974 Acta Mech. 20 153
[7] Phillips A, Zabinski M P 1972 Ingenieur. Archiv. 41 367
[8] Koshelev E A 1988 Soviet Mining 24 541
[9] Banerjee S, Roychoudhuri S K 1995 Comput. Math. Appl. 30 91
[10] Wang L L, Lai H W, Wang Z J, Yang L M 2013 Int. J. Impact Eng. 55 1
[11] Lu Q, Wang Z J, Wang L L, Lai H W, Yang L M 2013 Explosion and Shock Waves 33 463 (in Chinese) [卢强, 王占江, 王礼立, 赖华伟, 杨黎明 2013 爆炸与冲击 33 463]
[12] Lu Q, Wang Z J, Li J, Guo Z Y, Men C J 2012 Rock Soil Mech. 33 3292 (in Chinese) [卢强, 王占江, 李进, 郭志昀, 门朝举 2012 岩土力学 33 3292]
[13] Lai H W, Wang Z J, Yang L M, Wang L L 2013 Explosion and Shock Waves 33 1 (in Chinese) [赖华伟, 王占江, 杨黎明, 王礼立 2013 爆炸与冲击 33 1]
[14] Lai H W, Wang Z J, Yang L M, Wang L L 2013 Chin. J. High Pressure Phys. 27 245 (in Chinese) [赖华伟, 王占江, 杨黎明, 王礼立 2013 高压 27 245]
[15] Du Q Z 2004 Acta Phys. Sin. 53 4428 (in Chinese) [杜启振 2004 53 4428]
[16] Du Q Z, Yang H Z 2004 Acta Phys. Sin. 53 2801 (in Chinese) [杜启振, 杨慧珠 2004 53 2801]
[17] Feng Y L, Liu X Z, Liu J H, Ma L 2009 Chin. Phys. B 18 3909
[18] Yao G J, L W G, Song R L, Cui Z W, Zhang X L, Wang K X 2010 Chin. Phys. B 19 074301
[19] Lepage W R 1961 Complex Variables and the Laplace Transform for Engineers (America: Dover Publications Inc) pp372-378
[20] Crump K S 1976 J. Associat. Comput. Machin. 23 89
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[1] Garg S K 1968 J. Appl. Math. Phys. 19 243
[2] Garg S K 1968 J. Appl. Math. Phys. 19 778
[3] Li X L 2000 Explosion and Shock Waves 20 186 (in Chinese) [李孝兰 2000 爆炸与冲击 20 186]
[4] Li X L 2000 Explosion and Shock Waves 20 283 (in Chinese) [李孝兰 2000 爆炸与冲击 20 283]
[5] Perzyna P 1963 J. Appl. Math. Phys. 14 241
[6] Zabinski M P, Phillips A 1974 Acta Mech. 20 153
[7] Phillips A, Zabinski M P 1972 Ingenieur. Archiv. 41 367
[8] Koshelev E A 1988 Soviet Mining 24 541
[9] Banerjee S, Roychoudhuri S K 1995 Comput. Math. Appl. 30 91
[10] Wang L L, Lai H W, Wang Z J, Yang L M 2013 Int. J. Impact Eng. 55 1
[11] Lu Q, Wang Z J, Wang L L, Lai H W, Yang L M 2013 Explosion and Shock Waves 33 463 (in Chinese) [卢强, 王占江, 王礼立, 赖华伟, 杨黎明 2013 爆炸与冲击 33 463]
[12] Lu Q, Wang Z J, Li J, Guo Z Y, Men C J 2012 Rock Soil Mech. 33 3292 (in Chinese) [卢强, 王占江, 李进, 郭志昀, 门朝举 2012 岩土力学 33 3292]
[13] Lai H W, Wang Z J, Yang L M, Wang L L 2013 Explosion and Shock Waves 33 1 (in Chinese) [赖华伟, 王占江, 杨黎明, 王礼立 2013 爆炸与冲击 33 1]
[14] Lai H W, Wang Z J, Yang L M, Wang L L 2013 Chin. J. High Pressure Phys. 27 245 (in Chinese) [赖华伟, 王占江, 杨黎明, 王礼立 2013 高压 27 245]
[15] Du Q Z 2004 Acta Phys. Sin. 53 4428 (in Chinese) [杜启振 2004 53 4428]
[16] Du Q Z, Yang H Z 2004 Acta Phys. Sin. 53 2801 (in Chinese) [杜启振, 杨慧珠 2004 53 2801]
[17] Feng Y L, Liu X Z, Liu J H, Ma L 2009 Chin. Phys. B 18 3909
[18] Yao G J, L W G, Song R L, Cui Z W, Zhang X L, Wang K X 2010 Chin. Phys. B 19 074301
[19] Lepage W R 1961 Complex Variables and the Laplace Transform for Engineers (America: Dover Publications Inc) pp372-378
[20] Crump K S 1976 J. Associat. Comput. Machin. 23 89
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