率相关饱和多孔介质动力响应的数值分析
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摘要
在基于混合物理论的多孔介质模型的基础上,将固体相视为弹粘塑性体,建立了饱和多孔介质的弹粘塑性模型。模型的基本思想是在无粘弹塑性本构关系中引入一时间参数,使固体骨架具备了粘性效应。利用Galerkin加权残值法推导得到了罚有限元格式,并采用Newmark预估校正法求解率相关饱和多孔介质的非线性有限元动力方程,此算法可以很好的求解非线性的饱和多孔介质弹粘塑性模型的动力响应。数值算例验证了模型的率相关性和时效特性,并分析了动力载荷作用下的固体骨架的位移场、应力场、塑性区分布以及孔隙液体的速度场和孔压的变化。
In the light of porous media model developed from mixtures theories,the solid skeleton was considered as elasto-viscoplastic material,and an elasto-viscoplastic model of saturated porous media was established.By adding a time parameter in inviscid elasto-plastic constitutive relation,the viscoplasticity was introduced into the solid skeleton.A penalty finite element formulation was attained by using Galerkin weighted residual method,and a Newmark predictor-corrector iterative scheme was designed to solve the nonlinear finite element system equations of rate-dependent porous media.The scheme is good at calculating the dynamic response of saturated elasto-viscoplastic porous media model.Through two numerical examples,the saturated elasto-viscoplastic porous media exhibited obvious rate-dependent property and time effect.Not only the displacements,solid stresses,plastic zone of solid skeleton,but also the flow velocity,pore pressure of interstitial fluid were presented and discussed.
In the light of porous media model developed from mixtures theories,the solid skeleton was considered as elasto-viscoplastic material,and an elasto-viscoplastic model of saturated porous media was established.By adding a time parameter in inviscid elasto-plastic constitutive relation,the viscoplasticity was introduced into the solid skeleton.A penalty finite element formulation was attained by using Galerkin weighted residual method,and a Newmark predictor-corrector iterative scheme was designed to solve the nonlinear finite element system equations of rate-dependent porous media.The scheme is good at calculating the dynamic response of saturated elasto-viscoplastic porous media model.Through two numerical examples,the saturated elasto-viscoplastic porous media exhibited obvious rate-dependent property and time effect.Not only the displacements,solid stresses,plastic zone of solid skeleton,but also the flow velocity,pore pressure of interstitial fluid were presented and discussed.
引文
[1]Loret B,Prevost J H.Dynamic strain-localization in fluid-saturated porous media[J].Journal of Engineering Mechanics,ASCE,1991,117(4):907―922.
[2]陈少林,廖振鹏.两相介质动力学问题的研究进展[J].地震工程与工程振动,2002,22(2):1―8.Chen Shaolin,Liao Zhenpeng.Advances in research on two-pbase media dynamic problem[J].Earthquake Engineering and Engineering Vibration,2002,22(2):1―8.(in Chinese)
[3]Biot M A.The theory of propagation of elastic waves in a fluid-saturated porous solid[J].Journal of the Acoustical Society of America,1956,28(2):168―191.
[4]Bowen R M.Incompressible porous media models by use of the theory of mixtures[J].International Journal of Engineering Science,1980,18(9):19―45.
[5]Bowen R M.Compressible porous media models by use of the theory of mixtures[J].International Journal of Engineering Science,1982,20(6):697―735.
[6]Prevost J H.Wave propagation in fluid-saturated porous media:An efficient finite element procedure[J].Soil Dynamics and Earthquake Engineering,1985,4(4):183―202.
[7]Lai W M,Mow V C,Zhu W.Constitutive modeling of articular cartilage and biomacromolecular solutions[J].Journal of Biomechanical Engineering,1993,115:474―480.
[8]刘占芳,姜乃斌,李思平.饱和多孔介质一维瞬态波动问题的解析分析[J].工程力学,2006,23(7):19―24.Liu Zhanfang,Jiang Naibin,Li Siping.An analysis on one-dimensional transient wave motion in saturated porous media[J].Engineering Mechanics,2006,23(7):19―24.(in Chinese)
[9]Duvaut G,Lions J L.Les Inequations en Mecanique et en Physique[M].Paris,France:Dunod,1972.(in French)
[10]Owen D R J,Hinton E.Finite elements in plasticity:Theory and practice[M].Swansea,UK:Pineridge Press Limited,1980.
[2]陈少林,廖振鹏.两相介质动力学问题的研究进展[J].地震工程与工程振动,2002,22(2):1―8.Chen Shaolin,Liao Zhenpeng.Advances in research on two-pbase media dynamic problem[J].Earthquake Engineering and Engineering Vibration,2002,22(2):1―8.(in Chinese)
[3]Biot M A.The theory of propagation of elastic waves in a fluid-saturated porous solid[J].Journal of the Acoustical Society of America,1956,28(2):168―191.
[4]Bowen R M.Incompressible porous media models by use of the theory of mixtures[J].International Journal of Engineering Science,1980,18(9):19―45.
[5]Bowen R M.Compressible porous media models by use of the theory of mixtures[J].International Journal of Engineering Science,1982,20(6):697―735.
[6]Prevost J H.Wave propagation in fluid-saturated porous media:An efficient finite element procedure[J].Soil Dynamics and Earthquake Engineering,1985,4(4):183―202.
[7]Lai W M,Mow V C,Zhu W.Constitutive modeling of articular cartilage and biomacromolecular solutions[J].Journal of Biomechanical Engineering,1993,115:474―480.
[8]刘占芳,姜乃斌,李思平.饱和多孔介质一维瞬态波动问题的解析分析[J].工程力学,2006,23(7):19―24.Liu Zhanfang,Jiang Naibin,Li Siping.An analysis on one-dimensional transient wave motion in saturated porous media[J].Engineering Mechanics,2006,23(7):19―24.(in Chinese)
[9]Duvaut G,Lions J L.Les Inequations en Mecanique et en Physique[M].Paris,France:Dunod,1972.(in French)
[10]Owen D R J,Hinton E.Finite elements in plasticity:Theory and practice[M].Swansea,UK:Pineridge Press Limited,1980.
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