Modified cutting-plane integration scheme for elasto-viscoplastic models
LI Jian1,2, CAI Guo-qing1,2, YIN Zhen-yu3
1. Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China; 2. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China; 3. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China
Abstract：The elasto-viscoplastic model can be regarded as a combination of the modified Cam-clay model and the overstress theory. Firstly, the stress-strain formulas for the model are rearranged, in which an evolution equation for the hardening parameter of dynamic loading surface is deduced based on the overstress theory. Secondly, the rearranged stress-strain formulas are numerically implemented by the cutting-plane integration scheme. In an elastic prediction process, the viscoplastic strain rate is assumed to be constant, which guarantees the deviation of the current stress state from dynamic loading surface due to time increments. In a plastic corrector process, a Taylor series approximation of the dynamic loading function is used to obtain the increment of viscoplastic multiplier rate. Thirdly, an adaptive substepping method is proposed to maintain the accuracy and convergence of the proposed algorithm at a large loading step. Finally, the performances of the modified cutting-plane algorithm are analyzed by the calculated results of step-changed oedometer tests and undrained triaxial tests.
 YIN Z Y, ZHU Q Y, YIN J H, et al.Stress relaxation coefficient and formulation for soft soils[J]. Géotechnique Letters, 2014, 4(1): 45-51.  YAO Y P, KONG L M, ZHOU A N, et al.Time-dependent unified hardening model: three-dimensional elastoviscoplastic constitutive model for clays[J]. Journal of Engineering Mechanics, 2015, 141(6): 0414162.  尹振宇, 朱启银, 朱俊高. 软黏土蠕变特性试验研究:回顾与发展[J]. 岩土力学, 2013, 24(增刊2):1-17. (YIN Zhen-yu, ZHU Qi-yin, ZHU Jun-gao.Experimental investigation on creep behavior of soft clays: Review and development[J]. Rock and Soil Mechanics, 2013, 24(S2): 1-17. (in Chinese))  韩剑, 姚仰平, 尹振宇. 超固结度对超固结饱和黏土不排水蠕变特性的影响研究[J]. 岩土工程学报, 2018, 40(3): 426-430. (HAN Jian, YAO Yang-ping, YIN Zhen-yu.Influences of overconsolidation ratio on undrained creep behavior of overconsolidated saturated clay[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(3): 426-430. (in Chinese))  YIN Z Y, CHANG C S, KARSTUNEN M, et al.An anisotropic elastic-viscoplastic model for soft clays[J]. International Journal of Solids and Structures, 2010, 47(5): 665-677.  YIN Z Y, KARSTUNEN M, CHANG C S, et al.Modeling time-dependent behavior of soft sensitive clay[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2011, 137(11): 1103-1113.  殷建华. 等效时间和岩土材料的弹黏塑性模型[J]. 岩石力学与工程学报, 1999, 18(2): 124-128. (YIN Jian-hua.Equivalent time and elastic visco-plastic modelling of geomaterials[J]. Chinese Journal of Rock Mechanics and Engineering, 1999, 18(2): 124-128. (in Chinese))  王立忠, 但汉波. K0固结软黏土的弹黏塑性本构模型[J]. 岩土工程学报, 2007, 29(9): 1344-1354. (WANG Li-zhong, DAN Han-bo.Elastic viscoplastic constitutive model for K0-consolidated soft clays[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(9): 1344-1354. (in Chinese))  李兴照, 黄茂松, 王录民. 流变性软黏土的弹黏塑性边界面本构模型[J]. 岩石力学与工程学报, 2007, 26(7): 1393-1401. (LI Xing-zhao, HUANG Mao-song, WANG Lu-min.Bounding surface elasto-viscoplastic constitutive model for rheological behaviors of soft clays[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(7): 1393-1401. (in Chinese))  尹振宇. 天然软黏土的弹黏塑性本构模型:进展及发展[J]. 岩土工程学报, 2011, 33(9): 1357-1369. (YIN Zhen-yu, Elastic viscoplastic models for natural soft clay: review and development[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(9): 1357-1369. (in Chinese))  孔令明, 罗汀, 姚仰平. 率相关本构模型的临界状态描述[J]. 岩土力学, 2015, 36(9): 2442-2450. (KONG Ling-ming, LUO Ting, YAO Yang-ping.Description of critical state for rate-dependent constitutive models[J]. Rock and Soil Mechanics, 2015, 36(9): 2442-2450. (in Chinese))  ORTIZ M, SIMO J C.An analysis of a new class of integration algorithms for elastoplastic constitutive relations[J]. International Journal for Numerical Methods in Engineering, 1986, 23(3): 353-366.  PERZYNA P.Fundamental problems in viscoplasticity[J]. Advances in Applied Mechanics, 1966, 9: 243-377.  KATONA M G.Evaluation of viscoplastic cap model[J]. Journal of Geotechnical Engineering, 1984, 110(8): 1106-1125.  BORJA R I.Cam-clay plasticity: part II implicit integration of constitutive equation based on a nonlinear elastic stress predictor[J]. Computer Methods in Applied Mechanics and Engineering, 1991, 88: 225-240.  STOLLE D F E, VERMEER P A, BONNIER P G. Time integration of a constitutive law for soft clays[J]. Communications in Numerical Methods in Engineering, 1999, 15(8): 603-609.  HIGGINS W, CHAKRABORTY T, BASU D.A high strain-rate constitutive model for sand and its application in finite-element analysis of tunnels subjected to blast[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(15): 2590-2610.  YIN Z Y, LI J, JIN Y F, et al.Estimation of robustness of time integration algorithms for elasto-viscoplastic modeling of soils[J]. International Journal of Geomechanics, 2019, 19(2): 04018197.  SHENG D, SLOAN S W, GENS A, et al.Finite element formulation and algorithms for unsaturated soils: part I theory[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2003, 27(9): 745-765.  WANG W, DATCHEVA M, SCHANZ T, et al.A sub-stepping approach for elastoplasticity with rotational hardening[J]. Computational Mechanics, 2006, 37(3): 266-278.  SLOAN S W.Substepping schemes for the numerical integration of elastoplastic stress-strain relations[J]. International Journal for Numerical Methods in Engineering, 1987, 24(5): 893-911.