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FINITE DEFORMATION ELASTO-PLASTIC THEORY AND consistent algorithm

Acta Mechanica Solida Sinica 2001年第1期14卷 31-40页

作者： Liu Xuejun Li Mingrui Huang Wenbin Applied Mechanics Workshop China Agricultural UniversityEast Campus Beijing 100083 China Applied Mechanics Workshop China Agricultural UniversityEast Campus Beijing 100083 China Applied Mechanics Workshop China Agricultural UniversityEast Campus Beijing 100083 China

By using the logarithmic strain, the finite deformation plastic theory, corresponding to the infinitesimal plastic theory, is established successively. The plastic consistent algorithm with first order accuracy for the finite element method (FEM) is developed. Numerical examples are presented to illustrate the validity of the theory and effectiveness of the algorithm.

关键词： finite element finite deformation elasto-plasticity consistent algorithm

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A consistent return mapping algorithm for pressure-dependent elastoplastic Cosserat continua and modelling of strain localisation

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COMPUTERS & STRUCTURES 2005年第1期83卷 1-10页

作者： Li, XK Tang, HX Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Dalian Univ Technol Sch Civil & Hidraul Engn Dalian 116024 Peoples R China

A pressure-dependent elastoplastic Cosserat continuum model is presented in this paper. Splitting the scalar product of the stress rate and the strain rate into their deviatoric and spherical parts, the consistent algorithm, particularly the closed form of the consistent elastoplastic tangent modulus matrix, of the model is formulated in the framework of Cosserat continuum theory. The matrix inverse operation usually required in the calculation of elastoplastic tangent constitutive modulus matrix is avoided, that enhances computational efficiency of the model in numerical solution procedure with the second order convergence rate ensured. Numerical results illustrate the capability and performance of the present model in modelling strain localization phenomena due to strain softening. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： Cosserat continuum model pressure dependent elastoplasticity consistent algorithm closed form of tangent constitutive modulus matrix strain localization

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A unified consistent source term computational algorithm for the γ-based compressible multi-fluid flow model

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COMPUTERS & FLUIDS 2023年第1期259卷

作者： Li, Ge Li, Libin Liu, Qingquan Feng, Chun Wang, Xiaoliang Beijing Inst Technol Sch Aerosp Engn Dept Mech Beijing 100081 Peoples R China Chinese Acad Sci Inst Mech Beijing 100190 Peoples R China

Using the criterion of one-fluid preservation, we developed a consistent algorithm for the source term to solve the gamma-based compressible multi-fluid flow model with three approximate Riemann solvers, namely the Lax-Friedrichs (LxF), Kurganov, and Harten-Lax-van Leer contact (HLLC) solvers. The consistent algorithm comprises a stan-dard Godunov solver with a high-order reconstruction and a consistent source term integration part. We prove that the present algorithm is consistent with Abgrall's criterion of the moving-material-interface property in the finite volume method framework. The cell boundary velocity for the source term discretization is found to be the same as HLLC solvers from five-equation model, but for the first time for LxF and Kurganov Riemann solvers. We develop 12 compressible multi-fluid solvers by combining four reconstruction schemes and three approximate Riemann solvers together with their consistent-source-term integration algorithms. All 12 solvers can maintain the one-fluid preservation and moving-material-interface properties numerically in several one-and two-dimensional example cases. The simulation of an underwater explosion demonstrates that a boundary -variation-diminishing reconstruction predicts an interface with width controlled within approximately three cells which is independent of the Riemann solver. The simulation of an explosion near a free surface demon-strates that the proposed model can simulate a severe compressible multi-fluid flow involving an interface across which there are large differences in density, pressure and parameters in the equation of state. In conclusion, the proposed consistent algorithm provides a unified framework for one kind of non-conservative hyperbolic system into a conservative hyperbolic system and a source term with velocity divergence, where the former can be computed by classical Godunov-type algorithms and the latter can be solved by the proposed consistent algorithm.

关键词： Compressible multi-fluid flow consistent algorithm One-fluid preservation Moving interface Interface sharpening

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A Coupled Chemo-Elastoplastic-Damage Constitutive Model for Plain Concrete Subjected to High Temperature

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INTERNATIONAL JOURNAL OF DAMAGE MECHANICS 2010年第8期19卷 971-1000页

作者： Li, Rongtao Li, Xikui Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Dalian Univ Coll Civil & Architectural Engn Dalian 116622 Peoples R China

A coupled elastoplastic-damage constitutive model taking into account chemo-induced elastoplastic-damage effects for the modeling of coupled chemo-thermo-hygro-mechanical behavior of concretes at high temperature is proposed in this article. A three-step operator split algorithm for the integration of the rate coupled constitutive equations is developed. consistent tangent modulus matrices for coupled chemo-thermo-hygro-mechanical analysis are derived to preserve the quadratic rate of convergence of the global Newton iterative procedure. Numerical results demonstrate the validity of the presented algorithm and illustrate the capability of the proposed constitutive model in reproducing coupled chemo-thermo-hygro-mechanical behavior in concretes subjected to fire and thermal radiation.

关键词： chemo-elastoplastic-damage coupled constitutive model consistent algorithm concrete high temperature

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Simulation of strain localization with discrete element-Cosserat continuum finite element two scale method for granular materials

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2019年 122卷 450-471页

作者： Tang, Hongxiang Dong, Yan Wang, Ting Dong, Yifeng Dalian Univ Technol State Key Lab Coastal & Offshore Engn Dalian 116023 Peoples R China Chengdu Univ Technol State Key Lab Geohazard Prevent & Geoenvironm Pro Chengdu 610059 Sichuan Peoples R China

A multiscale method is proposed based on an individual particle provided with rotational freedom, which considers the kinematic connections and transformation consistency of physical parameters in micro-macro models, as well as the need for a regularization mechanism in the classical macroscopic continuum model to preserve the well-posedness of the localization problem. This method uses the discrete element method to incorporate both rolling resistances (rolling friction tangential force and rolling resistance moment) and the sliding friction tangential force between particles in the contact model on a microscopic scale, while the Cosserat continuum is used to describe the granular materials on a macroscopic scale. In addition, a consistent return mapping algorithm for the integration of the rate constitutive equation and the closed form of the consistent elastoplastic tangent modulus matrix for the generalized elastoplastic Cosserat continuum model are presented. The effectiveness of the developed multiscale method is demonstrated with two cases: one comparing discrete element computations with the Cosserat finite element analysis, and the other comparing a plane strain compression experiment using digital imaging measurements with the Cosserat finite element analysis. The rotational deformation and shear band failure modes are well reproduced in both cases. It also demonstrates that the present model has better performance in predicting the phenomena of shear bands than previous ones. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Strain localization Multiscale method Discrete element Finite element consistent algorithm Cosserat continuum

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Finite element method for gradient plasticity at large strains

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 1996年第4期39卷 619-633页

作者： Li, XK Cescotto, S UNIV LIEGE MSM DEPTB-4000 LIEGEBELGIUM

A finite element method for gradient elasto-plastic continuum in which the yield strength of strain hardening/softening materials not only depends on the effective plastic strain but also on its Laplacian is presented. The consistent integration algorithm to update the stress and the internal state variable at integration points and the consistent compliance matrix for the gradient plasticity are formulated in the non-local sense. The methodology to derive the finite element formulation for the gradient plasticity at large strains presented in this paper is applicable to general finite element analysis;the formulation in the context of the two-dimensional four-noded mixed finite element with one integration point and mean von Mises yield criterion is particularly derived. Numerical examples are tested to demonstrate the capability and performance of the present finite element method at large strain in solving for the strain localization problem.

关键词： gradient plasticity strain localization mixed strain element method large strain consistent algorithm

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Elastoplastic axisymmetric Cosserat continua and modelling of strain localization

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COMPUTERS AND GEOTECHNICS 2018年 101卷 159-167页

作者： Tang, Hongxiang Sun, Fabing Zhang, Yipeng Dong, Yan Dalian Univ Technol State Key Lab Coastal & Offshore Engn Dalian 116023 Peoples R China Chengdu Univ Technol State Key Lab Geohazard Prevent & Geoenvironm Pro Chengdu 610059 Sichuan Peoples R China

The theory and finite-element formula of the axisymmetric Cosserat continuum are presented by introducing an independent rotational degree of freedom into the axisymmetric continuum. A pressure-dependent elastic-plastic model and the corresponding consistent algorithm for the constitution integration of the model are presented in the framework of the axisymmetric Cosserat continuum theory. The numerical examples illustrate that the developed model can maintain the well-posedness of the boundary value problems;overcome the problems of mesh-dependency, which commonly occur in the classical continuum when the strain softening behaviour is incorporated;and capture the entire progressive failure process.

关键词： Axisymmetric Elastoplastic consistent algorithm Finite element Cosserat continua

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Constitutive relations in 3-D for a wide range of strain rates and temperatures - Application to mild steels

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2007年第17期44卷 5611-5634页

作者： Rusinek, A. Zaera, R. Klepaczko, J. R. Univ Metz CNRS Lab Phys & Mech Mat UMR 75 54 F-57045 Metz France Univ Carlos III Madrid Dept Continum Mech & Struct Anal Madrid 28911 Spain

An original phenomenological thermo-visco-plastic model is reported that encompasses strain hardening, strain rate and temperature sensitivity. The model is based to some extent on the concept of physical modeling proposed earlier by Klepaczko [Klepaczko, JR. 1975. Thermally activated flow and strain rate history effects for some polycrystalline FCC metals. Mater. Sci. Engng. 18, 121-135], and also by different authors, for example: [Becker, R. 1925. Uber die plastizitat amorpher und kristalliner fester korper. Z. Physik 26, 919-925;Seeger, A., 1957. Dislocations and Mechanical Properties of Crystals, Wiley, New York;Conrad, H., 1964. Thermally activated deformation of metals J. Metals 16, 582;Gilman, J.J. 1968. Dislocation dynamics and response of materials to impact Appl. Mech. Rev. 21, 767-783;Gibbs, G.B., 1969. Thermodynamic analysis of dislocation glide controlled by dispersed local obstacles. Mater. Sci. Engng. 4, 313-328;Kocks, U.F., Argon, A.S., Ashby, M.F., 1975. Thermodynamics and kinetics of slip. In: Progress in Materials Science, vol. 19. Pergamon Press, New York, p. 19;Kocks, U.F. 1976. Laws for work-hardening and low-temperature creep. J. Eng. Mater. Technol. 98, 76-85, and later by many others. The thermo-visco-plastic formulation, called RK and applied in this paper, has been verified experimentally for strain rates of 10(-4) s(-1) <= epsilon(p) <= 5 x 103 s(-1) and temperatures 213 K <=, T <= 393 K, it covers the range of dynamic loadings observed during crash tests and other impact problems. In order to implement the RK constitutive relation, a thermo-visco-plastic algorithm based on the J(2) theory of plasticity is constructed. The type of algorithm is a return mapping one that introduces the consistency condition (f = a sigma- sigma(y) = 0), without the overstress state proposed by Perzyna [Perzyna, P. 1966. Fundamental problems in viscoplasticity. Advances in Applied Mechanics, vol. 9. Academic Press, New York, pp. 243-377], The coupling of the

关键词： mild steel RK constitutive relation thermo-visco-plasticity consistent algorithm dynamic plasticity numerical simulations finite element code

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A consistent DXDR METHOD FOR ELASTIC-PLASTIC PROBLEMS

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 1995年第14期38卷 2413-2431页

作者： KADKHODAYAN, M ZHANG, LC UNIV SYDNEY DEPT MECH & MECHATRON ENGN SYDNEY NSW 2006 AUSTRALIA

This paper proposed a new efficient method, the consistent DXDR method, for analysing general elastic-plastic problems. Two important factors in computational plasticity, the convergence and stability, were addressed. The method was constructed through a natural combination of two vital components: the DXDR algorithm which had been proved to be a powerful equation solver developed by the authors and a stable consistent algorithm for the integration of the constitutive equations of plasticity. Numerical examples demonstrated in detail the efficiency, accuracy, and stability attainable in solving various engineering problems.

关键词： consistent algorithm PLASTIC DEFORMATION DYNAMIC RELAXATION COMPUTATIONAL STABILITY CONVERGENCE RATE

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A Modified Drucker-Prager Criterion for Transversely Isotropic Geomaterials and Its Numerical Implementation

A Modified Drucker-Prager Criterion for Transversely Isotrop...

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International Forum on Materials Analysis and Testing Technology (IFMATT 2013)

作者： Wu, Weiyu Liu, Guohua Zhejiang Univ Coll Civil Engn & Architecture Hangzhou 310058 Zhejiang Peoples R China

ISBN: (纸本)9783037859537

A failure criteria basing on Drucker-Prager yield criterion for geomaterials is modified in terms of the inherent anisotropy of the friction angle and the dilation angle. To implement the model in a numerical way, the corresponding consistent return mapping algorithm is formulated and by dividing the scalar product of the stress rate and the strain rate into the deviatoric and spherical parts, the consistent elastoplastic tangent modulus matrix is obtained. Then, the codes are introduced into finite element software ABAQUS via the UMAT. An example has been presented illustrating influence of the anisotropic degree on the bearing capacity and the pattern of strain localization.

关键词： geomaterials transversely isotropy failure criterion consistent algorithm strain localization UMAT

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