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Three optimal families of three-sub-step dissipative implicit integration algorithms with either second, third, or fourth-order accuracy for second-order nonlinear dynamics

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2023年第17期124卷 3733-3766页

作者： Li, Jinze Yu, Kaiping Zhao, Rui Fang, Yong Harbin Inst Technol Dept Astronaut Sci & Mech Harbin Peoples R China Harbin Inst Technol Sch Civil Engn Harbin Peoples R China Harbin Inst Technol Dept Astronaut Sci & Mech 92 West Dazhi St Harbin 150001 Peoples R China

This paper reviews the published composite three-sub-step implicit algorithms all of which adopt the trapezoidal rule in the first sub-step. Three optimal families of three-sub-step implicit algorithms are developed to achieve second, third, and fourth-order accuracy. The present second- and third-order methods achieve identical effective stiffness matrices, thus embedding optimal spectral characteristics. Besides, both of them impose two dissipative parameters (rho 2 infinity and rho 3 infinity) to control numerical dissipation imposed in the second and third sub-steps. The parameter rho 3 infinity adjusts overall numerical dissipation in the whole integration schemes, while the firstly used parameter rho 2 infinity can change numerical dissipation in the second sub-step. The numerical example has shown the superiority of controlling middle sub-step dissipation via rho 2 infinity$. The present fourth-order method is moderately dissipative due to achieving higher-order accuracy, but it presents a more reasonable sub-step division than the published fourth-order three-sub-step trapezoidal rule. Linear and nonlinear examples are simulated to show the numerical performance and superiority of the three novel methods. This paper recommends using the proposed second- and third-order three-sub-step methods to solve various dynamic problems.

关键词： controllable dissipation higher-order accuracy implicit integration algorithm second-order accuracy three-sub-step

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An efficient finite strain constitutive model for amorphous thermoplastics: Fully implicit computational implementation and optimization-based parameter calibration

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COMPUTERS & STRUCTURES 2023年第1期281卷

作者： Ferreira, Bernardo P. Alves, Francisca Carvalho Pires, Andrade Univ Porto Fac Engn DEMec Dept Mech Engn Rua Dr Roberto Frias P-4200465 Porto Portugal

In this paper, a new visco-elastic visco-plastic (three-dimensional) constitutive model is consistently formulated under isothermal conditions to describe the nonlinear behavior of thermoplastic polymers at finite strains. The constitutive equations include three well-established rheological elements to have well-defined parametric behavior and capture the experimental response. In particular, a visco-elastic generalized Maxwell element, a visco-plastic Eyring dashpot, and a plasticity-induced (nonlinear) hardening element are selected and consistently combined. A fully implicit integration algorithm is derived, and highly efficient implementation is obtained by simplifying the system of equations to a single (scalar) nonlinear residual equation. A new two-stage optimization-based calibration procedure is developed to identify the material parameters in a completely unsupervised way. The constitutive model is validated against results available in the literature for polycarbonate, accounting for temperature and strain rate dependencies. The results show the efficiency of the overall numerical strategy and demonstrate that quadratic convergence rates are attained. Despite the strongly nonlinear finite strain response, it is possible to observe an excellent agreement for all stages of deformation. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Amorphous thermoplastics Polycarbonate Finite strains Visco-elasticity Visco-plasticity Calibration implicit integration algorithm Finite Element Analysis

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Computational implementation of bounding surface model and its verification through cavity benchmark problems

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS 2022年第3期46卷 553-569页

作者： Chen, Shengli Abousleiman, Younane Muraleetharan, Kanthasamy K. Louisiana State Univ Dept Civil & Environm Engn Baton Rouge LA 70803 USA Univ Oklahoma Integrated PoroMech Inst ConocoPhillips Sch Geol & Geophys Mewbourne Sch Petr & Geol Engn Norman OK USA Univ Oklahoma Sch Civil Engn & Environm Sci Norman OK 73019 USA

This paper develops an implicit integration algorithm for a general form of the bounding surface model, using the return mapping approach (elastic predictor-plastic corrector), to obtain the updated stresses for given strain increments. The formulation of the constitutive integration requires the derivation of a supplementary differential equation to describe the evolution of a key variable, that is, the ratio between the image stress and the current stress quantities. The integration algorithm for the bounding surface model is implemented into the finite element analysis commercial program, ABAQUS, through the material interface of UMAT (user defined material subroutine), and then used for the analysis of cavity contraction (wellbore drilling/tunnel excavation) boundary value problems. The predictions from the ABAQUS simulations are found to be in excellent agreement with the analytical solutions, thus demonstrating the validity and accuracy of the proposed integration scheme.

关键词： bounding surface model cavity contraction implicit integration algorithm return mapping approach UMAT

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A truly self-starting implicit family of integration algorithms with dissipation control for nonlinear dynamics

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NONLINEAR DYNAMICS 2020年第4期102卷 2503-2530页

作者： Li, Jinze Yu, Kaiping Harbin Inst Technol Dept Astronaut Sci & Mech 92 West Dazhi St Harbin 150001 Peoples R China

In this paper, a novel implicit family of composite two sub-step algorithms with controllable dissipations is developed to effectively solve nonlinear structural dynamic problems. The primary superiority of the present method over other existing integration methods lies that it is truly self-starting and so the computation of initial acceleration vector is avoided, but the second-order accurate acceleration responses can be provided. Besides, the present method also achieves other desired numerical characteristics, such as the second-order accuracy of three primary variables, unconditional stability and no overshoots. Particularly, the novel method achieves adjustable numerical dissipations in the low and high frequency by controlling its two algorithmic parameters (gamma and rho(infinity)). The classical dissipative parameter rho(infinity) determines numerical dissipations in the high-frequency while gamma adjusts numerical dissipations in the low-frequency. Linear and nonlinear numerical examples are given to show the superiority of the novel method over existing integration methods with respect to accuracy and overshoot.

关键词： implicit integration algorithm Two sub-step scheme Controllable dissipation Truly self-starting Structural dynamics

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A constitutive model for amorphous thermoplastics from low to high strain rates: Formulation and computational aspects

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INTERNATIONAL JOURNAL OF PLASTICITY 2023年第1期169卷

作者： Alves, A. Francisca Carvalho Ferreira, Bernardo P. Pires, F. M. Andrade Univ Porto Fac Engn DEMec Dept Mech Engn Rua Dr Roberto Frias P-4200465 Porto Portugal Brown Univ Sch Engn 184 Hope St Providence RI 02912 USA

In this paper, a recently proposed finite strain visco-elastic visco-plastic (three-dimensional) constitutive model is extended to predict the nonlinear response of amorphous polymers from low to high strain rates. The model accounts for the influence of distinct molecular mechanisms, which become active at different deformation rates. Therefore, the constitutive equations include two relaxation phenomena to describe the strain rate sensitivity of amorphous polymers. Well established rheological elements are adopted to define visco-elasticity (generalized Maxwell elements) and visco-plasticity (Eyring dashpots). In addition, strain hardening is modeled with a plasticity-induced (nonlinear) hardening element which is extended to distinguish between the contribution of the two transitions. From a computational viewpoint, a fully implicit integration algorithm is derived, and a highly efficient implementation is obtained. It is shown that it is possible to reduce the return mapping system of equations to only two independent (scalar) nonlinear equations. A four-stage optimization-based calibration procedure is proposed to identify the model's material parameters in a completely unsupervised way. The predictive capability of the constitutive model is validated against literature results for polycarbonate and poly(methyl methacrylate), accounting for temperature and strain rate dependencies under different loading conditions. The results show that the model can capture the transition in the yield behavior and predict the post-yield large strain behavior over a wide range of strain rates. The efficiency of the calibration procedure and the overall numerical strategy is also demonstrated. Despite the adiabatic conditions observed under high strain rates, the model replicates the associated effect of temperature through strain rate dependency.

关键词： Finite Element Analysis implicit integration algorithm Calibration Strain-rate Visco-elasticity Visco-plasticity Amorphous polymers Polycarbonate Poly(methyl methacrylate)

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A novel family of composite sub-step algorithms with desired numerical dissipations for structural dynamics

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ARCHIVE OF APPLIED MECHANICS 2020年第4期90卷 737-772页

作者： Li, Jinze Yu, Kaiping Harbin Inst Technol Dept Astronaut Sci & Mech 92 West Dazhi St Harbin 150001 Peoples R China

A novel family of composite sub-step algorithms with controllable numerical dissipations is proposed in this paper to obtain reliable numerical responses in structural dynamics. The new scheme is a self-starting, unconditionally stable and second-order-accurate two-sub-step algorithm with the same computational cost as the Bathe algorithm. The new algorithm can control continuously numerical dissipations in the high-frequency range in an intuitive way, and the ability of numerical dissipations can range from the non-dissipative trapezoidal rule to the asymptotic annihilating Bathe algorithm. Besides, the new algorithm only involves one free parameter and always achieves the identical effective stiffness matrices inside two sub-steps, which is not always achieved in three Bathe-type algorithms, to reduce the computational cost in the analysis of linear systems. Some numerical examples are given to show the superiority of the new algorithm over the Bathe algorithm and the CH-alpha algorithm.

关键词： Sub-step algorithm Bathe algorithm implicit integration algorithm Controllable numerical dissipation

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Finite element implementation of non-unified visco-plasticity model considering static recovery

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MECHANICS OF TIME-DEPENDENT MATERIALS 2020年第1期24卷 59-72页

作者： Yang, Menghao Feng, Miaolin Shanghai Jiao Tong Univ Sch Naval Architecture Ocean & Civil Engn State Key Lab Ocean Engn Shanghai 200240 Peoples R China

In order to examine relaxation behaviors of materials, static recovery term is always conducted in the backstress components for kinematic hardening in time-dependent plasticity model. implicit integration algorithm for non-unified visco-plasticity model is derived. Plastic strain is divided into two parts: the visco-plastic strain, which is calculated based on the viscosity function, and the steady strain which only depends on the equivalent deviatoric backstress. Using the Newton iterative strategy, two sets of equations for deviatoric stress and relative stress tensors are solved. Additionally, the return mapping method is applied in numerical method, and consistent tangent stiffness modulus is progressed for convergence in finite element analysis. The model is implemented into commercial software ABAQUS as user subroutine UMAT. Dwell experiments of nickel-based superalloy under strain-controlled cyclic loading with holding periods for relaxation at high temperature are selected to verify the method. The results indicate that the user subroutine attains convergence with good speed even at large increment, and the additional static recovery terms can improve the simulation for relaxation behaviors.

关键词： Static recovery Non-unified visco-plasticity model implicit integration algorithm Return mapping User subroutine

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Application of the two-loop procedure in multibody dynamics with contact and constraint

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JOURNAL OF SOUND AND VIBRATION 2018年 427卷 15-27页

作者： Guo, Xian Zhang, Ding-Guo Li, Liang Zhang, Le Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Jiangsu Peoples R China

This paper focuses on the performance of the two two-loop implicit sparse matrix numerical integration (TLISMNI) methods as the numerical solution of index-3 differential algebraic equations (DAEs) of motion arising in stiff multibody dynamics with contact and constraint. The original TLISMNI method proposed for the first time by Shabana and Hussein uses the Newmark method or Hilber/Hughes/Taylor (HHT) method as the implicit integration algorithm [TLISMNI (Newmark/HHT) method]. These two integration algorithms consider the accelerations and Lagrange multipliers as basic unknowns and their numerical accuracy is no more than order 2. In order to have a higher integral precision, we propose a new two-loop implicit procedure based on an extended backward differentiation formula scheme [TLISMNI (EBDF) method] which considers coordinates and velocities as basic unknowns. The whole structure of this proposed method is different from the traditional one due to the different unknowns. Furthermore, we apply these two kinds of methods, TLISMNI (Newmark/HHT) method and TLISMNI (BDF/EBDF) method, to the contact and constraint problems of flexible multibody dynamics while few studies of TLISMNI methods have been done on these non-smooth problems. The Baumgarte method and HHT-alpha method are also used to solve the same contact and constraint problem, and the advantages and disadvantages of all these methods above are compared in this study. Results show that the proposed method only needs to perform less iterations to satisfy the same tolerance of error than the TLISMNI (HHT) method does. In some cases the Baumgarte method and HHT-alpha method cannot give reasonable results while the TLISMNI methods perform well when the contact and constraint problems are involved. Moreover, the numerical experiment also indicates that the numerical damping property of the HHT method employed in both the TLISMNI method and the GGL formulation (used in the HHT-alpha method) can behave in a differ

关键词： Differential algebraic equations implicit integration algorithm Impact Iteration

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An improved equivalent force control algorithm for hybrid seismic testing of nonlinear systems

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STRUCTURAL CONTROL & HEALTH MONITORING 2018年第2期25卷 1-1页

作者： Wang, Zhen Wu, Bin Xu, Guoshan Bursi, Oreste S. Harbin Inst Technol Minist Educ Key Lab Struct Dynam Behav & Control Harbin 150090 Heilongjiang Peoples R China Harbin Inst Technol Key Lab Prevent & Mitigat Civil Engn Disasters Minist Ind & Informat Technol Harbin 150090 Heilongjiang Peoples R China Harbin Inst Technol Sch Civil Engn Harbin 150001 Heilongjiang Peoples R China Univ Trento Dept Civil Environm & Mech Engn Via Mesiano 77 I-38123 Trento Italy

The equivalent force control (EFC) algorithm is a hybrid seismic testing method based on both an implicit integration algorithm and force feedback control. As it performs the computation of the numerical substructure with a fixed sampling number and some evaluations are not necessary, the EFC method is believed to be time-consuming for seismic testing of nonlinear systems with complicated numerical substructure model. In order to tackle this problem, the EFC method with varying sampling number (vEFC) has been conceived. The analysis of the vEFC method has shown that 2 traditional pseudodynamic testing (PDT) variants on the basis of implicit time integration schemes and numerical iteration, that is, the IPDT1 method and the IPDT2 method, can be recovered from the vEFC method. Moreover, the advantages of the vEFC method, such as fast response rate and compensation for control errors and possible slippage, are demonstrated.

关键词： equivalent force control method implicit integration algorithm iteration pseudodynamic testing slippage varying sampling number

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Return mapping algorithm for an enhanced generalized plasticity constitutive model of partially saturated soils

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COMPUTERS AND GEOTECHNICS 2012年 45卷 53-61页

作者： Zhang, H. W. Santagiuliana, R. Schrefler, B. A. Univ Padua Dept Civil Environm & Architectural Engn I-35131 Padua Italy Dalian Univ Technol Dept Engn Mech Res Inst Engn Mech State Key Lab Struct Anal & Ind Equipment Dalian 116024 Peoples R China

The objective of this paper is to investigate the stress update algorithm and the tangent operator for an enhanced generalized plasticity model developed recently for partially saturated soils, where on top of the hydrostatic and deviatoric components of the (effective) stress tensor suction has to be considered as an independent variable. The soil model used for the applications can be derived from a potential energy function and is thermodynamically consistent. The Galerkin method is used to obtain a weak form of the governing equations and a "stress-suction coupling matrix" is derived in the discretization in space by finite element method. The implicit integration algorithm is incorporated in a code for partially saturated soil dynamics. The framework of generalized plasticity is presented and examples are shown including subsidence above a model gas reservoir. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Generalized plasticity implicit integration algorithm Return mapping algorithm Consistent tangent stiffness matrix Partially saturated soils

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