New Approach for the Analysis of Damped Vibrations of Fractional Oscillators by Yuriy A. Rossikhin, Marina V. Shitikova

“…The dynamic behavior of linear and nonlinear mechanical oscillators with constitutive equations involving fractional derivatives defined as a fractional power of the operator of conventional time-derivative is considered. …”
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ANALYSIS OF THE INFLUENCE OF SOP LEAD SHAPE ON SOLDER JOINT RELIABILITY by REN Chao, SHAO Jiang, ZENG ChenHui, XUE HePing

“…3-D finite element models of SOP（ Small Outline Package） were constructed,in which Anand visco-plasticity constitutive equation was used to describe the mechanic behavior of solder joint. …”
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STUDY ON OPTIMIZATION OF REMANUFACTURING OF HYDRAULIC SUPPORT COLUMN by XIE Miao, CAO LiPing, TIAN Bo, LIU Xuan

“…The mathematical model of the radial shrinkage of the coating was established by using the constitutive equation,the geometric equation and the relation between the linear expansion coefficient and the temperature variation. …”
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Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method by H. M. Park

“…In this method, the hyperbolic constitutive equation is split such that the term for the convective transport of stress tensor is treated as a source which is updated iteratively. …”
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Numerical Simulation Method Study of Rock Fracture Based on Strain Energy Density Theory by Shuchen Li, Luchen Zhang, Qian Sun, Ma Tengfei

“…This paper establishes the damage constitutive equation by combining the bilinear strain softening constitutive model with energy dissipation principles, as well as the energy failure criterion of mesoscopic elements based on the strain energy density theory. …”
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Nonlinear Free and Forced Vibration Behavior of Shear-Deformable Composite Beams with Shape Memory Alloy Fibers by Ren Yongsheng, Du Chenggang, Shi Yuyan

“…A thermomechanical constitutive equation of SMA proposed by Brinson is used to calculate the recovery stress of the constrained SMA fibers. …”
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MILLING FORCE MODELING BASED ON EQUIVALENT TURNING FORCE AND OBLIQUE CUTTING FORCE MODEL (MT) by WU MingZhou, ZHANG GuangPeng, LIU MoHan, GOU JianFeng, ZHANG Peng

“…The accuracy of traditional milling force prediction model is low, and it is difficult to provide effective support for the reasonable selection of process parameters in practical production, by synthetically considering the equivalent turning force model of working angle, cutting edge arc and radius of tool tip arc, in this model, the actual turning tool is equivalent to the ideal turning tool model to identify the material constant, the chip flow angle and the average friction angle in the material constitutive equation, according to the oblique cutting model, the shear stress on the main shear plane and the F₀ vector of the unit cutting force at different cutting speeds are calculated, thus the instantaneous cutting force on the front face of the end mill can be calculated, the three-dimensional cutting force of end mill in X-Y-Z coordinate system is obtained by coordinate transformation. …”
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SIMULATION AND ANALYSIS OF COMPOUND ABRASIVE GRINDING PERFORMANCE OF SPIRAL BEVEL GEARS (MT) by LIU Bin, YAN ChangFeng, WEI LiLin, YANG HaoDong, ZHAO XiaoMan

“…A finite element model of composite abrasive grinding was established based on material constitutive equation of Johnson-Cook force-thermal coupling. …”
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STUDY ON TENSILE PROPERTIES OF ALUMINUM ALLOY WELDING JOINT USING DIC METHOD by CAO GuangLong, CHEN Liang, REN MingFa, CHEN JiLe, ZHANG YaHui

“…The elastic-plastic constitutive equation is employed to describe mechanical properties of the welding zone with its parameters determined by the measured strain history. …”
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Strain-gradient effect on the crack tip dislocations density by Valery Shlyannikov, Andrey Tumanov, Ruslan Khamidullin

“…In this study, the influence of a material’s plastic properties on the crack tip fields and dislocation density behavior is analytically and numerically analyzed using the conventional mechanism-based strain-gradient plasticity (CMSGP) theory established using the Taylor model. The material constitutive equation is implemented in a commercial finite element code by a user subroutine, and the crack tip fields are evaluated with novel parameters in the form of the intrinsic material length, characterizing the scale over which gradient effects become significant. …”
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A Damage Constitutive Model of Rock under Hydrochemical Cyclic Invasion by Lunan Sun, Yu Zhang, Zhe Qin, Tengfei Wang, Sheng Zhang

“…Based on the theory of microbody strength distribution, the constitutive equation for rock damage under the coupled effect of water chemistry and cyclic water invasion is established. …”
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Unsteady Electroosmotic Flow of Jeffrey Fluid in a Circular Microchannel under the Combined Action of Vertical Magnetic Field, External Electric Field, and Pressure at High Zeta Po... by Meirong Ren, Tiange Zhang, Jifeng Cui, Xiaogang Chen, Bixia Wu

“…The numerical solutions of the potential and velocity distributions are obtained by solving the nonlinear Poisson-Boltzmann equation, the constitutive equation of the Jeffrey fluid, and the Cauchy momentum equation applying the Chebyshev spectral method and the finite difference method. …”
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The Establishment of Segmented Constitutive Relationship of Coal under Triaxial Compression: Take the No. 3 Coal of Xinhe Colliery as an Example by Yongjie Yang, Yang Zhang, Tianli Zhang

“…Through fitting calculation of test data, the segmented constitutive equation of coal can be obtained, and the every segment span of strain.…”
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Analysis on Elastohydrodynamic Lubrication in Grease-lubricated Ball Bearings Considering Film Thickness Correction by Zhang Weiye, Zhang Chang, Jiang Ziyang, Ni Wenjun, Liao Fuqiang

“…This model is based on the Herschel-Bulkley rheological model of lubricating grease and includes the constitutive equation for grease, Reynolds equation, film thickness equation, viscosity-pressure equation, density-pressure equation, and load balance equation. …”
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Modeling and Dynamical Behavior of Rotating Composite Shafts with SMA Wires by Yongsheng Ren, Qiyi Dai, Ruijun An, Youfeng Zhu

“…A thermomechanical constitutive equation of SMA proposed by Brinson is employed and the recovery stress of the constrained SMA wires is derived. …”
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The Characteristic Transient Response of a Pressurized Cantilever Pipe Subjected to Transverse Impact at Its Tip by Feng Liu, Yuchao Yang, Yuelei Wu

“…Bending moment and axial force were uncoupled in the constitutive equation, and an experiment-based relationship between moment and curvature was adopted. …”
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A Rheological Model of Sandstones considering Response to Thermal Treatment by Xingang Wang, Lei Huang, Junrong Zhang

“…The investigation allows successful establishment of a three-dimensional constitutive equation considering the instantaneous elastic response to thermal treatment. …”
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A Nonmonotonous Damage Model to Characterize Mullins and Residual Strain Effects of Rubber Strings Subjected to Transverse Vibrations by Alex Elías-Zúñiga, Karen Baylón, Oscar Martínez-Romero, Ciro A. Rodríguez, Héctor R. Siller

“…This work focuses on the formulation of a constitutive equation to predict Mullins and residual strain effects of buna-N, silicone, and neoprene rubber strings subjected to small transverse vibrations. …”
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Constitutive Model of Rock Uniaxial Damage Based on Rock Strength Statistics by Ming Ji, Kai Chen, Hong Jun Guo

“…Based on the statistical damage constitutive model proposed in this paper, a numerical fitting analysis was conducted on the uniaxial compression testing data of laboratory sand rock and on experimental data from other literature, in order to validate the rationality of the constitutive equation and the determination of its parameters and to analyze the effect of internal friction variables on damage variables and compression strength. …”
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Constitutive Model and Damage Evolution of Mudstone under the Action of Dry-Wet Cycles by Ming Hu, Yuanxue Liu, Linbo Song, Yu Zhang

“…The decay rate and the damage variable are connected with each other and applied to the damage constitutive equation based on the energy principle to set up the damage evolution equation under the coupled action of dry-wet cycles and loads. …”
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