A three-dimensional constitutive model for the stress relaxation of articular ligaments

2013 ◽  
Vol 13 (3) ◽  
pp. 653-663 ◽  
Author(s):  
Frances M. Davis ◽  
Raffaella De Vita
Keyword(s):  
Stress Relaxation ◽  
Constitutive Model ◽  
Three Dimensional ◽  
Articular Ligaments

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Progressive failure analysis of scarf-repaired composite laminate based on damage constitutive model

2016 ◽  
Vol 233 (2) ◽  
pp. 180-188 ◽  
Author(s):  
Qiuyi Shen ◽  
Zhenghao Zhu ◽  
Yi Liu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Composite Laminate ◽  
Damage Mechanics ◽  
Cohesive Zone Model ◽  
Load Capacity ◽  
Three Dimensional ◽  
Zone Model ◽  
State Variables ◽  
Element Analysis

A three-dimensional finite element model for scarf-repaired composite laminate was established on continuum damage model to predict the load capacity under tensile loading. The mixed-mode cohesive zone model was adopted to the debonding behavior analysis of adhesive. Damage condition and failure of laminates and adhesive were subsequently addressed. A three-dimensional bilinear constitutive model was developed for composite materials based on damage mechanics and applied to damage evolution and loading capacity analyses by quantifying damage level through damage state variables. The numerical analyses were implemented with ABAQUS finite element analysis by coding the constitutive model into material subroutine VUMAT. Good agreement between the numerical and experimental results shows the accuracy and adaptability of the model.

Study on the generalized k-Hilfer–Prabhakar fractional viscoelastic–plastic model

2021 ◽  
pp. 108128652110258
Author(s):  
Yi-Ying Feng ◽  
Xiao-Jun Yang ◽  
Jian-Gen Liu ◽  
Zhan-Qing Chen
Keyword(s):  
Constitutive Model ◽  
Three Dimensional ◽  
Sensitivity Analyses ◽  
Creep Process ◽  
Fractional Operator ◽  
Modified Model ◽  
Proposed Model ◽  
Accelerated Creep ◽  
The Laplace Transform ◽  
Classical Models

The general fractional operator shows its great predominance in the construction of constitutive model owing to its agility in choosing the embedded parameters. A generalized fractional viscoelastic–plastic constitutive model with the sense of the k-Hilfer–Prabhakar ( k-H-P) fractional operator, which has the character recovering the known classical models from the proposed model, is established in this article. In order to describe the damage in the creep process, a time-varying elastic element [Formula: see text] is used in the proposed model with better representation of accelerated creep stage. According to the theory of the kinematics of deformation and the Laplace transform, the creep constitutive equation and the strain of the modified model are established and obtained. The validity and rationality of the proposed model are identified by fitting with the experimental data. Finally, the influences of the fractional derivative order [Formula: see text] and parameter k on the creep process are investigated through the sensitivity analyses with two- and three-dimensional plots.

Chemical Stress Relaxation of NR Networks Prepared in the Swollen State

1986 ◽  
Vol 59 (4) ◽  
pp. 541-550 ◽  
Author(s):  
Kyung-Do Suh ◽  
Hidetoshi Oikawa ◽  
Kenkichi Murakami
Keyword(s):  
Stress Relaxation ◽  
Network Structure ◽  
Three Dimensional ◽  
Polymer Chains ◽  
Chemical Stress ◽  
Network Chain ◽  
Crosslinking Process ◽  
Dimensional Network ◽  
Chemical Relaxation ◽  
The Difference

Abstract From the experimental results of the present investigation, it is apparent that two kinds of networks which have a different three-dimensional network structure give quite different behavior of chemical stress relaxation, even if both networks have the same network chain density. The difference in three-dimensional network structure for the two kinds of rubber arises from the degree of entanglement, which changes with the concentration of the polymer chains prior to the crosslinking process. The direct cause of chemical relaxation is due to the scission of network chains by degradation, whereas the total relaxation is caused by the change of geometrical conformation of network chains. This then casts doubt on the basic concept of chemorheology which is represented by Equation 2.

scholarly journals Stress relaxation of three-dimensional warp-knitted fabrics in compression

2018 ◽  
Vol 459 ◽  
pp. 012069 ◽  
Author(s):  
S Vassiliadis ◽  
D Matsouka ◽  
L Rešetárová ◽  
L Bouin ◽  
A Marmarali
Keyword(s):  
Stress Relaxation ◽  
Three Dimensional ◽  
Knitted Fabrics

Prediction of Stress Relaxation in Power Plant Components Based on a Constitutive Model

2017 ◽  
Author(s):  
Y. Kostenko ◽  
K. Naumenko
Keyword(s):  
Power Plant ◽  
Stress Relaxation ◽  
Constitutive Model ◽  
Evolution Equations ◽  
Material Behavior ◽  
Assessment Procedure ◽  
Reliable Prediction ◽  
Inelastic Material ◽  
Plant Components

Many power plant components and joint connections are subjected to complex thermo-mechanical loading paths under severe temperature environments over a long period. An important part in the lifetime assessment is the reliable prediction of stress relaxation using improved creep modeling to avoid possible integrity or functionality issues and malfunction in such components. The aim of this work is to analyze the proposed constitutive model for advanced high chromium steels with the goal of predicting stress relaxation over the long term. The evolution equations of the constitutive model for inelastic material behavior are introduced to account for hardening and softening phenomena. The material properties were identified for 9–12%CrMoV steels in the creep range. The model is applied to the stress relaxation analysis of power plant components. The results for long-term assessment, which are encouragingly close to reality, will be presented and discussed. An outlook on further developments of the model and assessment procedure is also provided.

scholarly journals On Computational Modelling Of Strain-Hardening Material Dynamics

2012 ◽  
Vol 11 (5) ◽  
pp. 1525-1546 ◽  
Author(s):  
Philip Barton ◽  
Evgeniy Romenski
Keyword(s):  
Relaxation Time ◽  
Stress Relaxation ◽  
Plastic Strain ◽  
Strain Hardening ◽  
Three Dimensional ◽  
Computational Modelling ◽  
Constitutive Models ◽  
Successful Implementation ◽  
Hardening Material ◽  
Dislocation Mechanics

AbstractIn this paper we show that entropy can be used within a functional for the stress relaxation time of solid materials to parametrise finite viscoplastic strain-hardening deformations. Through doing so the classical empirical recovery of a suitable irreversible scalar measure of work-hardening from the three-dimensional state parameters is avoided. The success of the proposed approach centres on determination of a rate-independent relation between plastic strain and entropy, which is found to be suitably simplistic such to not add any significant complexity to the final model. The result is sufficiently general to be used in combination with existing constitutive models for inelastic deformations parametrised by one-dimensional plastic strain provided the constitutive models are thermodynamically consistent. Here a model for the tangential stress relaxation time based upon established dislocation mechanics theory is calibrated for OFHC copper and subsequently integrated within a two-dimensional moving-mesh scheme. We address some of the numerical challenges that are faced in order to ensure successful implementation of the proposedmodel within a hydrocode. The approach is demonstrated through simulations of flyer-plate and cylinder impacts.

Nonlinear Finite Element Analysis of Super-Long Pile and Soil Interaction in Soft Soil

2011 ◽  
Vol 201-203 ◽  
pp. 1601-1605 ◽  
Author(s):  
Shang Ping Chen ◽  
Wen Juan Yao ◽  
Sheng Qing Zhu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Soft Soil ◽  
Three Dimensional ◽  
Nonlinear Behavior ◽  
Element Model ◽  
Element Analysis ◽  
Friction Resistance ◽  
Tip Resistance ◽  
Side Friction

In this paper, a nonlinear three-dimensional finite element model for super-long pile and soil interaction is established. In this model, contact elements are applied to simulate the nonlinear behavior of interaction of super-long pile and soil. A nonlinear elastic constitutive model for concrete is employed to analyze stress-strain relation of pile shaft under the axial load and the Duncan-Chang’s nonlinear constitutive model is used to reflect nonlinear and inelastic properties of soil. The side friction resistance, axial force, pile-tip resistance, and developing trend of soil plastic deformation are obtained and compared with measured results from static load tests. It is demonstrated that a super-long pile has the properties of degradation of side friction resistance and asynchronous action between side and pile-tip resistance, which is different from piles with a short to medium length.

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