Constitutive Equations and Finite Element Implementation of Isochronous Nonlinear Viscoelastic Behavior

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Hossein Sepiani ◽  
Maria Anna Polak ◽  
Alexander Penlidis
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Constitutive Relations ◽  
Viscoelastic Behavior ◽  
Material Behavior ◽  
Constitutive Law ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Behavior ◽  
Stress Dependent

We present a phenomenological three-dimensional (3D) nonlinear viscoelastic constitutive model for time-dependent analysis. Based on Schapery's single integral constitutive law, a solution procedure has been provided to solve nonlinear viscoelastic behavior. This procedure is applicable to 3D problems and uses time- and stress-dependent material properties to characterize the nonlinear behavior of material. The equations describing material behavior are chosen based on the measured material properties in a short test time frame. This estimation process uses the Prony series material parameters, and the constitutive relations are based on the nonseparable form of equations. Material properties are then modified to include the long-term response of material. The presented model is suitable for the development of a unified computer code that can handle both linear and nonlinear viscoelastic material behavior. The proposed viscoelastic model is implemented in a user-defined material algorithm in abaqus (UMAT), and the model validity is assessed by comparison with experimental observations on polyethylene for three uniaxial loading cases, namely short-term loading, long-term loading, and step loading. A part of the experimental results have been conducted by (Liu, 2007, “Material Modelling for Structural Analysis of Polyethylene,” M.Sc. thesis, University of Waterloo, Waterloo, ON Canada), while the rest are provided by an industrial partner. The research shows that the proposed finite element model can reproduce the experimental strain–time curves accurately and concludes that with proper material properties to reflect the deformation involved in the mechanical tests, the deformation behavior observed experimentally can be accurately predicted using the finite element simulation.

Nonlinear viscoelastic approach to model damage-associated performance behavior of asphaltic mixture and pavement structure

2013 ◽  
Vol 40 (4) ◽  
pp. 313-323 ◽  
Author(s):  
Hoki Ban ◽  
Soohyok Im ◽  
Yong-Rak Kim
Keyword(s):  
Finite Element ◽  
Viscoelastic Material ◽  
Material Properties ◽  
Asphalt Mixtures ◽  
Finite Element Software ◽  
Nonlinear Viscoelastic ◽  
Linear Viscoelastic ◽  
Heavy Truck ◽  
Pavement Structure ◽  
Stress Dependent

This paper presents an integrated experimental–numerical effort to more accurately model the damage characteristics of asphalt mixtures and pavement structures than conventional elastic and (or) linear viscoelastic approaches can. To this end, Schapery's nonlinear viscoelastic constitutive model was implemented into a finite element software via user defined subroutine (user material, or UMAT) to analyze an asphalt pavement subjected to heavy truck loads. Then, a series of creep and recovery tests were conducted at various stress levels and at different temperatures to obtain the stress-dependent and temperature-sensitive viscoelastic material properties of asphalt mixtures. With the viscoelastic material properties characterized and the UMAT code, a typical pavement structure subjected to repeated heavy truck loads was modeled with the consideration of the effect of material nonlinearity with a realistic tire loading configuration. Three-dimensional finite element simulations of the pavement structure present significant differences between the linear viscoelastic approach and the nonlinear viscoelastic modeling in the prediction of pavement performance with respect to rutting and fatigue cracking. The differences between the two approaches underline the importance of proper and more realistic characterization of pavement materials and should be addressed in the process of performance-based pavement design.

Enabling Integrated Material and Product Design Under Uncertainty Through Stochastic Constitutive Relations

2010 ◽  
Author(s):  
M. Steven Greene ◽  
Yu Liu ◽  
Wei Chen ◽  
Wing Kam Liu ◽  
Hong-Zhong Huang
Keyword(s):  
Product Design ◽  
Constitutive Relation ◽  
Material Properties ◽  
Constitutive Relations ◽  
High Strength ◽  
Material Behavior ◽  
Constitutive Law ◽  
Copula Functions ◽  
Computational Framework ◽  
Uncertainty Sources

This paper presents a computational framework that mathematically propagates material microstructure uncertainties to coarser system resolutions for use in multiscale design frameworks. The computational framework uses a homogenized stochastic constitutive relation that links microstructure uncertainty with stochastic material properties. The stochastic constitutive relation formulated in this work serves as the critical link between the material and product domains in integrated material and product design. Ubiquitous fine resolution uncertainty sources influencing prediction of material properties based on their structures are categorized, and stochastic cell averaging is achieved by two advanced uncertainty quantification methods: random process polynomial chaos expansion and statistical copula functions. Both methods confront the mathematical difficulty in randomizing constitutive law parameters by capturing the marked correlation among them often seen in complex materials, thus the results proffer a more accurate probabilistic estimation of constitutive material behavior. The method put forth in this research, though quite general, is applied to a plastic, high strength steel alloy for demonstration.

A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments

2005 ◽  
Vol 128 (3) ◽  
pp. 449-457 ◽  
Author(s):  
P. Vena ◽  
D. Gastaldi ◽  
R. Contro
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Biological Tissues ◽  
Relaxation Behavior ◽  
Constitutive Law ◽  
Time Dependent ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Behavior ◽  
Constitutive Parameters

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67–76;Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306–312;Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908–214;Weiss et al., 2002, J. Biomech., 35, pp. 943–950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.

Nonlinear Viscoelastic Finite Element Analysis of Adhesive Joints

1988 ◽  
Vol 16 (3) ◽  
pp. 146-170 ◽  
Author(s):  
S. Roy ◽  
J. N. Reddy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Viscoelastic Behavior ◽  
Bonded Joints ◽  
Adhesively Bonded ◽  
Element Analysis ◽  
Adhesively Bonded Joints ◽  
Nonlinear Viscoelastic ◽  
Structural Failures ◽  
Updated Lagrangian

Abstract A good understanding of the process of adhesion from the mechanics viewpoint and the predictive capability for structural failures associated with adhesively bonded joints require a realistic modeling (both constitutive and kinematic) of the constituent materials. The present investigation deals with the development of an Updated Lagrangian formulation and the associated finite element analysis of adhesively bonded joints. The formulation accounts for the geometric nonlinearity of the adherends and the nonlinear viscoelastic behavior of the adhesive. Sample numerical problems are presented to show the stress and strain distributions in bonded joints.

scholarly journals Tridimensional Long-Term Finite Element Analysis of Reinforced Concrete Structures with Rate-Type Creep Approach

2020 ◽  
Vol 10 (14) ◽  
pp. 4772
Author(s):  
Giovanni Di Luzio ◽  
Luigi Cedolin ◽  
Carlo Beltrami
Keyword(s):  
Finite Element ◽  
General Procedure ◽  
Constitutive Relations ◽  
Danube River ◽  
The Black Sea ◽  
Research Association ◽  
Time Step ◽  
Retardation Spectrum ◽  
Rate Type

This paper presents a general procedure for a rate-type creep analysis (based on the use of the continuous retardation spectrum) which avoids the need of recalculating the Kelvin chain stiffness elements at each time step. In this procedure are incorporated three different creep constitutive relations, two recommended by national codes such as the ACI (North-American) and EC2 (European) building codes and one by the RILEM research association. The approximate expressions of the different creep functions with the corresponding Dirichlet series are generated using the continuous retardation spectrum approach based on the Post–Widder formula. The proposed rate-type formulation is implemented into a 3D finite element code and applied to study the long-term deflections of a prestressed concrete bridge built in Romania, which crosses a wide artificial channel that connects the Danube river to the port of Constanta in the Black Sea.

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