Finite element simulations constitutive model

Adolf et al [89] focused primarily on epoxy systems. They consider the key to the success of a constitutive model to be its choice of strain measure and the inclusion of free-energy-accelerated relaxations. The model only requires linear properties (i.e., properties that may be predictable by the methods developed in this book) for materials prior to their synthesis, since nonlinear behavior arises naturally from the formalism. Thermal properties and epoxy curing are also treated by their model. The authors have also attempted to treat failure by identifying a critical hydrostatic tension consistent with glassy failure. The model has been validated with a wide variety of types of material tests. The finite element simulations are performed in three dimensions. These authors have, thus far, done only a limited amount of preliminary work with heterophasic systems, but they report that the results were encouraging. 

After a constitutive model has been chosen, calibrated, and validated for a particular fluoropolymer, it becomes as easy to perform multiaxial deformation simulations as it is to simulate uniaxial deformation. If the material model considers time dependence, temperature dependence, or damage evolution, then thermomechanical or fatigue loading can also easily be simulated. Since almost all commercial finite element (FE) software packages allow for nonlinear simulations including considerations of large deformations, the key component of performing accurate finite element simulations lies within the specification and calibration of the constitutive model. 

The finite element simulations were performed using the DNF constitutive model presented in Sec. 

A key step in this procedure is prescribing the material or constitutive model, that is, the relationship between the stress the material experiences and the resulting deformation it undergoes. Conventional macro-scale finite element simulations assume that the material can be described by measurable macroscopic material properties. Typical examples for solids include materials that are modeled as elastic, viscoelastic, plastic, and viscoplastic. The presentation in this chapter will be confined to linear elastic materials. 

Non-isothermal viscoelastic steady two-dimensional finite element simulations were performed by solving the well-known mass, momentum and energy equations using the commercially available Compuplast software VEL 6.1. In this study, the modified White-Metzner (mWM) constitutive equation according to Barnes and Roberts [8] is employed. The non-isothermal mWM model is given by Eqs. (2) - (5). 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

The success of the developed model in predicting uniaxial and equi-biaxi-al stress strain curves correctly emphasizes the role of filler networking in deriving a constitutive material law of reinforced rubbers that covers the deformation behavior up to large strains. Since different deformation modes can be described with a single set of material parameters, the model appears well suited for being implemented into a finite element (FE) code for simulations of three-dimensional, complex deformations of elastomer materials in the quasi-static Emit. 

From the standpoint of the continuum simulation of processes in the mechanics of materials, modeling ultimately boils down to the solution of boundary value problems. What this means in particular is the search for solutions of the equations of continuum dynamics in conjunction with some constitutive model and boundary conditions of relevance to the problem at hand. In this section after setting down some of the key theoretical tools used in continuum modeling, we set ourselves the task of striking a balance between the analytic and numerical tools that have been set forth for solving boundary value problems. In particular, we will examine Green function techniques in the setting of linear elasticity as well as the use of the finite element method as the basis for numerical solutions. 

Recognizing the importance of the coupled hydro-mechanical effects on the performance of civil engineering structures involving fractured rocks, the stress-flow coupling mechanism of the dam-foundation system at Longyangxia site was simulated using a three-dimensional Finite Element code, supported by two visco-elastic constitutive models to represent the time-dependent material behaviour of the dam concrete and the foundation rock. The calculated results were concord with the measured ones and helped to interpret the causes of this continuous displacement at the 13" dam section of the Longyangxia hydropower project, towards the left bank. 

Experimental data collection on the material, that can be used to perform accurate finite element numerical simulations of the trays. Two examples are statistical models for strength and constitutive equations of creep... 

For finite element modeling of reinforced concrete wall segments subjected to nonlinear shear actions (e.g., squat walls, wall piers, wall spandrels), although a number of cyclic constitutive models have been proposed for simulating the nonlinear responses of constitutive panel elements of the finite element model, most of these model formulations are not included in commonly-used structural analysis platforms due to complexities in their implementation. A new constitutive... 

To help understand and quantitatively evaluate the secondary movement shown above, Debbaut et al. [75, 77] augmented this experimental work with a three-dimensional flow simulation that incorporated viscoelastic effects. The finite element method, using a 4-mode Giesekus model as the viscoelastic constitutive equation, was used for the simulation. The polymer used for the experiment and simulation was a low-density polyethylene. Figures 12.20 and 12.21 show the experimental observations and the numerical predictions of the deformations of the interface for the rectangular straight channel [78], and for the teardrop channel [75], respectively. 

Ke5words foam, compression behavior, constitutive models, numerical simulation, energy absorption, finite-element modelling, compressive stress-strain behavior, damage, modelling. 

ABSTRACT In the present paper a multiphase model including a hypoplastic formulation of the solid phase is presented and its application to earthquake engineering problems discussed. The macroscopic soil model, which is based on the theory of porous media, comprises three distinct phases namely, solid, fluid and gas phase. For each of these the compressibility of the respective medium is taken into account in the mathematical formulation of the model. The solid phase is modelled using the hypoplastic constitutive equation including intergranular strain to allow for a realistic description of material behaviour of cohesionless soils even under cyclic loading. The model was implemented into the finite element package ANSYS via the user interface and also allows the simulation of soil-structure interaction problems. 

Experimental load-displacement history and creep data were used to estimate the partitioned viscoplastic constitutive properties. Load isplacement loops from double lap-shear tests were used in conjunction with finite element (FE) models to refine the estimates of the effective viscoplastic constitutive properties of the three Pb-free solders and eutectic Sn Pb. The constitutive equations for the four solders were used as initial estimates when iterating to match experimental and predicted hysteresis loops. That is, experimentally determined double lap-shear specimen load-displacement hysteresis loops were compared with the FE simulations. The constitutive properties were then adjusted iteratively to improve agreement the equations and properties are presented in Table 16. 

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