ANCF Analysis of Textile Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Liang Wang ◽  
Yongxing Wang ◽  
Antonio M. Recuero ◽  
Ahmed A. Shabana
Keyword(s):  
Constitutive Equations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Transversely Isotropic ◽  
Textile Material ◽  
Deformation Tensor ◽  
Material Forces ◽  
Isotropic Component ◽  
Filament Bundles

This paper presents a new flexible multibody system (MBS) approach for modeling textile systems including roll-drafting sets used in chemical textile machinery. The proposed approach can be used in the analysis of textile materials such as lubricated polyester filament bundles (PFBs), which have uncommon material properties best described by specialized continuum mechanics constitutive models. In this investigation, the absolute nodal coordinate formulation (ANCF) is used to model PFB as a hyperelastic transversely isotropic material. The PFB strain energy density function is decomposed into a fully isotropic component and an orthotropic, transversely isotropic component expressed in terms of five invariants of the right Cauchy–Green deformation tensor. Using this energy decomposition, the second Piola–Kirchhoff stress and the elasticity tensors can also be split into isotropic and transversely isotropic parts. The constitutive equations are used to define the generalized material forces associated with the coordinates of three-dimensional fully parameterized ANCF finite elements (FEs). The proposed approach allows for modeling the dynamic interaction between the rollers and PFB and allows for using spline functions to describe the PFB forward velocity. The paper demonstrates that the textile material constitutive equations and the MBS algorithms can be used effectively to obtain numerical solutions that define the state of strain of the textile material and the relative slip between the rollers and PFB.

Use of ANCF Finite Elements in MBS Textile Applications

2015 ◽  
Author(s):  
Liang Wang ◽  
Yongxing Wang ◽  
Antonio M. Recuero ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Elements ◽  
Constitutive Equations ◽  
Textile Industry ◽  
Numerical Solutions ◽  
Transversely Isotropic ◽  
Textile Material ◽  
Deformation Tensor ◽  
Isotropic Component ◽  
Filament Bundles ◽  
Chemical Textile

The objective of this investigation is to present a new flexible multibody system (MBS) approach for modeling textile roll-drafting sets used in chemical textile industry. The proposed approach can be used in the analysis of textile materials which have un-common material properties best described by specialized continuum mechanics constitutive models, for instance, the lubricated polyester filament bundles (PFB) presented in this paper. In this investigation, PFB is modeled as a hyper-elastic transversely isotropic material using absolute nodal coordinate formulation (ANCF). The PFB strain energy density function is decomposed into a fully isotropic component and an orthotropic, transversely isotropic component expressed in terms of five invariants of the right Cauchy-Green deformation tensor. Using this energy decomposition, the second Piola-Kirchhoff stress and the elasticity tensors can also be split into isotropic and transversely isotropic parts. Constitutive equations are used to evaluate the generalized material forces associated with the coordinates of three-dimensional fully-parameterized ANCF finite elements. The proposed model allows for modeling the dynamic interaction between the rollers and PFB and allows for using spline functions to specify the PFB forward velocity. The paper demonstrates that the textile material constitutive equations and the MBS algorithms can be used effectively to obtain numerical solutions that define the state of strain of the textile material and the relative slip between rollers and PFB and therefore provide a good method to study the roll-drafting process in the chemical textile industry.

Linear theory of Cosserat surface and elastic plates of variable thickness

1971 ◽  
Vol 69 (1) ◽  
pp. 227-254 ◽  
Author(s):  
A. E. Green ◽  
P. M. Naghdi ◽  
M. L. Wenner
Keyword(s):  
Linear Theory ◽  
Variable Thickness ◽  
Constitutive Equations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Approximation Procedure ◽  
Initial Surface ◽  
Elastic Plates ◽  
Cosserat Surface ◽  
Plates Of Variable Thickness

AbstractWithin the scope of the linear isothermal theory of an elastic Cosserat surface, constitutive equations are derived for an initially flat Cosserat surface in which the initial director (along the normal to the initial surface) is allowed to depend on the surface coordinates. These constitutive equations correspond to those for bending and stretching of a transversely isotropic three-dimensional plate. Special attention is given to the relevance and applicability of the results to bending of (three-dimensional) plates of variable thickness and comparison is made with a set of equations for elastic plates of variable thickness obtained, by an approximation procedure, from the three-dimensional equations.

scholarly journals Torsional Vibrations of Fluid-Filled Multilayered Transversely Isotropic Finite Circular Cylinder

2016 ◽  
Vol 08 (03) ◽  
pp. 1650032 ◽  
Author(s):  
Wafik Abassi ◽  
Adil El Baroudi ◽  
Fulgence Razafimahery
Keyword(s):  
Viscous Fluid ◽  
Boundary Conditions ◽  
Constitutive Equations ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Transversely Isotropic ◽  
Frequency Equation ◽  
Torsional Vibrations ◽  
Isotropic Cylinder ◽  
Transversely Isotropic Cylinder

An analytical and numerical study for the torsional vibrations of viscous fluid-filled three-layer transversely isotropic cylinder is presented in this paper. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equations of a viscous fluid. The analytical solution of the frequency equation is obtained using the boundary conditions at the free surface of the solid layer and the boundary conditions at the fluid–solid interface. The frequency equation is deduced and analytically solved using the symbolic Software Mathematica. The finite element method using Comsol Multiphysics Software results are compared with present method for validation and an acceptable match between them were obtained. It is shown that the results from the proposed method are in good agreement with numerical solutions. The influence of fluid dynamic viscosity is thoroughly analyzed and the effect of the isotropic properties on the natural frequencies is also investigated.

A micromechanical investigation of interfacial transport processes. II. Interfacial constitutive equations

1993 ◽  
Vol 345 (1675) ◽  
pp. 209-228 ◽  
Keyword(s):  
Constitutive Equations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transport Processes ◽  
Interfacial Stress ◽  
Matched Asymptotic Expansion ◽  
Immiscible Fluid ◽  
Interfacial Transport ◽  
Fluid Systems ◽  
Phenomenological Coefficients

Macroscale interfacial constitutive equations, as well as expressions for the phenomenological functions appearing therein, are derived via a rigorous matched asymptotic expansion scheme for transport processes occurring in immiscible fluid—fluid systems possessing moving and deforming interfaces. The usefulness of an asymptotic approach is demonstrated by examining a model in which the three-dim ensional microscale fluid continuum is assumed to obey an incompressible, transversely-isotropic, linear, newtonian-type constitutive equation possessing position-dependent phenomenological coefficients which depend strongly upon distance normal to the interface. In such circumstances, them acroscale interfacial stress tensor reduces to the familiar isotropic Boussinesq-Scriven form . Similarly, a two-dimensional, isotropic, macroscale interfacial Fick’s law relation is derived from a comparable, three-dimensional, transversely-isotropic, microscale fickian form for the case of a diffusion-controlled surfactant transport exchange between the bulk phases and the interface.

scholarly journals On a nonlinear rod exhibiting only axial and bending deformations: mathematical modeling and numerical implementation

2021 ◽  
Author(s):  
Cristian Guillermo Gebhardt ◽  
Ignacio Romero
Keyword(s):  
Mathematical Formulation ◽  
Time Integration ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Transversely Isotropic ◽  
Natural State ◽  
Numerical Implementation ◽  
New Model ◽  
Rod Model ◽  
Push Forward

AbstractIn this work, we present the mathematical formulation and the numerical implementation of a new model for initially straight, transversely isotropic rods. By adopting a configuration space that intrinsically avoids shear deformations and by systemically neglecting the energetic contribution due to torsion, the proposed model admits an unconstrained variational statement. Moreover, as the natural state of the rod is the trivial one and the mechanical properties are homogeneous on the cross section, the need for pull-back and push-forward operations in the formulation is totally circumvented. These features impose, however, some smoothness requirements on the stored energy function that need to be carefully considered when adopting general constitutive models. In addition to introducing the rod model, we propose a spatial discretization with the finite element method, and a time integration with a hybrid, implicit scheme. To illustrate the favorable features of the new model, we provide results corresponding to numerical simulations for plane and three-dimensional problems that are investigated in the static and dynamic settings. Finally, and to put the presented ideas in a suitable context, we compare solutions obtained with the new model against a rod model that allows for torsion and shear.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

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