J.L. Curiel-Sosa

Homotopy semi-numerical simulation of peristaltic flow of generalised Oldroyd-B fluids with slip effects.

This investigation deals with the peristaltic flow of generalised Oldroyd-B fluids (with the fractional model) through a cylindrical tube under the influence of wall slip conditions. The analysis is carried out under the assumptions of long wavelength and low Reynolds number. Analytical approximate solutions are obtained by using the highly versatile and rigorous semi-numerical procedure known as the homotopy analysis method. It is assumed that the cross section of the tube varies sinusoidally along the length of the tube. The effects of the dominant hydromechanical parameters, i.e. fractional parameters, material constants, slip parameter, time and amplitude on the pressure difference across one wavelength, are studied. Graphical plots reveal that the influence of both fractional parameters on pressure is opposite to each other. Interesting responses to a variation in the constants are obtained. Pressure is shown to be reduced by increasing the slip parameter. Furthermore, the pressure in the case of fractional models (fractional Oldroyd-B model and fractional Maxwell model) of viscoelastic fluids is considerably more substantial than that in the corresponding classical viscoelastic models (Oldroyd-B and Maxwell models). Applications of the study arise in biophysical food processing, embryology and gastro-fluid dynamics.

Finite element analysis of structural instability using an implicit/explicit switching technique

In this paper, we present a study of finite element analysis (FEA) of structural instability by using a switching implicit-explicit algorithm embedded into the finite element method. Snap-through or snap-back buckling problems often cause divergence of the finite element method if arc-length methods are not used. The origin of divergence is often associated with critical points. An alternative to the latter is considered herein, the implicit–explicit FEA. The numerical results showed the effectiveness of this switching technique for solving divergence when simulating structural instabilities such as buckling of an elastic–plastic arch.

3-D elasto-plastic large deformations

Numerical analysis of 3-D elasto-plastic large deformations is presented.Isogeometric analysis based on Bzier extraction of NURBS is extended to 3-D elasto-plastic large deformation.The Bzier extraction operator can integrate isogeometric analysis into the existing finite element codes.Higher accuracy is obtained as compared with that of finite element method. This paper is devoted to the numerical simulation of elasto-plastic large deformation in three-dimensional (3-D) solids using isogeometric analysis (IGA) based on Bzier extraction of NURBS (non-uniform rational B-splines), due to some inherently desirable features. The Bzier extraction operation decomposes the NURBS basis functions into a set of linear combination of Bernstein polynomials and a set of C0-continuity Bzier elements. Consequently, the IGA based on Bzier extraction of NURBS can be embedded in existing FEM codes, and more importantly, as have been shown in literature that higher accuracy over traditional FEM can be gained. The main features distinguishing between the IGA and FEM are the exact geometry description with fewer control points, high-order continuity, high accuracy. Unlike the standard FEM, the NURBS basis functions are capable of precisely describing both geometry and solution fields. The present kinematic is based on the Total Lagrange description due to the elasto-plastic large deformation with deformation history. The results for the distributions of displacements, von Mises stress, yielded zones, and force-displacement curves are computed and analyzed. For the sake of comparison of the numerical results, the same numerical examples have additionally been computed with the FEM using ABAQUS. IGA numerical results show the robustness and accuracy of the technique.

Finite element analysis of the damage mechanism of 3D braided composites under high-velocity impact

AbstractThe integrated near-net-shape structure of 3D braided composites provides excellent impact resistant properties over laminated composites. However, the load distribution and damage mechanism throughout the braided structures become more complicated. In this paper, a finite element model based on three unit-cells is established to assess the penetration process of 3D braided composites under high-velocity impact. A 3D rate-dependent constitutive model is employed to determine the constituent behavior in the three unit-cells. An instantaneous degradation scheme is proposed initiated by appropriate failure criteria of yarns and matrix. All these constitutive models are coded by a user-material subroutine VUMAT developed in ABAQUS/Explicit. The whole process of ballistic damage evolution of 3D braided composites is simulated, and the impact resistance and damage mechanisms are analyzed in detail in the simulation process. The effects of impact velocity on the ballistic properties and energy absorption characteristics of the composite structures are also discussed.

Three-Dimensional Static and Dynamic Analysis of a Composite Cruciform Structure Subjected to Biaxial Loading: A Discontinuum Approach

A three-dimensional structural integrity analysis using the eXtended Finite Element Method (XFEM) is considered for simulating the crack behaviour of a chopped fibre-glass-reinforced polyester (CGRP) cruciform specimen subjected to a quasi-static tensile biaxial loading. This is the first time this problem is accomplished for computing the stress intensity factors (SIFs) produced in the biaxially loaded area of the cruciform specimen. A static crack analysis for the calculation of the mixed-mode SIFs is carried out. SIFs are calculated for infinite plates under biaxial loading as well as for the CGRP cruciform specimens in order to review the possible edge effects. A ratio relating the side of the central zone of the cruciform and the crack length is proposed. Additionally, the initiation and evolution of a three-dimensional crack are successfully simulated. Specific challenges such as the 3D crack initiation, based on a principal stress criterion, and its front propagation, in perpendicular to the principal stress direction, are conveniently addressed. No initial crack location is pre-defined and an unique crack is developed. Finally, computational outputs are compared with theoretical and experimental results validating the analysis.

Computational techniques for simulation of damage and failure on composites

This chapter presents some of the most recent and relevant computational techniques for modelling and simulation of damage and/or failure on composite materials. In the last few years, the number of computer methods dedicated to virtual composite damage simulation has exploded as a consequence of progress on a number of numerical methods such as the Partition of Unity Methods (Extended Finite Element Method, Phantom Node Method,...), meshfree methods (Particle Methods, Element Free Galerkin Method,..) or semi-numerical approaches linking novel strategies for computation of damage based on phenomenological theories and effective replication of cracks embedded within the Finite Element Method. Although, this chapter deals mainly with computer methods applied to fibre reinforced composites based on a polymeric matrix, many of them are applicable to a broader range of composite materials as well as other anisotropic materials.

A Large Strains Finite Element Multiscale Approach

A novel formulation for multiscale finite element analysis of multiphase solids undergoing large strains is proposed in this paper. Within the described homogenization technique no constitutive assumptions are made at the macrolevel. A crucial aspects of the approach is the modeling of antiperiodic traction on the boundary of the representative volume element, condensation technique and the formulation performed on a deformation-driven context whereby the macroscopic deformation gradient is prescribed. Numerical tests on solids with voids demonstrated the robustness of the technique.

An enhanced void-crack based Rousselier damage model for ductile fracture with the XFEM

This work presents a modelling strategy for ductile fracture materials by implementing the Rousselier damage model with the extended finite element method (XFEM). The implicit integration scheme and consistent tangent modulus based on a radial return mapping algorithm for this constitutive model are developed by the user-defined material subroutine UMAT in ABAQUS/Standard. To enhance the modelling of the crack development in the materials, the XFEM is used that allows modelling of arbitrary discontinuities, where the mesh does not have to be aligned with the boundaries of material interfaces. This modelling strategy, so-called Rousselier-UMAT-XFEM (RuX) model, is proposed to connect both concepts, which gives an advantage in predicting the material behaviour of ductile material in terms of voids and crack relation. This is the first contribution where XFEM is used in ductile fracture analysis for micromechanical damage problems. The results indicate that the RuX model is a promising technique for predicting the void volume fraction damage and crack extension in ductile material, which shows a good agreement in terms of stress–strain and force–displacement relationships.

Meso-Scale Finite Element Simulations of 3D Braided Textile Composites: Effects of Force Loading Modes

Meso-scale finite element method (FEM) is considered as the most effective and economical numerical method to investigate the mechanical behavior of braided textile composites. Applying the periodic boundary conditions on the unit-cell model is a critical step for yielding accurate mechanical response. However, the force loading mode has not been employed in the available meso-scale finite element analysis (FEA) works. In the present work, a meso-scale FEA is conducted to predict the mechanical properties and simulate the progressive damage of 3D braided composites under external loadings. For the same unit-cell model with displacement and force loading modes, the stress distribution, predicted stiffness and strength properties and damage evolution process subjected to typical loading conditions are then analyzed and compared. The obtained numerical results show that the predicted elastic properties are exactly the same, and the strength and damage evolution process are very close under these two loading modes, which validates the feasibility and effectiveness of the force loading mode. This comparison study provides a suitable reference for selecting the loading modes in the unit-cell based mechanical behavior analysis of other textile composites.

Meso-Scale Finite Element Analysis of Mechanical Behavior of 3D Braided Composites Subjected to Biaxial Tension Loadings

In many engineering applications, 3D braided composites are designed for primary loading-bearing structures, and they are frequently subjected to multi-axial loading conditions during service. In this paper, a unit-cell based finite element model is developed for assessment of mechanical behavior of 3D braided composites under different biaxial tension loadings. To predict the damage initiation and evolution of braiding yarns and matrix in the unit-cell, we thus propose an anisotropic damage model based on Murakami damage theory in conjunction with Hashin failure criteria and maximum stress criteria. To attain exact stress ratio, force loading mode of periodic boundary conditions which never been attempted before is first executed to the unit-cell model to apply the biaxial tension loadings. The biaxial mechanical behaviors, such as the stress distribution, tensile modulus and tensile strength are analyzed and discussed. The damage development of 3D braided composites under typical biaxial tension loadings is simulated and the damage mechanisms are revealed in the simulation process. The present study generally provides a new reference to the meso-scale finite element analysis (FEA) of multi-axial mechanical behavior of other textile composites.