scholarly journals Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Haofei Liu ◽  
Wei Sun
Keyword(s):  
Finite Element ◽  
Approximation Method ◽  
Numerical Approximation ◽  
Evaluation Process ◽  
Elasticity Tensor ◽  
Fe Analysis ◽  
Tangent Modulus ◽  
Material Models ◽  
Complex Material ◽  
Objective Stress

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

scholarly journals Numerical Approximation of Tangent Moduli for Finite Element Implementations of Nonlinear Hyperelastic Material Models

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Wei Sun ◽  
Elliot L. Chaikof ◽  
Marc E. Levenston
Keyword(s):  
Finite Element ◽  
Numerical Approximation ◽  
Structural Model ◽  
Large Strain ◽  
Deformation Gradient ◽  
Mathematical Formulation ◽  
Hyperelastic Material ◽  
Material Models ◽  
Tangent Stiffness Matrix ◽  
Tangent Moduli

Finite element (FE) implementations of nearly incompressible material models often employ decoupled numerical treatments of the dilatational and deviatoric parts of the deformation gradient. This treatment allows the dilatational stiffness to be handled separately to alleviate ill conditioning of the tangent stiffness matrix. However, this can lead to complex formulations of the material tangent moduli that can be difficult to implement or may require custom FE codes, thus limiting their general use. Here we present an approach, based on work by Miehe (Miehe, 1996, “Numerical Computation of Algorithmic (Consistent) Tangent Moduli in Large Strain Computational Inelasticity,” Comput. Methods Appl. Mech. Eng., 134, pp. 223–240), for an efficient numerical approximation of the tangent moduli that can be easily implemented within commercial FE codes. By perturbing the deformation gradient, the material tangent moduli from the Jaumann rate of the Kirchhoff stress are accurately approximated by a forward difference of the associated Kirchhoff stresses. The merit of this approach is that it produces a concise mathematical formulation that is not dependent on any particular material model. Consequently, once the approximation method is coded in a subroutine, it can be used for other hyperelastic material models with no modification. The implementation and accuracy of this approach is first demonstrated with a simple neo-Hookean material. Subsequently, a fiber-reinforced structural model is applied to analyze the pressure-diameter curve during blood vessel inflation. Implementation of this approach will facilitate the incorporation of novel hyperelastic material models for a soft tissue behavior into commercial FE software.

Finite Element Analysis of Tire and Pavement Interaction

2011 ◽  
Author(s):  
Kwangwon Kim ◽  
Jaehyung Ju ◽  
Doo-Man Kim ◽  
Swangwa Rhie
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Interaction Model ◽  
Fe Analysis ◽  
Nonlinear Material ◽  
Stress Distributions ◽  
Element Analysis ◽  
Material Models ◽  
Interaction Models ◽  
Pavement Material

Nonlinear material models of a tire and a pavement appear to be important to precisely evaluate both tire performance and stresses of a pavement. In this paper, nonlinear tire and pavement material models are used and their contract pressures of a tire and stresses of a pavement are investigated. The results with the nonlinear material models are compared with those of simplified tire and pavement models. Finite element (FE) analysis with ABAQUS is used for simulating four different interaction models of tire and pavement. An interaction model with a hyperelastic tire and an elasto-viscoplastic pavement shows accurate contract pressures of a tire and stress distributions of a pavement.

scholarly journals A Practical Finite Element Modeling Strategy to Capture Cracking and Crushing Behavior of Reinforced Concrete Structures

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 506 ◽  
Author(s):  
Alexandre Mathern ◽  
Jincheng Yang
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Constitutive Relations ◽  
Fe Analysis ◽  
Rc Beams ◽  
Cracking Behavior ◽  
Concrete Cracking ◽  
Rc Structures ◽  
Nonlinear Fe Analysis ◽  
Modeling Strategy

Nonlinear finite element (FE) analysis of reinforced concrete (RC) structures is characterized by numerous modeling options and input parameters. To accurately model the nonlinear RC behavior involving concrete cracking in tension and crushing in compression, practitioners make different choices regarding the critical modeling issues, e.g., defining the concrete constitutive relations, assigning the bond between the concrete and the steel reinforcement, and solving problems related to convergence difficulties and mesh sensitivities. Thus, it is imperative to review the common modeling choices critically and develop a robust modeling strategy with consistency, reliability, and comparability. This paper proposes a modeling strategy and practical recommendations for the nonlinear FE analysis of RC structures based on parametric studies of critical modeling choices. The proposed modeling strategy aims at providing reliable predictions of flexural responses of RC members with a focus on concrete cracking behavior and crushing failure, which serve as the foundation for more complex modeling cases, e.g., RC beams bonded with fiber reinforced polymer (FRP) laminates. Additionally, herein, the implementation procedure for the proposed modeling strategy is comprehensively described with a focus on the critical modeling issues for RC structures. The proposed strategy is demonstrated through FE analyses of RC beams tested in four-point bending—one RC beam as reference and one beam externally bonded with a carbon-FRP (CFRP) laminate in its soffit. The simulated results agree well with experimental measurements regarding load-deformation relationship, cracking, flexural failure due to concrete crushing, and CFRP debonding initiated by intermediate cracks. The modeling strategy and recommendations presented herein are applicable to the nonlinear FE analysis of RC structures in general.

Recent Advances in Lower Bound Shakedown Analysis

2009 ◽  
Author(s):  
Dieter Weichert ◽  
Abdelkader Hachemi
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Process Engineering ◽  
Operating Conditions ◽  
Structural Elements ◽  
Shakedown Analysis ◽  
Material Models ◽  
Practical Engineering ◽  
Safe Operating ◽  
New Algorithms

The special interest in lower bound shakedown analysis is that it provides, at least in principle, safe operating conditions for sensitive structures or structural elements under fluctuating thermo-mechanical loading as to be found in power- and process engineering. In this paper achievements obtained over the last years to introduce more sophisticated material models into the framework of shakedown analysis are developed. Also new algorithms will be presented that allow using the addressed numerical methods as post-processor for commercial finite element codes. Examples from practical engineering will illustrate the potential of the methodology.

Design and Analysis of Viscoelastic Seismic Dampers

2002 ◽  
Author(s):  
N. Shimizu ◽  
H. Nasuno ◽  
T. Yazaki ◽  
K. Sunakoda
Keyword(s):  
Finite Element ◽  
Constitutive Relation ◽  
Time Domain ◽  
Dynamic Properties ◽  
Design Procedure ◽  
Fe Analysis ◽  
Damping Capacity ◽  
Element Formulation ◽  
Element Analysis ◽  
Equivalent Viscous Damping

This paper describes a methodology of design and analysis of viscoelastic seismic dampers by means of the time domain finite element analysis. The viscoelastic constitutive relation of material incorporating with the fractional calculus has been derived and the finite element formulation based on the constitutive relation has been developed to analyze the dynamic property of seismic damper. A time domain computer program was developed by using the formulation. Dynamic properties of hysteresis loop, damping capacity, equivalent viscous damping coefficient, and equivalent spring constant are calculated and compared with the experimental results. Remarkable correlation between the FE analysis and the experiment is gained, and consequently the design procedure with the help of the FE analysis has been established.

Analysis and Modeling of Defects in Unsupported Overhanging Features in Micro-Stereolithography

2016 ◽  
Author(s):  
Vito Basile ◽  
Francesco Modica ◽  
Irene Fassi
Keyword(s):  
Finite Element ◽  
Numerical Models ◽  
Numerical Approach ◽  
Fe Analysis ◽  
Test Cases ◽  
Layer By Layer ◽  
Failure Condition ◽  
Micro Scale ◽  
Part Geometry ◽  
Shape Component

In the present paper, a numerical approach to model the layer-by-layer construction of cured material during the Additive Manufacturing (AM) process is proposed. The method is developed by a recursive mechanical finite element (FE) analysis and takes into account forces and pressures acting on the cured material during the process, in order to simulate the behavior and investigate the failure condition sources, which lead to defects in the final part geometry. The study is focused on the evaluation of the process capability Stereolithography (SLA), to build parts with challenging features in meso-micro scale without supports. Two test cases, a cantilever part and a bridge shape component, have been considered in order to evaluate the potentiality of the approach. Numerical models have been tuned by experimental test. The simulations are validated considering two test cases and briefly compared to the printed samples. Results show the potential of the approach adopted but also the difficulties on simulation settings.

Lateral Impact of Railroad Bridges With Hybrid Composite Beams: Finite Element Modeling and Preliminary Dynamic Behavior Study of HCB

2014 ◽  
Author(s):  
Yuan Jing ◽  
Z. John Ma ◽  
Richard M. Bennett ◽  
David B. Clarke
Keyword(s):  
Finite Element ◽  
Impact Loading ◽  
Hybrid Composite ◽  
Composite Beam ◽  
Glass Fibers ◽  
Fe Analysis ◽  
Future Research ◽  
Lateral Impact ◽  
Time Duration ◽  
Hybrid Composite Beam

Grade separations have been used along High-Speed Rail (HSR) to decrease traffic congestion and the danger that occurs at grade crossings. However, the concern with grade separations is the potential damage due to lateral impact of bridge superstructures by over-height vehicles. This is a concern with existing bridges, and lateral impact is not included in standard bridge code provisions. A new bridge technology, Hybrid Composite Beam (HCB), was proposed to meet the requirements of another HSR objective, that of a sustainable solution for the construction of new and replacement bridges in rail infrastructure. The hybrid composite beam combines advanced composite materials with conventional concrete and steel to create a bridge that is stronger and more resistance to corrosion than conventional materials. The HCB is composed of three main parts; the first is a FRP (fiber reinforced polymer) shell, which encapsulates the other two parts. The second part is the compression reinforcement which consists of concrete or cement grout that is pumped into a continuous conduit fabricated into the FRP shell. The third part of the HCB is the tension reinforcement that could consist of carbon or glass fibers, prestressed strands, or other materials that are strong in tension, which is used to equilibrate the internal forces in the compression reinforcement. The combination of conventional materials with FRP exploits the inherent benefits of each material and optimizes the overall performance of the structure. The behavior of this novel system has been studied during the last few years and some vertical static tests have been performed, but no dynamic or lateral impact tests have been conducted yet. Therefore, the main objective of this study is to evaluate the performance of HCB when subjected to lateral impact loading caused by over-height vehicles. This paper explains the advantages of HCB when used in bridge infrastructures. The commercial software ABAQUS was used to perform the finite element (FE) modeling of a 30ft long HCB. Test data was used to validate the results generated by FE analysis. A constant impact loading with a time duration of 0.1 second was applied to an area at the mid-span of the HCB. Lateral deflection and stress distribution were obtained from FE analysis, and local stress concentration can be observed from the stress contour. Full-scale beam dynamic testing will be conducted in the future research to better study the behavior of HCB when subjected to over-height vehicles.

Comparison of Different Material Models to Simulate 3-D Breast Deformations Using Finite Element Analysis

2013 ◽  
Vol 42 (4) ◽  
pp. 843-857 ◽  
Author(s):  
Maximilian Eder ◽  
Stefan Raith ◽  
Jalil Jalali ◽  
Alexander Volf ◽  
Markus Settles ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Element Analysis ◽  
Material Models
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