scholarly journals Invariant Theory for Dispersed Transverse Isotropy: An Efficient Means for Modeling Fiber Splay

2004 ◽  
Author(s):  
D. R. Einstein ◽  
A. D. Freed ◽  
I. Vesley
Keyword(s):  
Invariant Theory ◽  
Soft Tissues ◽  
Structural Model ◽  
Transverse Isotropy ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Fiber Direction ◽  
Fiber Stress ◽  
Element Analysis ◽  
Model Modification

Microstructual studies suggest that in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. However, such descriptions are computationally cumbersome for two-dimensional fiber distributions, let alone for fully three dimensional fiber populations. We have developed a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The model is polyconvex and fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no re-formulation of the constitutive tangent matrix, making the model flexible for different types of soft-tissues. Most importantly, the model is computationally expedient in a finite element analysis.

Plastic Deformation Theory Application in Finite Element Analysis

2012 ◽  
Vol 594-597 ◽  
pp. 2723-2726
Author(s):  
Wen Shan Lin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Element Analysis ◽  
Finite Element Program ◽  
Theory Of Plasticity ◽  
Element Program

In the present study, the constitutive law of the deformation theory of plasticity has been derived. And that develop the two-dimensional and three-dimensional finite element program. The results of finite element and analytic of plasticity are compared to verify the derived the constitutive law of the deformation theory and the FEM program. At plastic stage, the constitutive laws of the deformation theory can be expressed as the linear elastic constitutive laws. But, it must be modified by iteration of the secant modulus and the effective Poisson’s ratio. Make it easier to develop finite element program. Finite element solution and analytic solution of plasticity theory comparison show the answers are the same. It shows the derivation of the constitutive law of the deformation theory of plasticity and finite element analysis program is the accuracy.

scholarly journals Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation

2021 ◽  
Vol 5 (3) ◽  
pp. 132
Author(s):  
Matthias Hinze ◽  
André Schmidt ◽  
Remco I. Leine
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Algebraic Equations ◽  
State Representation ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Infinite State

In this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.

scholarly journals Elastic Characterization of Transversely Isotropic Soft Materials by Dynamic Shear and Asymmetric Indentation

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
R. Namani ◽  
Y. Feng ◽  
R. J. Okamoto ◽  
N. Jesuraj ◽  
S. E. Sakiyama-Elbert ◽  
...  
Keyword(s):  
Soft Matter ◽  
Transverse Isotropy ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Soft Materials ◽  
Fiber Direction ◽  
Dynamic Shear ◽  
Fibrin Gels ◽  
Linear Elastic

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B = 11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20–40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08 ± 0. 42 kPa (mean ± std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58 ± 0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material.

Comparison of a Multi-Layer Structural Model for Arterial Walls With a Fung-Type Model, and Issues of Material Stability

2004 ◽  
Vol 126 (2) ◽  
pp. 264-275 ◽  
Author(s):  
Gerhard A. Holzapfel ◽  
Thomas C. Gasser ◽  
Ray W. Ogden
Keyword(s):  
Structural Model ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Point Of View ◽  
Constitutive Law ◽  
Type Model ◽  
Finite Element Program ◽  
Highly Nonlinear ◽  
Element Program

The goals of this paper are (i) to re-examine the constitutive law for the description of the (passive) highly nonlinear and anisotropic response of healthy elastic arteries introduced recently by the authors, (ii) to show how the mechanical response of a carotid artery under inflation and extension predicted by the structural model compares with that for a three-dimensional form of Fung-type strain-energy function, (iii) to provide a new set of material parameters that can be used in a finite element program, and (iv) to show that the model has certain mathematical features that are important from the point of view of material and numerical stability.

A Study on 3D Isolation Effect on High-Rise Building Subjected to Near-Field Ground Motions

2010 ◽  
Vol 150-151 ◽  
pp. 659-662
Author(s):  
Jie Ping Liu ◽  
Ling Xin Zhang ◽  
Qing Li Meng
Keyword(s):  
Structural Model ◽  
Ground Motions ◽  
Near Field ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Isolation Effect ◽  
Reinforced Concrete Frame ◽  
Element Analysis ◽  
Concrete Frame ◽  
High Rise

Isolation technology is widely applied in civil engineering nowadays, while it is indicated by seismic damage investigations that the effect of vertical motion on buildings under earthquake couldn’t be ignored. In order to study the 3D isolation effect on high-rise buildings subjected to near-field ground motions, the finite element analysis of an 11-story reinforced concrete frame-shear wall building is conducted, three ground motions are selected, three kinds of structural model are calculated, which are without isolation, with horizontal isolation and with three-dimensional isolation. By analyzing and comparing the seismic response results of models, the 3D isolation effect is studied, and some conclusions are obtained.

MECHANICAL ASPECTS OF A SINGLE-BUNDLE TIBIAL INTERFERENCE SCREW FIXATION IN A TENDON GRAFT ACL RECONSTRUCTION

2010 ◽  
Vol 22 (04) ◽  
pp. 271-278 ◽  
Author(s):  
Mahmoud Chizari ◽  
Bin Wang ◽  
Martyn Snow ◽  
Mel Barrett
Keyword(s):  
Soft Tissues ◽  
Bone Structure ◽  
Cruciate Ligament ◽  
Three Dimensional ◽  
Image Data ◽  
Qualitative Evaluation ◽  
Tendon Graft ◽  
Single Bundle ◽  
Element Analysis ◽  
Reconstructed Knee

Numerical methods applicable to the tibia bone and soft tissue biomechanics of an anterior cruciate ligament (ACL) reconstructed knee are presented in this paper. The aim is to achieve a better understanding of the mechanics of an ACL reconstructed knee. The paper describes the methodology applied in the development of an anatomically detailed three-dimensional ACL reconstructed knee model for finite element analysis from medical image data obtained from a computed tomography scan. Density segmentation techniques are used to geometrically define the knee bone structure and the encapsulated soft tissues configuration. Linear and nonlinear elastic constitutive material models are implemented to mechanically characterize the behavior of the biological materials. Preliminary numerical results for the model qualitative evaluation are presented.

Effect of In-Core Temperature on the Life Evaluation of Graphite Component

2009 ◽  
Author(s):  
Xiang Fang ◽  
Suyuan Yu ◽  
Haitao Wang
Keyword(s):  
Fast Neutron ◽  
Core Temperature ◽  
Three Dimensional ◽  
Reactor Core ◽  
Vertical Direction ◽  
Constitutive Law ◽  
Fast Neutrons ◽  
Element Analysis ◽  
Temperature Levels ◽  
The Impact

Graphite is widely used as a major internal structural material in high temperature gas-cooled reactors (HTRs). In order to evaluate service lives of graphite components, both the fast neutrons and temperature distributions inside the reactor core are required as input data for the irradiation-induced stress analysis. Since the fast neutron distributions may vary along the vertical direction due to the movement of the control rods, the corresponding location of the maximum neutron fluence changes with different in-core temperature levels. In this paper, the effect of the in-core temperature on both the stresses of graphite components due to irradiation and the corresponding life evaluations are studied numerically. The associated constitutive law for the simulation of irradiated graphite covering properties, dimensional changes and creep is briefly reviewed. A FORTRAN code based on user subroutines of MSC.MARC is developed in INET in order to perform three-dimensional finite element analysis of irradiated behavior of the graphite components for the HTRs. A side reflector graphite model is established and analyzed under a prescribed fast neutron distribution and several temperature levels. The results of irradiation-induced stresses and failure probability of the side reflector are obtained and the impact of temperature levels is discussed.

A Coupled Thermal Structural Finite Element Analysis of a Single Pulse Micro-EDM Process

2013 ◽  
Vol 579-580 ◽  
pp. 86-90
Author(s):  
Cheng Guo ◽  
Yu Kui Wang ◽  
Zhen Long Wang ◽  
Bao Cheng Xie
Keyword(s):  
Temperature Field ◽  
Thermal Stress ◽  
Stress Field ◽  
Structural Model ◽  
White Layer ◽  
Three Dimensional ◽  
Single Pulse ◽  
Discharge Process ◽  
Element Analysis ◽  
Thermal Stress Field

A three-dimensional coupled thermal structural model for micro electrical discharge is presented in this paper. Temperature field and thermal stress field of a single spark discharge process are analysed using this model by indirect coupling method. Temperature field is firstly solved which acts as the foundation of solving thermal stress field. To make the simulation results more reliable, these important elements are also taken into account, such as temperature-dependent properties of material, the phenomenon of plasma channel radius expanding, the percentage of discharge energy transferred to the workpiece and Gaussian distribution of heat flux. The results can explain the formation of cracks around the discharge crater. The thickness of the white layer and residual stresses can be predicated using this model.

Automated Estimation of Elastic Material Parameters of a Transversely Isotropic Material Using Asymmetric Indentation and Inverse Finite Element Analysis

2015 ◽  
Author(s):  
Yuan Feng ◽  
Chung-Hao Lee ◽  
Lining Sun ◽  
Ruth J. Okamoto ◽  
Songbai Ji
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Biological Tissues ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Soft Biological Tissues ◽  
Tissue Properties ◽  
Brain White Matter

Anisotropy exists in many soft biological tissues. The most common anisotropy is transverse isotropy, which is typical for fiber-reinforced structures, such as the brain white matter, tendon and muscle. Although many methods have been proposed to determine tissue properties, techniques to characterize transversely isotropic materials remain limited. The goal of this study is to investigate the feasibility of asymmetric indentation coupled with numerical optimization based on inverse finite element (FE) simulation to characterize transversely isotropic soft biological tissues. The proposed approach combining indentation and optimization may provide a useful general framework to characterize a variety of fiber-reinforced soft tissues in the future.

Microplane-Triad Model for Elastic and Fracturing Behavior of Woven Composites

2016 ◽  
Vol 83 (4) ◽  
Author(s):  
Kedar Kirane ◽  
Marco Salviato ◽  
Zdeněk P. Bažant
Keyword(s):  
Virtual Work ◽  
Process Zone ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Woven Composites ◽  
Warp Yarn ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
The Continuum

A multiscale model based on the framework of microplane theory is developed to predict the elastic and fracturing behavior of woven composites from the mesoscale properties of the constituents and the weave architecture. The effective yarn properties are obtained by means of a simplified mesomechanical model of the yarn, based on a mixed series and parallel coupling of the fibers and of the polymer within the yarns. As a novel concept, each of the several inclined or aligned segments of an undulating fill and warp yarn is represented by a triad of orthogonal microplanes, one of which is normal to the yarn segment while another is normal to the plane of the laminate. The constitutive law is defined in terms of the microplane stress and strain vectors. The elastic and inelastic constitutive behavior is defined using the microplane strain vectors which are the projections of the continuum strain tensor. Analogous to the principle of virtual work used in previous microplane models, a strain energy density equivalence principle is employed here to obtain the continuum level elastic and inelastic stiffness tensors, which in turn yield the continuum level stress tensor. The use of strain vectors rather than tensors makes the modeling conceptually clearer as it allows capturing the orientation of fiber failures, yarn cracking, matrix microcracking, and interface slip. Application of the new microplane-triad model for a twill woven composite shows that it can realistically predict all the orthotropic elastic constants and the strength limits for various layups. In contrast with the previous (nonmicroplane) models, the formulation can capture the size effect of quasi-brittle fracture with a finite fracture process zone (FPZ). Explicit finite-element analysis gives a realistic picture of progressive axial crushing of a composite tubular crush can initiated by a divergent plug. The formulation is applicable to widely different weaves, including plain, twill, and satin weaves, and is easily extensible to more complex architectures such as hybrid weaves as well as two- and three-dimensional braids.

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