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.

Damage Initiation and Evolution in Woven Composites

2001 ◽  
Author(s):  
Xiaodong Tang ◽  
John D. Whitcomb
Keyword(s):  
Three Dimensional ◽  
Woven Composites ◽  
Element Analysis ◽  
Damage Initiation ◽  
Loss And Damage ◽  
Dimensional Finite Element ◽  
Strain Relationship ◽  
Three Dimensional Finite Element ◽  
Stiffness Loss ◽  
Damage Initiation And Evolution

Abstract The damage initiation and evolution mechanisms in plain and satin weave composites were studied using three-dimensional finite element analysis. The tow paths of the weave were selected such that the wavy region of the tows were identical in both weaves. The damage initiation and evolution behaviors in these comparable wavy regions were compared and discussed in terms of stress components that initiate damage, the overall stress/strain relationship and the accumulation of the damaged volume in the warp tow, fill tow and matrix pockets. The results showed significant similarities in many aspects of the damage behaviors such as damage modes, stiffness loss and damage accumulation processes.

Dynamic Performance of Composite Pavements Under Impact

1997 ◽  
Vol 1570 (1) ◽  
pp. 163-171 ◽  
Author(s):  
Samir N. Shoukry ◽  
D. R. Martinelli ◽  
Olga I. Selezneva
Keyword(s):  
Impact Load ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Deep Understanding ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Asphalt Overlay ◽  
Explicit Finite Element Analysis ◽  
Vertical Displacements ◽  
Pavement Layers

The importance of developing a deep understanding of the behavior of pavement layers under the action of dynamic loads, and the availability of cutting-edge computational and visualization technologies, led to the study presented in this paper. Explicit finite-element analysis was used to investigate the propagation of dynamic displacements induced in pavement layers under the action of an impact load similar to the one applied in a falling weight deflectometer test. The time-dependent dynamic response of a rigid pavement with straight asphalt concrete overlay was studied for two cases of unbonded and fully bonded interfaces between different layers. Significant differences in behavior were observed. Three-dimensional computer graphics and animation of the deformed model were used to display the propagation of vertical dynamic displacements through pavement layers. It was found that in the absence of a perfect bond between all pavement layers, the displacements measured on the top surface correlated little with the deformation measured in subsequent layers. In this case, a complicated pattern of behavior took place between the asphalt overlay and the concrete. The time histories of vertical displacements at selected surface locations and on the top and bottom of every layer were plotted. The plots revealed the existence of time shifts between the maximum displacements experienced by each layer, irrespective of the type of bond assumed between the interfaces.

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 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.

Optimum cutting depth and spacing of roadheader picks: a numerical simulation using a three-dimensional cracking method

2019 ◽  
Vol 43 (3) ◽  
pp. 366-375
Author(s):  
Weihuang Liu ◽  
Jun Cao ◽  
Tao He ◽  
Gengyuan Gao ◽  
Hulin Li ◽  
...  
Keyword(s):  
Optimum Design ◽  
Three Dimensional ◽  
Mining Operation ◽  
Optimization Method ◽  
Stress Distributions ◽  
Cutting Depth ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Explicit Finite Element Analysis ◽  
Cutting Model

Cutting depth and spacing are two important parameters for the efficiency of a roadheader in mining operation. In this study, the case of a roadheader excavating a coal gallery is taken into account. Based on explicit finite element analysis (FEA), the minimum cutting specific energy (SE) was obtained by a series of numerical simulations. According to the actual cutting process, a three-dimensional (3D) double-pick cutting model was established. The validation for the cutting model showed that it was not only reliable to predict the value of cutting SE, but also capable of accurately simulating the cutting morphology. The variation of cutting moments, stress distributions, and character of coal fragment formation were investigated. The reasons for the different SEs are explained and an optimum design for cutting depth and spacing is given. The results show that SE shrinks by 22.82% using the optimum design compared to the original parameters. Overall, it is believed that the novel 3D double-pick cutting model and the optimization method used in this study are highly appropriate to better understand coal fragmentation and improved mining efficiency.

scholarly journals Response of laterally loaded rigid monopiles and poles in multi-layered elastic soil

2016 ◽  
Vol 53 (8) ◽  
pp. 1281-1292 ◽  
Author(s):  
Bipin K. Gupta ◽  
Dipanjan Basu
Keyword(s):  
Parametric Study ◽  
Virtual Work ◽  
Three Dimensional ◽  
Element Analysis ◽  
Head Displacement ◽  
Rigid Pile ◽  
Dimensional Interaction ◽  
Laterally Loaded ◽  
Pile Response ◽  
Elastic Soil

A new method of analysis of rigid monopiles and poles based on the principle of virtual work is developed. The analysis considers three-dimensional interaction between the rigid pile and surrounding soil, and quickly produces pile response while maintaining accuracy comparable with that obtained from equivalent finite element analysis. Using this method, a systematic parametric study is performed to investigate the response of rigid piles in soil profiles where properties change either continuously or discretely with depth. Equations are developed based on the parametric study, which can be used to calculate pile head displacement and rotation. Numerical examples are provided that illustrate the use of the method.

A Discrete Meshless Lagrangian Based Approach for Soft Impact Damage Modeling in Advanced Propulsion Systems

2010 ◽  
Author(s):  
Aaron Siddens ◽  
Javid Bayandor
Keyword(s):  
Impact Damage ◽  
Three Dimensional ◽  
Jet Engines ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Interactive Behavior ◽  
Explicit Finite Element Analysis ◽  
Highly Nonlinear ◽  
Soft Objects ◽  
Crashworthiness Analysis

Soft impact on aircraft occurs in several forms, such as bird and hail strike. A discrete meshless Lagrangian based approach has been developed for modeling the fluidic behavior of soft objects during impact. This approach shows promise for developing an overall predictive methodology for accurately capturing and assessing dynamic damage in jet engines. This paper focuses on a part of this study aiming to develop a methodology capable of predicting full details of soft impact damage in turbofan engine forward sections. The initial scenario being simulated was a bird strike. Through modeling of the bird in a Lagrangian domain, the method’s suitability for simulating soft impact damage in fan section structures was evaluated. Three-dimensional explicit finite element analysis models were employed to simulate the highly nonlinear and transient response of the interactions between the non-Newtonian bird and the forward engine section resulting from impact and to capture the associated turbofan blade damage, fan assembly vibrations, and subsequent engine casing destruction. Critical features under investigation were the degradation and fracture of the turbofan blades and the engine casing. Results indicated that a meshless soft impactor model was able to produce the fluid-solid interactive behavior expected from a bird. The methodology further succeeded in effectively predicting the intricate subsequent fluid-fan assembly violent interactions. Several important considerations for crashworthiness analysis of forward sections were highlighted.

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.

The contact and friction problem in the rolling process

2000 ◽  
Vol 214 (1) ◽  
pp. 61-69
Author(s):  
J D Lee ◽  
S Shen
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Large Strain ◽  
Three Dimensional ◽  
Rolling Process ◽  
Shear Stresses ◽  
Time Step ◽  
Element Analysis ◽  
Friction Law ◽  
Updated Lagrangian

In this work, a new generalized non-Euclidean friction law is proposed. This friction law allows the friction coefficients in the tangential and axial directions of the roll to be different. A three-dimensional, large-strain, non-steady state elastic-plastic finite element analysis has been performed for the flat rolling process. The contact and friction problem at the interface between the workpiece and the rolls is treated rigorously. The finite element procedures are based on the updated Lagrangian virtual work equations in incremental form. The solution at each time step is accepted only if the equilibrium of nodal forces, the calculation of which is an exact treatment, is reached pointwise. The numerical results, including the interfacial normal and shear stresses, are presented and discussed.

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