A Three-Dimensional Constitutive Theory for Fiber Composite Laminated Media

1990 ◽  
Vol 57 (4) ◽  
pp. 948-955 ◽  
Author(s):  
R. M. Christensen ◽  
E. Zywicz
Keyword(s):  
Fiber Composite ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Constitutive Theory ◽  
Constitutive Relationship ◽  
Elastic Behavior ◽  
Specific Subset ◽  
The Matrix ◽  
Scale Properties ◽  
Using Data

A three-dimensional elastic constitutive theory is developed for application to fiber composite laminated media. The lamina level constitutive relationship is a specific subset of general, transversely isotropic media behavior. This special class of lamina behavior permits the development of an exact lamination procedure for systems assembled from a single lamina type. The three-dimensional constitutive form for the laminate is determined in terms of the subscale lamina properties and the orientations of each lamina. The extension of this specific constitutive relationship to general transversely isotropic lamina involves separation of the five lamina-scale properties into fiber-dominated versus matrix-dominated classifications and the development of a generalized averaging procedure for the matrix-dominated properties. The resulting three-dimensional constitutive/lamination theory is evaluated through comparisons between exact solutions, using data bases appropriate for graphite and glass epoxy systems in quasi-isotropic layups. The theory remains highly effective through the transition from thin laminate to thick laminate behavior and even beyond that through the transition from thick laminate behavior to fully and strongly three-dimensional elastic behavior. The generalized averaging procedure for the matrix-dominated properties produces variations in results that are the same or less than the variations in results due to the experimental uncertainty in the matrix-dominated properties themselves. The theory is fairly simple and extremely versatile in its application.

scholarly journals Failure of a Fiber Composite Lamina Under Three-Dimensional Stresses

1999 ◽  
Author(s):  
Steven J. DeTeresa
Keyword(s):  
Fiber Composite ◽  
Three Dimensional ◽  
Uniaxial Stress ◽  
Failure Criteria ◽  
Fiber Composites ◽  
Test System ◽  
Failure Model ◽  
Pressure Test ◽  
Using Data ◽  
Carbon Fiber Epoxy

Abstract The efficient use of thick-section fiber composites requires a proven three-dimensional failure model. Numerous failure criteria have been proposed, but the lack of critical experimental results makes it difficult to assess the accuracy of these models. It is shown that the various predictions for failure of a lamina due to the simple state of uniaxial stress plus superposed hydrostatic pressure are disparate. These differences are sufficient to allow evaluation of failure criteria using data that has the normal scatter found for composite materials. A high-pressure test system for fiber composites is described and results for the effects of pressure on the transverse and longitudinal compression strengths of a carbon fiber/epoxy lamina are discussed. Results are compared with a few representative failure models.

Design Optimization of a Curved Actuator with Piezoelectric Fibers

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1971-1975 ◽  
Author(s):  
Cheol Kim ◽  
Dong Yeub Lee
Keyword(s):  
Fiber Composite ◽  
Matrix Material ◽  
Three Dimensional ◽  
Linear Elastic ◽  
The Matrix ◽  
Dimensional Finite Element ◽  
Structural Responses ◽  
Piezoelectric Fiber Composite ◽  
Three Dimensional Finite Element ◽  
Piezoelectric Fiber

Piezoelectric Fiber Composite with Interdigitated Electrodes (PFCIDE) was previously introduced as an alternative to monolithic wafers with conventional electrodes for applications of structural actuation. This paper is an investigation into the performance improvement of piezoelectric fiber composite actuators by optimizing the stacking sequence and changing the matrix material. This paper presents the numerical optimization of a piezoelectric fiber/piezoelectric matrix composite actuator with IDE (PFPMIDE). Various concepts from different backgrounds, including three-dimensional linear elastic and dielectric theories, have been incorporated into the present linear piezoelectric model. To see the structural responses of the actuator integrated with the PFPMIDE, three dimensional finite element formulations were derived. Numerical analyses show larger center displacement of the curved actuator with the PFPMIDE due to optimization of the piezoelectric fiber angles. This paper presents the concept of a curved actuator that occurs naturally via thermal residual stress during the curing process, as well as the optimization of the maximum curved actuator displacement, which is accomplished using the Davidon-Fletcher-Powell (DFP) method.

Application of Variational Asymptotic Micromechanical Method to Strength Analysis of Composite Materials

2019 ◽  
Vol 801 ◽  
pp. 95-100
Author(s):  
Dileep Kumar ◽  
Dineshkumar Harursampath
Keyword(s):  
A Priori ◽  
Plastic Region ◽  
Mathematical Formulation ◽  
Matrix Material ◽  
Transversely Isotropic ◽  
Constitutive Relationship ◽  
Strength Analysis ◽  
The Matrix ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method

One of the most important features of a material to know before using it is the maximum limit of the load at which it fails. This paper presents a micromechanical strength theory to estimate the tensile strength of the unidirectional fiber reinforced composite. The fibers used can be considered transversely isotropic and elastic till failure, but the matrix material is considered to be Elastic-plastic. The mathematical formulation used is the Variational-Asymptotic Method (VAM), which is used to construct the asymptotically-correct a reduced-dimensional model that is free of a priori assumption regarding the kinematics. The 3-D strain generated in each constituent material is explicitly expressed in 1-D strains and initial curvatures. The advantage of using VAM is that the stress state correlation of constituent materials is taken care of while applying warping constraints. Prandtl-Reuss plasticity theory has been implemented for the plastic region constitutive relationship. The other advantage of this work is that the load-bearing capacity of the composite beyond the elastic region has been considered. Good agreement has been found between experimental data and VAM analysis.

Design Optimization of a Piezoelectric Fiber Actuator With a Natural Curvature

2002 ◽  
Author(s):  
Cheol Kim ◽  
Dong-Yeub Lee
Keyword(s):  
Fiber Composite ◽  
Matrix Material ◽  
Three Dimensional ◽  
Linear Elastic ◽  
The Matrix ◽  
Dimensional Finite Element ◽  
Structural Responses ◽  
Piezoelectric Fiber Composite ◽  
Three Dimensional Finite Element ◽  
Piezoelectric Fiber

Piezoelectric Fiber Composite with Interdigitated Electrodes (PFCIDE) was previously introduced as an alternative to monolithic wafers with conventional electrodes for applications of structural actuation. This paper is an investigation into the performance improvement of piezoelectric fiber composite actuators by optimizing the stacking sequence and changing the matrix material. This paper presents the numerical optimization of a piezoelectric fiber/piezoelectric matrix composite actuator with IDE (PFPMIDE). Various concepts from different backgrounds, including three-dimensional linear elastic and dielectric theories, have been incorporated into the present linear piezoelectric model. To see the structural responses of the actuator integrated with the PFPMIDE, three-dimensional finite element formulations were derived. Numerical analysis shows larger center displacement of the curved actuator with the PFPMIDE due to optimization of the piezoelectric fiber angles. This paper presents the concept of a curved actuator that occurs naturally via thermal residual stress during the curing process, as well as the optimization of the maximum curved actuator displacement, which is accomplished using the Davidon-Fletcher-Powell (DFP) method.

Vibration analysis of transversely isotropic hollow cylinder considering three different theories using the matrix Frobenius method

2019 ◽  
Vol 15 (6) ◽  
pp. 1212-1237 ◽  
Author(s):  
Siddhartha Biswas
Keyword(s):  
Hollow Cylinder ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Free Vibrations ◽  
Radial Coordinate ◽  
Phase Lag ◽  
Content Type ◽  
Frobenius Method ◽  
Mechanical Coupling ◽  
The Matrix

Purpose The purpose of this paper is to deal with the three-dimensional analysis of free vibrations in a stress-free and rigidly fixed homogeneous transversely isotropic hollow cylinder in the context of three-phase-lag (TPL) model of hyperbolic thermoelasticity. Design/methodology/approach The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate. Findings The natural frequency, dissipation factor and inverse quality factor in the stress-free and rigidly fixed hollow cylinder get significantly affected due to thermal vibrations and thermo-mechanical coupling. Originality/value The modified Bessel functions and matrix Frobenius method have been directly used to study the vibration model of a homogeneous, transversely isotropic hollow cylinder in the context of TPL model based on three-dimensional thermoelasticity.

scholarly journals Quantitative Description for Sand Void Fabric with the Principle of Stereology

2021 ◽  
Vol 11 (23) ◽  
pp. 11158
Author(s):  
Xuefeng Li ◽  
Zhigang Ma ◽  
Fanchao Meng
Keyword(s):  
Quantitative Description ◽  
Three Dimensional ◽  
Discrete Distribution ◽  
Transversely Isotropic ◽  
Theoretical Description ◽  
Constitutive Relationship ◽  
Fabric Tensor ◽  
Mathematical Probability ◽  
Scan Line ◽  
Definition Of

Based on the principle of stereology to describe void fabric, the fabric tensor is redefined by the idea of normalization, and a novel quantitative description method for the orthotropic fabric of granular materials is presented. The scan line is described by two independent angles in the stereo space, and the projection of the scan line on three orthogonal planes is used to determine the plane tensor. The second-order plane tensor can be described equivalently by two invariants, which describe the degree and direction of anisotropy of the material, respectively. In the three-dimensional orthogonal space, there are three measurable amplitude parameters on the three orthogonal planes. Due to the normalized definition of tensor in this paper, there are only two independent variations of the three amplitude parameters, and any two amplitude parameters can be used to derive the three-dimensional orthotropic fabric tensor. Therefore, the same orthorhombic anisotropy structure can be described by three fabrics, which enriches the theoretical description of orthotropy greatly. As the geometric relationship of the stereoscopic space scan line changes, the three sets of orthotropic fabrics degenerate into different forms of transversely isotropic and isotropic fabrics naturally and have a clear physical meaning. The novel fabric tensor is quantitatively determined based on mathematical probability and statistics. The discrete distribution of voids in space is projected as a scalar measurable parameter on a plane. This parameter is related to the macroscopic constitutive relationship directly and can be used to describe the effect of microscopic voids on the macroscopic phenomenon of materials.

Designing TIMP (tissue inhibitor of metalloproteinases) variants that are selective metalloproteinase inhibitors

2003 ◽  
Vol 70 ◽  
pp. 201-212 ◽  
Author(s):  
Hideaki Nagase ◽  
Keith Brew
Keyword(s):  
Three Dimensional ◽  
Therapeutic Interventions ◽  
Tissue Inhibitors Of Metalloproteinases ◽  
Structural Basis ◽  
Structural Elements ◽  
Ridge Structure ◽  
Extracellular Matrix Components ◽  
Metalloproteinase Inhibitors ◽  
The Matrix ◽  
A Disintegrin And Metalloproteinase

The tissue inhibitors of metalloproteinases (TIMPs) are endogenous inhibitors of the matrix metalloproteinases (MMPs), enzymes that play central roles in the degradation of extracellular matrix components. The balance between MMPs and TIMPs is important in the maintenance of tissues, and its disruption affects tissue homoeostasis. Four related TIMPs (TIMP-1 to TIMP-4) can each form a complex with MMPs in a 1:1 stoichiometry with high affinity, but their inhibitory activities towards different MMPs are not particularly selective. The three-dimensional structures of TIMP-MMP complexes reveal that TIMPs have an extended ridge structure that slots into the active site of MMPs. Mutation of three separate residues in the ridge, at positions 2, 4 and 68 in the amino acid sequence of the N-terminal inhibitory domain of TIMP-1 (N-TIMP-1), separately and in combination has produced N-TIMP-1 variants with higher binding affinity and specificity for individual MMPs. TIMP-3 is unique in that it inhibits not only MMPs, but also several ADAM (a disintegrin and metalloproteinase) and ADAMTS (ADAM with thrombospondin motifs) metalloproteinases. Inhibition of the latter groups of metalloproteinases, as exemplified with ADAMTS-4 (aggrecanase 1), requires additional structural elements in TIMP-3 that have not yet been identified. Knowledge of the structural basis of the inhibitory action of TIMPs will facilitate the design of selective TIMP variants for investigating the biological roles of specific MMPs and for developing therapeutic interventions for MMP-associated diseases.

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

scholarly journals Macroporous chitosan/methoxypoly(ethylene glycol) based cryosponges with unique morphology for tissue engineering applications

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Pradeep Kumar ◽  
Viness Pillay ◽  
Yahya E. Choonara
Keyword(s):  
Tissue Engineering ◽  
Polymer Network ◽  
Three Dimensional ◽  
Hysteresis Loops ◽  
Interpenetrating Polymer Network ◽  
Morphological Data ◽  
Porous Scaffolds ◽  
Morphological Variations ◽  
Molecular Stability ◽  
The Matrix

AbstractThree-dimensional porous scaffolds are widely employed in tissue engineering and regenerative medicine for their ability to carry bioactives and cells; and for their platform properties to allow for bridging-the-gap within an injured tissue. This study describes the effect of various methoxypolyethylene glycol (mPEG) derivatives (mPEG (-OCH3 functionality), mPEG-aldehyde (mPEG-CHO) and mPEG-acetic acid (mPEG-COOH)) on the morphology and physical properties of chemically crosslinked, semi-interpenetrating polymer network (IPN), chitosan (CHT)/mPEG blend cryosponges. Physicochemical and molecular characterization revealed that the –CHO and –COOH functional groups in mPEG derivatives interacted with the –NH2 functionality of the chitosan chain. The distinguishing feature of the cryosponges was their unique morphological features such as fringe thread-, pebble-, curved quartz crystal-, crystal flower-; and canyon-like structures. The morphological data was well corroborated by the image processing data and physisorption curves corresponding to Type II isotherm with open hysteresis loops. Functionalization of mPEG had no evident influence on the macro-mechanical properties of the cryosponges but increased the matrix strength as determined by the rheomechanical analyses. The cryosponges were able to deliver bioactives (dexamethasone and curcumin) over 10 days, showed varied matrix degradation profiles, and supported neuronal cells on the matrix surface. In addition, in silico simulations confirmed the compatibility and molecular stability of the CHT/mPEG blend compositions. In conclusion, the study confirmed that significant morphological variations may be induced by minimal functionalization and crosslinking of biomaterials.

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