Evolution of Mechanical Properties in Tissues Undergoing Deformation-Related Fiber Remodeling Processes

We consider a biological fibrous soft tissue in which fibers are distributed in all directions. The mechanical properties of the fibers evolve due to a continuous remodeling process. The model to describe these fiber properties is based on the strain energy density of the protofibers and a survival kernel which describes the deformation-related property changes. In particular, this study investigates the development of the fiber orientation density for different choices of the fiber creation rate and fiber dissolution rate models. It has been shown that the fiber orientation density depends on both the history of the deformation and the deformation state of the fibers at the time of their creation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Emergence and disappearance of load induced fiber kinking surfaces in transversely isotropic hyperelastic materials

The kinematics of shearing deformation in fiber reinforced materials can lead to fibers that (a) first shorten, (b) then return to their original length, and (c) then elongate. In a hyperelastic constitutive treatment this can cause the shear stress to be a nonmonotone function of the amount of shear if the fibers are sufficiently more stiff than the matrix. Here, we explore how this effects the emergence and development of kink surfaces in the context of a variety of boundary value problems. Kink surfaces are surfaces across which the deformation gradient is discontinuous. For fiber reinforced materials such surfaces generate an abrupt change in the fiber orientation (a kink). We characterize the appearance of kink surfaces in terms of three general mechanisms: fade-in, pair creation, and boundary emission. Each has a counterpart for kink surface disappearance. These mechanisms are highly sensitive both to changes in the original fiber orientation field, including spatial variation in this field, and to changes in the nature of the applied boundary conditions. A variety of examples are presented.     

Emergence and disappearance of load induced fiber kinking surfaces in transversely isotropic hyperelastic materials

The kinematics of shearing deformation in fiber reinforced materials can lead to fibers that (a) first shorten, (b) then return to their original length, and (c) then elongate. In a hyperelastic constitutive treatment this can cause the shear stress to be a nonmonotone function of the amount of shear if the fibers are sufficiently more stiff than the matrix. Here, we explore how this effects the emergence and development of kink surfaces in the context of a variety of boundary value problems. Kink surfaces are surfaces across which the deformation gradient is discontinuous. For fiber reinforced materials such surfaces generate an abrupt change in the fiber orientation (a kink). We characterize the appearance of kink surfaces in terms of three general mechanisms: fade-in, pair creation, and boundary emission. Each has a counterpart for kink surface disappearance. These mechanisms are highly sensitive both to changes in the original fiber orientation field, including spatial variation in this field, and to changes in the nature of the applied boundary conditions. A variety of examples are presented.     

Effect of structural changes on the sorptivity and mechanical properties of polyformaldehyde fibers

The dependence of the mechanical and sorption properties and structure of polyformaldehyde fibers on the degree of extension has been investigated. By x-ray structural analysis and sorption techniques it is shown that an increase in stretch ratio is accompanied by an increase in structural orientation with a simultaneous increase in porosity. It is established that the change in the mechanical properties associated with drawing depends both on orientation and on the presence of macrodefects in the fiber.Kiev Technological Institute of Light Industry. Translated from Mekhanika Polimerov, No. 6, pp. 1103–1106, November–December, 1971.     

Anisotropy of torsional rigidity of sheet polymer composite materials

Wide application of polymer composite materials (PCM) in modern technology calls for detailed evaluation of their stress-strain properties in a broad temperature range. To obtain such information, we use the dynamic mechanical analysis and with the help of a reverse torsion pendulum measure the dynamic torsional rigidity of PCM bars of rectangular cross section in the temperature range up to 600 K. It is found that the temperature dependences of the dynamic rigidity of the calculated values of dynamic shear moduli are governed by the percentage and properties of the binder and fibers, the layout of fibers, the phase interaction along interfaces, etc. The principles of dynamic mechanical spectrometry are used to substantiate and analyze the parameters of anisotropy by which the behavior of a composite can be described in the temperature range including the transition of the binder from the glassy into a highly elastic state. For this purpose, the values of dynamic rigidity are measured under low-amplitude vibrations of the PCM specimens with a fiber orientation angle from 0 to 90°. It is shown that for unidirectional composites the dependence between the dynamic rigidity and the fiber orientation angle is of extreme character. The value and position of the peak depend on the type of the binder and fibers and change with temperature. It is found that the anisotropy degree of PCM is dictated by the molecular mobility and significantly changes in the temperature range of transition of the binder and reinforcement from the glassy into a highly elastic state (in the case of SVM fibers). The possibility of evaluating the anisotropy of composites with other reinforcement schemes, in particular, of orthogonally reinforced PCMs, is shown.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 291–308, May–June, 1999.     

Finite element modeling of finite deformable,biphasic biological tissues with transversely isotropic statistically distributed fibers: toward a practical solution

The distribution of collagen fibers across articular cartilage layers is statistical in nature. Based on the concepts proposed in previous models, we developed a methodology to include the statistically distributed fibers across the cartilage thickness in the commercial FE software COMSOL which avoids extensive routine programming. The model includes many properties that are observed in real cartilage: finite hyperelastic deformation, depth-dependent collagen fiber concentration, depth- and deformation-dependent permeability, and statistically distributed collagen fiber orientation distribution across the cartilage thickness. Numerical tests were performed using confined and unconfined compressions. The model predictions on the depth-dependent strain distributions across the cartilage layer are consistent with the experimental data in the literature.     

Microscale modelling and homogenization of fiber structured materials

Various phenomena occurring on the macrosscale result from physical and mechanical behaviour on the microscale [1]. For the mechanical modeling and simulation of the heterogeneous composition of fiber structured material, in addition to the material properties the contact between the fibers has to be taken into account. The material behaviour is strongly influenced by the material properties of the fiber, but also by the geometrical structure. Periodically arranged fibers like woven, knitted or plaited fabrics and randomly oriented ones like fleece can be distinguished in their arrangement. In consideration of different lengthscales the problem involves, it is necessary to introduce a multiscale approach based on the concept of a representative volume element (RVE). The macro-micro scale transition requires a method to impose the deformation gradient on the RVE by suited boundary conditions. The reversing scale transition, based on the HILL-MANDEL condition, requires the equality of the macroscopic average of the variation of work on the RVE and the local variation of the work on the macroscale [2]. For the micro-macro transition the averaged stresses have to be extracted by a homogenization scheme. From these results an effective material law can be derived. Beside the theoretical aspects, we present the stress-strain relation for RVE-models and different boundary conditions. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural theory of elastomeric composites based on fiber systems — Invariant description

A three-dimensional theory of elastomeric composites with elastomeric matrices reinforced by systems of fibers is presented. The theory is based on a structural approach in which the matrix and the reinforcement of the composite are considered separately without reduction to a medium having continuously changing characteristics. The approach is based on the idea of a vector field of macroscopic displacements given by the positions of the axial lines of the fibers in the curret (deformed) configuration of the composite. The vector field determines the current macroscopic configuration, the tensor fields of the measures of macroscopic strain, and the field of the macroscopic stress tensor in the composite. The displacement, strain, and stress fields in the elastomeric matrix and the fibers of the reinforcing systems are regarded as derivatives of the field of macroscopic displacements of the medium. Relations are presented to describe the kinematics of the fibers in the current configuration of the composite, including the evolution of their orientation and the frequency of their planar and spatial distribution. Equations are obtained for the macroscopic motion of the fiber-reinforced matrix, and the dynamic variational principle that governs this motion is established. The elastic macroscopic potential of the matrix is found and related to the components of the macroscopic stress tensor. The procedure to be followed in constructing the constitutive equations of the composite is described. The proposed system of equations, relations, and algorithms is closed and can be used to solve problems involving the deformation of products made of fiber-reinforced elastomers and the creation of elastomeric composite products, based on fiber systems, that possess the requisite properties.     

Some laws of the elastic properties of oriented fibrous polymers and fibers

The author considers the results of calculations of the limiting values of the elastic properties (modulus of elasticity and load-extension diagram) of the main types of chemical fibers, using a model with "ideal orientation" of the molecules and the derived laws of deformation of polymer chains. A method is proposed for calculating the elastic properties of "ideally oriented" polymers from the velocity of propagation of an elastic deformation pulse and the effective density of the "skeletons" of the polymer chains. Values of the moduli of elasticity of the amorphous regions of the structure of oriented polymers are calculated. The calculated results are compared with experimental data on the elastic properties of fibers.Mekhanika Polimerov, Vol. 2, No. 1, pp. 34–42, 1966Paper read at the XIV All-Union Conference on High-Molecular Compounds, Oriented State.     

Investigation of the stability of the physicomechanical properties of carbon fibers 1. Dependence of Young's modulus on the cross-sectional area of the fiber

The modulus of elasticity in tension and the density of various carbon fibers (re-inforcement for high-modulus carbon-reinforced plastics) have been studied. There is an experimentally confirmed dependence of the modulus of elasticity on the orientation and density of the monofilament which explains the variation of this characteristic in a fiber bundle. It is shown that the principal factor determining the modulus of elasticity and its stability in a bundle of carbon fibers is the orientation and its variation for the individual fibers.     

Numerical simulation of a flexible fiber deformation in a viscous flow by the immersed boundary-lattice Boltzmann method

In this paper, deformation of a mass-less elastic fiber with a fixed end, immersed in a two-dimensional viscous channel flow, is simulated numerically. The lattice-Boltzmann method (LBM) is used to solve the Newtonian flow field and the immersed-boundary method (IBM) is employed to simulate the deformation of the flexible fiber interacting with the flow. The results of this unsteady simulation including fiber deformation, fluid velocity field, and variations of the fiber length are depicted in different time-steps through the simulation time. Similar trends are observed in plots representing length change of fibers with different values of stretching constant. Also, the numerical solution reaches a steady state equivalent to the fluid channel flow over a flat plate.     

Comparative analysis of the structural order and defectiveness of reinforcing fibers on the basis of normalized values of mechanical properties

Experimental data on mechanical properties referred to their limiting values for a flawless polymer crystal with long molecular chains is used in a comparative analysis of the degree of ordering of the structure (crystallinity, orientation) and the defectiveness of the reinforcing fibers. The actual elastic moduli and limiting (theoretical) elastic modulus are used to obtain coefficients that characterize the overall order of the structure of the fibers but are independent of their defectiveness. Values of true strength in tension and the limitingly attainable or theoretical strength are used to calculate conditional coefficients that depend both on the overall order and the defectiveness of the fiber structure. The difference in the coefficients makes it possible to detect dangerous local defects that lead to fiber failure. Results are presented from calculations for more than 20 types of reinforcing fibers. Despite the approximate nature of these representations, the data that is obtained permits comparisons of different types of fibers, characterization of their quality, and evaluation of the degree of perfection of the fiber production technology.Paper presented at the IX International Conference on the Mechanics of Composite Materials, Riga, October, 1995.St. Petersburg State University for Technology and design, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 444–453, July–August, 1996.     

Biaxial orientation of amorphous linear polymers

The mechanical properties of biaxially oriented polymethyl methacrylate, obtained on a broad range of stretch ratios and under a variety of orientation conditions, have been investigated. There is a fundamental difference between the variation of the forced elastic limit with increase in stretch ratio, which is monotone increasing, and the variation of such properties as the brittle strength, brittle temperature, true strength and elongation at break, which have an optimum at a certain stretch ratio. It is shown that the presence of an optimum is associated with the transformation of the supermolecular structures in the process of biaxial high-elastic deformation. A relation is established between the mechanical properties of biaxially oriented polymethyl methacrylate (orientation hardening) and the density of the molecular network.For communication 1 see [3].Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 586–593, July–August, 1971.     

Homogenization of Elastic Properties of Short Fiber Reinforced Composites Based on Discrete Microstructure Data

Since the microstructure of short fiber reinforced composites is inhomogeneous, the application of micromechanical models is useful, that take into account their characteristics like the fiber orientation and the aspect ratio of fibers. Two different methods are considered in this work: A two-step approach is utilized to get approximately the upper and lower bounds of the elastic properties. Furthermore, an approximation for the elastic properties is calculated by the self-consistence method. Both methods use discretely microstructural information including the length, the diameter and the orientation of each single fiber. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Properties of rigid polyurethane foams filled with milled carbon fibers

The effect of milled carbon fibers of two types (differing in length) on the properties of rigid polyurethane foams in the density range from 50 to 90 kg/m³ is investigated. The coefficient of thermal expansion and properties of the foams in tension and compression as functions of fiber content in them are determined. It is found that the long fibers are more efficient in improving the properties of the foams in their rise direction. The elongation at break of the foams decreases significantly with increasing fiber content.     

Flow-induced anisotropic viscosity in short fiber reinforced polymers

The commonly used flow models for fiber reinforced polymers often neglect the flow induced mechanical anisotropy of the suspension. With an increasing fiber volume fraction, this plays, however, an important role. There are some models which count on this effect, they are, however, phenomenological and require a fitted model parameter. In this paper, a micromechanically based constitutive law is proposed which considers the flow induced anisotropic viscosity of the fiber suspension. The introduced viscosity tensor can handle arbitrary anisotropy of the fluid-fiber mixture depending on the actual fiber orientation distribution. A homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described by Jeffery's equation. A numerical implementation of the introduced model is applied to representative flow modes. The calculated stress values are analyzed in transient and stationary flow cases. They show a less pronounced anisotropic viscous behaviour in every investigated case compared to the results obtained by the use of the Dinh-Armstrong constitutive law. The reason for the qualitative difference is that the presented model depends on the complete orientation information, while the other one is linear in the fourth-order fiber orientation tensor. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of fiber structure modification on the mechanical properties of flax fiber-epoxy composites

The mechanical characteristics of flax fibers were optimized by using the NaOH treatment process to improve the properties of composite materials. Shrinkage of the fibers during this treatment had a significant effect on the structure and, as a result, on the mechanical properties of the fibers and the composites based on them. Due to the higher mechanical strength and stiffness of flax fibers after NaOH treatment under isometric conditions, the strength and stiffness of composites in general increase. Further, NaOH treatment leads to a rougher surface morphology, as shown, e.g., for jute fibers, compared with the surface of untreated fibers without improved fiber/matrix adhesion.     

Efficient Simulation of Short Fibre Reinforced Composites

Lightweight structures become more and more important and one great class within these structures are parts produced by injection moulding. To improve the mechanical properties of these parts short fibers are injected within the molten plastics. Now a way to describe these properties without knowing the fibre orientation exactly is needed. We show an intuitive way, how mechanical properties of short fibre reinforced composites for linear thermoelasticity can be described and show the relation to other approaches. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of parameters of the distribution of the length and orientation of short fibers on characteristics of the dynamic viscoelasticity of a polymer composite

Conclusion An algorithm for calculating the dynamic viscoelastic characteristics of a composite reinforced with short fibers was developed and realized in the form of a computer program. An analysis was made of the dependence of the characteristics of the composite on the volume content and length of its fibers, as well as on statistical distributions of fiber length and orientation in the material. It was shown that a change in the parameters of the statistical distributions has a significant effect on both the elastic and the dissi-pative properties of the composite. It was found that ignoring the statistical fiber-length distribution might lead to overestimation of the real component of the complex modulus and underestimation of the mechanical loss tangent.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 13–17, January–February, 1990.     

Effect of hot-drawing conditions on the orientation characteristics of carbon-chain fibers determined by the acoustic method

The orientation characteristics of polypropylene, polyacrylonitrile, and chlorinated PVC fibers, determined by the acoustic method, have been investigated in relation to the fiber drawing conditions (draw ratio, speed, and temperature). It is shown that there is a correlation between the mechanical characteristics and the degree of acoustic anisotropy.Tashkent Institute of the Textile and Light Industries. Translated from Mekhanika Polimerov, No. 3, pp. 552–554, May–June, 1971.