Torsion of a fiber reinforced hyperelastic cylinder for which the fibers can undergo dissolution and reassembly

In previous work, the authors have developed a theory for treating microstructural changes in fiber reinforced hyperelastic materials. In this theory, fibers undergo dissolution as a result of increasing elongation and then reassemble in a direction defined as part of the model. Processes in which the fibers reassemble in the direction of maximum principal stretch of the matrix were specifically considered. This model was previously illustrated for various cases of homogeneous deformation. The present work studies the implications of the model during the non-homogeneous deformation of axial stretch and torsion of a circular solid cylinder composed of an isotropic matrix and families of helically wound fibers. It is shown that the process of fiber dissolution and reassembly produces complex morphological changes in the fibrous structure and hence, in the response of the cylinder. Such events can give rise to an outer layer of material in which the fibers have undergone dissolution and reassembly. The interface between this region and the as yet unaltered core material can then move radially inward as axial stretch and/or twist increase. Gradual reassembly of the fibers with increasing stretch and twist changes their contributions to the torque and axial force and their helical orientation. Different sequences of axial stretch and twist result in different morphologies in the fibrous structure.     

On the matrix cracking stress and the redistribution of internal stresses in brittle-matrix composites

A concept is proposed to increase the matrix cracking stress of some brittle-matrix composites by taking advantage of the redistribution of internal stresses that occurs when a composite with phases that have dissimilar creep behavior is subjected to thermomechanical loading. The concept is elaborated through the stress analysis of a model unidirectional composite with constituents that exhibit linear viscoelastic behavior. It is shown that if a composite with a matrix that is less creep resistant than the fibers is subjected to a treatment involving both thermal and mechanical loading (e.g. creep test), stresses can be transferred from the matrix to the fibers, resulting in the stress–relaxation of the matrix. Furthermore, it is also shown that by the elastic recovery of the fibers, the matrix can be subjected to large compressive residual stresses at the end of the treatment. The conditions for the viability of this concept and the implications of fiber overloading and potential loss of composite-like behavior are discussed.     

Mechanical properties of electrospun collagen–chitosan complex single fibers and membrane

Collagen and chitosan blends were fabricated into ultrafine fibers to mimic the native extracellular matrix (ECM). So far less mechanical property investigation of electrospun fibers has been reported because of the small dimensions of micro and nanostructures that pose a tremendous challenge for the experimental study of their mechanical properties. In this paper, the electrospun collagen–chitosan complex single fibers and fibrous membrane were collected and their mechanical properties were investigated with a nano tensile testing system and a universal materials tester, respectively. The mechanical properties were found to be dependent on fiber diameter and the ratio of collagen to chitosan in fibers. Fibers with a smaller diameter had higher strength but lower ductility due to the higher draw ratio that was applied during the electrospinning process. For the electrospun single fibers, the fibers demonstrated excellent tensile ductility at chitosan content of 10% and 20% and the highest tensile strength and Young's modulus at chitosan content from 40% to 60%. For the electrospun fibrous membrane, the ultimate tensile strength of the fibrous membrane decreased with the increase of chitosan content in fibers and the trend in the ultimate tensile elongation is similar to that of the single fiber.     

Emergence of fibrous fan morphologies in deformation directed reformation of hyperelastic filamentary networks

Recently, the authors generalized a theory for modelling the scission and reforming of crosslinks in isotropic polymeric materials to include materials in which elastic fibers are embedded in an elastic matrix. The fibers were assumed to dissolve with increasing deformation and then to immediately reassemble in a direction defined as part of the model. The model was illustrated in detail for uniaxial stretching along the direction of the fibers. Fiber reassembly was along the original fiber direction and did not result in a change in fiber alignment. The present work examines the implications of this model when the direction of reassembly is uncorrelated with the original fiber direction. In particular, the fibers are assumed to reassemble in the direction of maximum principal stretch of the matrix. The specific case is treated when the deformation is simple shear and the initial fiber direction is perpendicular to the direction of shear. The resulting fiber elongation with increasing shear results in fiber dissolution over a constitutively determined interval of the amount of simple shear. Newly formed fibers align in the current principal direction of maximum stretch, which is a direction that changes with the amount of simple shear. The resulting interval of alignment angles generates a fan-like fiber morphology at each material point. The formation and structure of the fan is described. In addition, the relation between the shear and normal stresses and the amount of shear is discussed, both during loading and unloading. It is shown that there can be a state of permanent set that is related to the original shape by triaxial extension and shear.     

A continuum model for remodeling in living structures

A new remodeling theory accounting for mechanically driven collagen fiber reorientation in cardiovascular tissues is proposed. The constitutive equations for the living tissues are motivated by phenomenologically based microstructural considerations on the collagen fiber level. Homogenization from this molecular microscale to the macroscale of the cardiovascular tissue is performed via the concept of chain network models. In contrast to purely invariant-based macroscopic approaches, the present approach is thus governed by a limited set of physically motivated material parameters. Its particular feature is the underlying orthotropic unit cell which inherently incorporates transverse isotropy and standard isotropy as special cases. To account for mechanically induced remodeling, the unit cell dimensions are postulated to change gradually in response to mechanical loading. From an algorithmic point of view, rather than updating vector-valued microstructural directions, as in previously suggested models, we update the scalar-valued dimensions of this orthotropic unit cell with respect to the positive eigenvalues of a tensorial driving force. This update is straightforward, experiences no singularities and leads to a stable and robust remodeling algorithm. Embedded in a finite element framework, the algorithm is applied to simulate the uniaxial loading of a cylindrical tendon and the complex multiaxial loading situation in a model artery. After investigating different material and spatial stress and strain measures as potential driving forces, we conclude that the Cauchy stress, i.e., the true stress acting on the deformed configuration, seems to be a reasonable candidate to drive the remodeling process.     

三维机织碳/碳复合材料双轴压缩载荷下的力学行为

基于三维机织碳/碳复合材料的细观结构特征, 设计平板十字形试样, 在材料双轴力学性能试验机上开展了复合材料单轴、 双轴加载压缩试验, 对比分析了三维机织碳/碳复合材料在双轴压缩载荷下的力学行为。研究表明: 三维机织碳/碳复合材料的压缩行为表现为非线性、 脆性断裂; 双轴载荷作用下非线性特征更为显著, 压缩模量随应力的增加而增大, 强度与模量相较于单轴有较大幅度增加, 双轴压缩载荷作用下材料的强化效应显著; 试样破坏位置并未出现在试样中心区, 而是发生在试样的加载端部或十字形试样的加载分枝根部, 主要表现为基体开裂、 纤维断裂和层间脱粘, 碳布及其层间界面剪切强度的强弱直接影响材料的压缩强度。     

Micro-Macro Analysis of Viscoelastic Unidirectional Laminated Composite Plates Using DR Method

The Dynamic Relaxation (DR) technique together with finite difference discritization is used to study the bending behavior of Mindlin composite plate including geometric nonlinearity. The overall behavior of the unidirectional composite is obtained from a three-dimensional (3D) micromechanical model, in any combination of normal and shear loading conditions, based on the assumptions of Simplified Unit Cell Method (SUCM). The composite system consists of nonlinear viscoelastic matrix reinforced by transversely isotropic elastic fibers. A recursive formulation for the hereditary integral of the Schapery viscoelastic constitutive equation in multiaxial stress state is used to model the nonlinear viscoelastic matrix material in the material level. The creep tests data is used for verification of the predicted response of the current approach. Under uniform lateral pressure, the laminated plate deformation with clamped and hinged edged constraints is predicted for various time steps.     

Experimental Analysis of the Influence of Structural Parameters on the Behavior of Glass-Fiber Reinforced Polypropylene Composites

In a composite material reinforced by short random fibers, damage results from different elementary failure mechanisms such as matrix microcracking, fiber pull out, failure of the fiber/matrix interface, failure of fibers, etc. These damages influence greatly the macroscopic behavior of composite materials. To obtain good mechanical performance of a composite material, it is important to optimize the fiber ratio and the quality of the fiber/matrix interface, which have a direct influence on the damage mentioned above. The main objective of this study is to determine the influence of structural parameters on the evolution of damage for two types of polypropylene glass-fiber reinforced composites. In parallel with the classical approach of the mechanical theory of damage, which consists in load–unload tensile tests, the use of acoustic emission allows one to follow in real time the character and the importance of damage mechanisms in the course of loading. In addition, fractographic analysis makes it possible to confirm different assumptions and conclusions from this study.     

Growth and remodeling with application to abdominal aortic aneurysms

In this paper, we apply a mixture theory of growth and remodeling to study the formation and dilatation of abdominal aortic aneurysms. We adapt the continuum theory of mixtures to formalize the processes of production and removal of constituents from a loaded body. Specifically, we consider a mixture of elastin and collagen fibers which endow the material with anisotropic properties. An evolving recruitment variable defines the intermediate configuration from which the elastic stretch of collagen is measured. General formulations of the equations governing homeostatic state and aneurysm development are provided. In the homeostatic state, the idealized geometry of the aorta is a thick-walled tube subject to constant internal pressure and axial stretch. The formation of an aneurysm induces an increase of mass locally achieved via production of new material that exceeds the removal of old material. The combined effects of loss of elastin, degradation of existing and deposition of new collagen, as well as fiber remodeling results in a continuous enlargement of the aneurysm bulge. The numerical method makes use of a purposely written material subroutine, called UMAT, which is based on the constitutive formulation provided in the paper. Numerical results based on patient-based material parameters are illustrated.     

A structural constitutive model for chemically treated planar tissues under biaxial loading

Chemically treated, biologically derived soft collagenous tissues are used extensively in medical devices. To enable prosthesis design through computational methods, physically realistic constitutive models are required. In the present study, a structural approach was utilized that incorporated experimentally measured angular distribution of collagen fibers. Using biaxial mechanical data from our previous study (Annals of Biomedical Engineering, vol. 26(5), pp. 892–902, 1998), the effective fiber and matrix stress–strain responses were predicted. The agreement with the experimental data supported the assumption that the mechanical effects of chemical treatment are equivalent to the addition of an isotropic elastic matrix. An important utility of this model is its ability to separate the effects of chemical treatment on the fibers and matrix. Applications of this approach include utilization in the design of novel chemical treatments that produce specific mechanical responses, the study of fatigue damage, and finite element implementation for tissue engineering scaffold design. Received 4 November 1999     

A numerical approach for predicting the failure locus of fiber reinforced composites under combined transverse compression and axial tension

A computational model based on the finite element method is presented for the estimation of strength of a fiber-reinforced lamina subjected to a combination of the transverse compression and axial tension. A complex damage mechanism including fiber breakage, fiber/matrix debonding and matrix plastic deformation is reproduced in the proposed model by using appropriate constitutive equations. The numerical simulation of mechanical response of the unidirectional lamina under biaxial loading is used to obtained the failure locus. Subsequently, the model is verified against an analytical solution and experimental data. It was found that the numerical calculations agree better with experimental results than analytical predictions.     

Stress integration procedures for a biaxial isotropic material model of biological membranes and for hysteretic models of muscle fibres and surfactant

Stress calculation for a biaxial isotropic material model of a biological membrane and for hysteretic models of muscle fibres and surfactant is presented in the paper. The non‐linear elastic membrane model is defined by uniaxial and biaxial stress–stretch relations, while the hysteretic models of tissue fibres and surfactant are described by the stress–stretch and surface tension–surfactant area ratio constitutive relationships, respectively. The conditions when tissue is or is not covered by surfactant are considered. It is assumed that the material is subjected to cyclic loading. Quasi‐static and steady conditions are considered. The models are implemented in large strain finite element incremented‐iterative analysis of shell deformations. Numerical examples demonstrate characteristics of the computational procedures and structural response of biological membranes when subjected to cyclic loading. Hysteretic response of biological membranes subjected to cyclic loading is caused by hysteresis of fibres and hysteresis of surfactant. The hysteretic effects may play an important role in the physiology of human body. Copyright © 2006 John Wiley & Sons, Ltd.     

Mechanical and statistical analyses of fracture of whisker-reinforced ceramic-matrix composites

This paper analyzes the fracture toughness of short-fiber reinforced ceramic-matrix composites (CMC). The effects of crack deflection and fiber pullout on matrix cracking are examined using a combination of mechanical and statistical models. First, the stress intensity factors of a deflected crack subjected to closure stress due to fiber pullout are analyzed based upon the mechanical model. Distributed dislocation method is used for the elastic analysis. Since the deflected crack is subjected to biaxial loading, a mixed mode fracture criterion in linear elastic fracture mechanics is applied to calculate the fracture toughness. Secondly, the number of pullout fibers on the fracture surface is treated as a random variable, and the statistical distribution of these fibers has been determined. The pullout force acting on a deflected crack is also obtained as a random variable by assuming a simple mechanism of fiber pullout. The probability of failure of CMC can thus be estimated from the strength characteristics of the fiber and matrix as well as the interface between these two.     

Stress-intensity factors of r-cracks in fiber-reinforced composites under thermal and mechanical loading

This paper is concerned with the problem of the calculation of stress-intensity factors at the tips of radial matrix cracks (r-cracks) in fiber-reinforced composites under thermal and/or transverse uniaxial or biaxial mechanical loading. The crack is either located in the immediate vicinity of a single fiber or it terminates at the interface between the fiber and the matrix. The problem is stated and solved numerically within the framework of linear elasticity using Erdogan's integral equation technique. It is shown that the solutions for purely thermal and purely mechanical loading can simply be superimposed in order to obtain the results of the combined loading case. Stress-intensity factors (SIFs) are calculated for various lengths and distances of the crack from the interface for each of these loading conditions. The behavior of the SIFs for cracks growing towards or away from the interface is examined. The role of the elastic mismatch between the fibers and the matrix is emphasized and studied extensively using the so-called Dundurs' parameters. It is shown that an r-crack, which is remotely located from the fiber, can either be stabilized or destabilized depending on both the elastic as well as the thermal mismatch of the fibrous composite. Furthermore, Dundurs' parameters are used to predict the exponent of the singularity of the crack tip elastic field and the behavior of the corresponding SIFs for cracks which terminate at the interface. An analytical solution for the SIFs is derived for all three loading conditions under the assumption that the elastic constants of the matrix and the fiber are equal. It is shown that the analytical solution is in good agreement with the corresponding numerical results. Moreover, another analytical solution from the literature [15], which is based upon Paris' equation for the calculation of stress-intensity factors, is compared with the numerical results and it is shown to be valid only for extremely short r-cracks touching the interface. The numerical results presented are valid for practical fiber composites with r-cracks close to or terminating at the interface provided the matrix material is brittle and the crack does not interact with other neighboring fibers. They may be applied to predict the transverse mechanical behavior of high strength fiber composites.     

粘弹性基体中环绕纤维的环形裂纹的型和型应力强度因子

分析了粘弹性基体中环绕纤维的环形裂纹的 型和 型应力强度因子及其时间相关性。根据文献 [1 ]、文献 [2 ]中的弹性解 ,求出了粘弹性基体中环绕纤维的环形裂纹的 型和 型应力强度因子在 L aplace变换域内的解。对其进行 Laplace数值反演后 ,得到了相应的 型和 型应力强度因子在时间域内的变化曲线。结果表明 ,给定长度的环形裂纹在尚未接触界面时 ,其两端正则化的 型和 型应力强度因子均随时间增大而减小。     

粘弹性基体中环绕纤维的环形裂纹的&Iota|型和ΙΙ&Iota|型应力强度因子

分析了粘弹性基体中环绕纤维的环形裂纹的é 型和? 型应力强度因子及其时间相关性。根据文献[ 1 ]、文献[2 ]中的弹性解, 求出了粘弹性基体中环绕纤维的环形裂纹的é 型和? 型应力强度因子在Laplace 变换域内的解。对其进行Laplace 数值反演后, 得到了相应的é 型和? 型应力强度因子在时间域内的变化曲线。结果表明, 给定长度的环形裂纹在尚未接触界面时, 其两端正则化的é 型和? 型应力强度因子均随时间增大而减小。     

Behavior of high performance fiber reinforced cement composites under multi-axial compressive loading

Experiments were conducted to better understand the behavior of strain hardening, high performance fiber reinforced cement composites (HPFRCC) when subjected to uniaxial, biaxial, and triaxial compression. The experimental parameters were: type of fiber, fiber volume fraction, and loading path. Two types of commercially available fibers, namely high-strength hooked steel fiber and ultra high molecular weight polyethylene fiber, with volume fractions ranging from 1.0% to 2.0%, were used in a 55-MPa mortar matrix. The selected loading paths consisted of uniaxial compression and tension, equal biaxial compression, and triaxial compression with two levels of lateral compression. The test results revealed that the inclusion of short fibers can significantly increase both strength and ductility under uniaxial and biaxial loading paths, but that the role of volume fraction is rather small for the range of fiber volume contents considered. The results also showed that the confining effect introduced by the fibers becomes minor in triaxial compression tests, where there is relatively high external confining pressure. The experimental information documented herein can serve as input for the development of multiaxial constitutive models for HPFRCCs.     

Rate-dependent tensile behavior of high performance fiber reinforced cementitious composites

High Performance Fiber Reinforced Cementitious Composites (HPFRCC) show strain hardening behavior accompanied with multiple micro-cracks under static tension. The high ductility and load carrying capacity resulting from their strain hardening behavior is expected to increase the resisting capacity of structures subjected to extreme loading situations, e.g., earthquake, impact or blast. However, the promise of HPFRCCs for dynamic loading applications stems from their observed good response under static loading. In fact, very little research has been conducted to investigate if their good static response translates into improved dynamic response and damage tolerance. This experimental study investigates the tensile behavior of HPFRCC using High strength steel fibers (High strength hooked fiber and twisted fiber) under various strain rates ranging from static to seismic rates. The test results indicate that the tensile behavior of HPFRCC using twisted fiber shows rate sensitivity while that using hooked fiber shows no rate sensitivity. The results also show that rate sensitivity in twisted fibers is dependent upon both fiber volume fraction and matrix strength, which influences the interface bond properties.     

Structure-mechanical properties relationship of natural tendons and ligaments

The mechanical characterization of rabbit Achilles' tendon and anterior cruciate ligament is presented. Both static and dynamic mechanical tests have been performed on fresh explanted tissues. Experimental results are presented and discussed in terms of a relationship between structural architecture and mechanical properties. The differences in collagen fibre configuration and composition between tendon and ligament influence the tensile and viscoelastic properties. In particular, tendons and ligaments showed a gradual transition from a rubber-like to a glassy-like behaviour during the loading process due to the traightening of collagen fibres.     

A combined experimental and modelling approach to aortic valve viscoelasticity in tensile deformation

The quasi-static mechanical behaviour of the aortic valve (AV) is highly non-linear and anisotropic in nature and reflects the complex collagen fibre kinematics in response to applied loading. However, little is known about the viscoelastic behaviour of the AV. The aim of this study was to investigate porcine AV tissue under uniaxial tensile deformation, in order to establish the directional dependence of its viscoelastic behaviour. Rate dependency associated with different mechanical properties was investigated, and a new viscoelastic model incorporating rate effects developed, based on the Kelvin-Voigt model. Even at low applied loads, experimental results showed rate dependency in the stress–strain response, and also hysteresis and dissipation effects. Furthermore, corresponding values of each parameter depended on the loading direction. The model successfully predicted the experimental data and indicated a ‘shear-thinning’ behaviour. By extrapolating the experimental data to that at physiological strain rates, the model predicts viscous damping coefficients of 8.3 MPa s and 3.9 MPa s, in circumferential and radial directions, respectively. This implies that the native AV offers minimal resistance to internal shear forces induced by blood flow, a potentially critical design feature for substitute implants. These data suggest that the mechanical behaviour of the AV cannot be thoroughly characterised by elastic deformation and fibre recruitment assumptions alone.