Elastic Reinforcement Research Articles

Tibial lengthening over a bioactive degradable intramedullary implant: a case report

Introduction Long duration of distraction osteosynthesis remains an unsolved problem. One of the promising ways to stimulate reparative regeneration of bone tissue is the technology of combined osteosynthesis with intramedullary elastic reinforcement with titanium wires coated with hydroxyapatite. A significant drawback of this combined distraction osteosynthesis is the planned removal of intramedullary wires several months after disassembling the Ilizarov apparatus.The purpose of this work is to demonstrate the possibility of stimulating reparative regeneration and reducing the duration of distraction osteosynthesis using an intramedullary degradable implant with bioactive filling.Methods We present the first in clinical practice case of surgical leg lengthening in a female 10-year-old patient using the Ilizarov apparatus an intramedullary degradable implant made of polycaprolactone (PCL) saturated with hydroxyapatite to stimulate reparative regeneration in the tibia. Monthly radiographic monitoring of the process of reparative regeneration of bone tissue was supplemented by computed tomography after disassembling the Ilizarov apparatus.Results The process of lengthening the tibia was accompanied by pronounced formation of a bone “sleeve” around the implant, which was directly connected to the endosteum of the tibia. The density of bone substance in the medullary canal reached 496.6 HU. The cortical layer of the tibia in the elongation zone increased to 4 mm, and its density was equal to 1288.8 HU.Discussion Leg lengthening of 4 cm was achieved along with simultaneous correction of valgus recurvatum bone deformity at IO = 15 days/cm, that is two times shorter than the generally accepted excellent IO in distraction osteosynthesis according to Ilizarov.Conclusions Biodegradable polycaprolactone implants saturated with hydroxyapatite might be not inferior to titanium wires coated with hydroxyapatite in regard to the degree of osteoinduction and do not require repeated surgical intervention to remove them.

A multiscale viscoelastic constitutive model of unidirectional carbon fiber reinforced PEEK over a wide temperature range

Due to super toughness and good repairability, the fiber reinforced polyether ether ketone (PEEK) composites are promising to replace metals in the primary-load bearing structures for the next generation aircraft. However, at the high service temperature close to or even above the glass transition temperature of PEEK, composite properties strongly depend on the loading temperature and time, bringing great challenges to their applications. How to evaluate their temperature/time dependent properties over a wide temperature range is the key issue in both the structure design and the process design. This study proposes a multiscale viscoelastic constitutive model for the composites to separately consider the individual contribution of the intrinsic matrix properties and the fiber induced strain concentration. The generalized Maxwell model for the PEEK viscoelastic properties was extended to a three-dimensional case by the genetic integration method. Based on the bottom-up approach, the isotropic viscoelastic matrix and the anisotropic linear elastic reinforcement were considered to construct a multiscale model of the fiber reinforced PEEK composites. To verify the developed model, the unidirectional carbon fiber reinforced PEEK composite samples were fabricated and tested. By the PEEK matrix relaxation tests, the composite transverse tensile tests and the representative volume element (RVE) simulations, the model parameters were calibrated step by step. Good agreements among the experimental results, the RVE simulations, and the model predictions under different tensile states over a wide temperature range (25–200 °C), proved that this model could be used to predict and to design the relaxation behaviors of the fiber reinforced PEEK composites.

Elastic reinforcement and yielding of starch-filled lipid gels

Many foods involve complex suspensions of assorted particles in a Newtonian liquid or viscoelastic medium. In this work, we study the case of suspensions of non-Brownian non-interacting rigid particles: starch, embedded in a soft solid: a colloidal lipid gel. We relate the macroscopic properties of the suspensions to the mechanics of the colloidal gel and the particle volume fraction. As particle volume fraction increases, the suspension gradually stiffens and becomes brittle as the system approaches its maximum packing fraction. The latter is independently determined from a geometric theory of random close packing for polydisperse hard spheres based on the log normal distribution of starch particles dispersed in oil. The elastic modulus, yield stress and yield strain are interrelated through simple scaling laws from a micromechanical homogenization analysis of hard spheres isotropically-distributed in yield stress fluids. • The rheology of non-Brownian non-interacting starch particles filling a viscoelastic colloidal lipid gel was investigated. • As starch volume fraction increases the suspension stiffens, turns brittle as it approaches its maximum packing fraction. • The maximum packing fraction is determined from a geometric theory of random close packing for polydisperse hard spheres. • Linear and nonlinear rheology are interrelated through simple scaling laws from a homogenization micromechanical analysis.

Impact action of a projectiles on special protective structures and ways to increase their protective capacity

A method for studying the reaction of elastic elements of protective structures to a series of impact actions of shells has been developed. In the work, the elastic elements of the protective structure are modeled by homogeneous beams, and the dynamic action of the shells is simulated by instantaneous point-applied forces. A mathematical model of this dynamic process is constructed, which is a boundary value problem for a hyperbolic equation with an irregular right-hand side. The latter is described using Dirac delta functions. Cases of both fixed and free ends of protective elements are considered. The main ideas of perturbation methods are used for the researches carried out in the work. Analytical dependences for the description of elastic deformations of a protective element which are basic for definition of its strength characteristics are received. They and the graphical dependences built on their basis for specific cases show that the dynamic deformations of the protective element for the fixed ends are greater in the case of the projectile closer to its middle, at the same time for the free ends – closer to the end. With regard to the modernization of protective structures, the dynamic effect on their elements can be reduced by using elastic reinforcement or changing the method of fixing the ends of the protective element: elastic or with a certain angle of inclination of the bearing surfaces. It is proposed to use special plastics, soil layer, flexible wood flooring, etc. as elastic reinforcement. The technique used in the work is the basis for determining the strength characteristics of protective elements, and from so – to check the reliability of the protective structure; study of the dynamics of protective and similar types of structures, taking into account the nonlinear characteristics of the elastic elements of protective structures; study of more complex oscillations of elements of protective structures. In the case of a series of impacts, it is obvious that the amplitude of deflection of the protective element after each impact will increase over time, because the model does not take into account the force of viscoelastic friction. These tasks will be the subject of further research.

Microrheological study of PVA/borax physical gels: Effect of chain length and elastic reinforcement by sodium hydroxide addition

In the present work, we have applied DWS-based microrheology to study poly (vinyl alcohol) (PVA) + borax physically cross-linked gels which are typically “living” networks. At observation times longer than the lifetime of the network connection (non-covalent reversible links based on hydrogen bonds) the system flows, but exhibits elastic character at shorter time scales. We determined gel points Cb* in borax concentration at ~27 °C using viscoelastic loss tangent uniqueness method for two molecular masses of PVA (89,000 and 205,000 g mol−1) at polymer concentration CP = 4.4% below Ce. We verified that loss tangent independency of frequency is equivalent to the Winter-Chambon (W-C) law in the critical regime for elastic and viscous moduli: G′ ∝ G″~ωn. The continuity between the terminal flow regime ω <100 rd/s and the high frequency W-C one is established allowing to cover [~1–105 rad/s]. The proportionality found between Cb* and the molecular mass needs to be verified on other chain lengths. We then studied the effect of sodium hydroxide addition to PVA/borax systems since borax dissociation in water gives borate ions (responsible for establishing “elastic active” reversible reticulations between PVA chains) and boric acid which doesn't contribute to elasticity building. The results show that NaOH addition (i.e. pH increase) transforms almost all boric acid, already attached to PVA chains by monodiol complexation, into borate ions leading to didiol complexation. This, therefore, induces gelation for systems initially in sol state or elastically reinforces physical gels. Lifetime measurements of physical reticulations with and without NaOH reveal a change in borax dependency, possibly due to the increase of the association rate compared to the dissociation one i.e. an enhancement in the reforming-breaking ratio rates.

The justification of a way for improving the protection of special buildings from shock effect of the projectile

To increase the protection of engineering structures from the impact of projectiles, it is proposed to use an elastic reinforcement of the outer surface of the coating. It is shown that its use significantly reduces the dynamic deflection of the structure, and, on the contrary, its protective properties. The results are based on an analytical analysis of the constructed mathematical model of dynamics of an elastically reinforced upper part of the protective structure under the condition of a shock effect on it of the projectile. The results obtained simultaneously, under certain constraints, may be the basis for studying the dynamics of the specified structure from the action of a shock wave or a series of strikes of projectiles.

Stress management in composite biopolymer networks

Living tissues show an extraordinary adaptiveness to strain, which is crucial for their proper biological functioning. The physical origin of this mechanical behaviour has been widely investigated using reconstituted networks of collagen fibres, the principal load-bearing component of tissues. However, collagen fibres in tissues are embedded in a soft hydrated polysaccharide matrix which generates substantial internal stresses whose effect on tissue mechanics is unknown. Here, by combining mechanical measurements and computer simulations, we show that networks composed of collagen fibres and a hyaluronan matrix exhibit synergistic mechanics characterized by an enhanced stiffness and delayed strain-stiffening. We demonstrate that the polysaccharide matrix has a dual effect on the composite response involving both internal stress and elastic reinforcement. Our findings elucidate how tissues can tune their strain-sensitivity over a wide range and provide a novel design principle for synthetic materials with programmable mechanical properties.

EXTERNAL REINFORCEMENT OF CONCRETE STRUCTURES USING COMPOSITE MATERIALS

The paper describes the main directions of non-metallic composite application in concrete reinforcement. The development routes of the structural analysis with composite reinforcement are formulated. The reinforced concrete structure combines the elastic reinforcement element with an adhesive composition having inelastic properties. It is shown that the structural reliability is ensured by adhesion of composite core reinforcement to the concrete. When performing external reinforcement of composite materials, it is necessary to ensure the joint operation of reinforcing elements and the main structure. Today, design methods of concrete structure reinforcement with composite materials do not take into account shear strains in the contact seam. Adhesion of composite material to concrete is indirectly assessed by introducing the service factor of composite material when its design resistance is assigned. Experimental studies concern concrete structures reinforced by bent elements with external reinforcement made of various composite materials. Reinforced concrete beams with A500 and A600 class reinforcement are considered. Test beams are reinforced with fiberglass, coal and carbonates canvases. Some of test beams have U-shaped anchors at the ends and are made of composite materials. Reinforced beams fracture by different schemes: composite peeling due to the adhesive destruction in the area of formation of normal and inclined cracks, compositepeeling with the destruction of protective layer, composite rupture. A part of reinforced concrete beams before the reinforcement are cracked in the stretched zone. Cracks do not affect the load-bearing capacity of reinforced beams.

Результаты применения интрамедуллярного трансфизарного эластичного армирования у пациентов с тяжелыми формами несовершенного остеогенеза

Introduction The work analyzes the results of using elastic opposite-directional transphyseal reinforcement for treatment of severe orthopedic complications in patients with osteogenesis imperfecta as well as the ways and their effectiveness to overcome the shortcomings of this technique. Material and methods The series included 24 patients. Among them, four patients had osteogenesis imperfecta of Type III, 19 were of Type IV, and one patient had Type VIII. The patients’ mean age was 14.4±2.8 years (range: 2-46 years). A total of 52 reconstructive surgical interventions were performed. Elastic intramedullary reinforcement was used in 83 segments. The combined osteosynthesis technique (the Ilizarov fixator and/or subperiosteal reinforcement) was used in 27 cases. Results Correction of deformities was achieved in all the cases. Consolidation at the osteotomy level was obtained after 26.2±7.8 days on the average (from 3 to 12 weeks postoperatively). The period of follow-ups was from 6 months to 4 years. Twenty-four complications were observed in 8 patients (33.3 % of cases). Twenty three additional interventions due to the problems of correction were performed in 20 patients (unplanned surgeries were necessary in 83.3 % of cases). The ability to stand in the vertical position and bear weight on the lower limbs with the use of auxiliary supports or without them was achieved in 22 cases out of 24 (91.7 %). Patients’ ambulation ability was evaluated with the Gillette scale and improved in 21 cases out of 24 (87.5 %). In all the cases, patient’s care facilitated, self-service capabilities improved, and patients’ social activity increased. A more comfortable position for sitting was achieved in 22 patients. In 100 % of the cases, pain reduced or disappeared by doingexercises or during walking, including exercise therapy or hygiene procedures. Conclusion The technique of transphyseal reinforcement using elastic titanium nails is indicated for deformity correction in children with severe types of osteogenesis imperfecta. Lower limb deformity correction and increased bone strength contributed to patients’ motor activity and improved their quality of life. Complications were not rare after surgical treatment but their timely correction enabled to retain the achieved anatomical and functional results. The use of a minimum fixation, the Ilizarov apparatus following corrective osteotomies and intramedullary reinforcement, assisted in achieving patient’s early verticalization and full weight-bearing on the operated limb as well as helped avoid a number of complications. Osseointegration of intramedullary implants with bioactive coating prevented their migration in the long-term period. Telescopic constructs of such nails should not be used in children under the age of 10 in order to avoid their locking in the medullary canal due to osseointegration.

Contact Phenomenon of Free-Rolling Wide-Base Tires: Effect of Speed and Temperature

AbstractThe finite-element method was used to quantify the effect of temperature and speed on contact area, deflection, and three-dimensional contact stresses of a free-rolling wide-base tire. The tire model comprised material properties identified in the laboratory and/or provided by the tire manufacturer (hyperviscoelastic rubber and linear elastic reinforcement) and accurate geometry. The model was validated using measured deflection and contact area. The analysis matrix consisted of 81 cases resulting from a combination of three loads, tire-inflation pressures, speeds, and temperatures. Four criteria were used to compare contact stresses: range, average, root-mean-square error, and coefficient of determination. Speed and temperature influence the contact area more than deflection. Longitudinal contact stresses were the most affected, followed by transverse contact stresses. In general, under constant load and tire-inflation pressure, the influence of temperature was more significant on the considered ...

On the long-term deformation process in viscoelastic composites around an elliptical hole

This paper deals with the dependence of stress redistribution around an elliptical hole in a composite on viscoelastic properties of the composite components. The results are obtained for composites with elastic and viscoelastic reinforcement. It is shown that the stress on a surface of the hole can change non-monotonically for the case of viscoelastic reinforcement, i.e., there can be maxima on the stress–time diagrams during the lifetime of the composite.

INFLUENCE OF COMPOSITE ELASTIC MODULUS AND LATERAL LOAD PATTERN ON DEFLECTION OF ANTI-SLIDE PILE HEAD

This paper develops a new method to directly determine the composite elastic modulus of the reinforced con­crete cantilever pile rather than adopt theoretical or empirical approaches. On the basis of the theory of material mecha­nism, the load-deflection equation was deduced to create the relationship between the elastic modulus and the ratio of load-deflection. The numerical modelling tests based on ANSYS separation modelling technology were carried out to determine the composite elastic modulus under different reinforcement ratio, concrete strength grade and distribution pat­tern of driving force. The results can be used to create the quantitative relationship between the composite elastic modulus and reinforcement ratio as well as concrete strength grade. Comparison amongst various lateral load pattern were made to show that the deflection of pile head is obviously affected by the lateral load pattern, and the corresponding equations of the deflection of the pile head under different lateral load pattern were proposed, which can reflect the ranking of the great influence on the deflection of the pile head, rectangular, trapezoidal and triangular lateral load pattern in order.

Determination of the Eshelby tensor in mean-field schemes for evaluation of mechanical properties of elastoplastic composites

The conventional Eshelby solution based mean-field schemes may dramatically over-estimate the stress in composites consisting of elastoplastic matrix and elastic reinforcement particles. A new and rational approach is presented to determine the Eshelby tensor of elastoplastic medium to solve this problem. We assume that, during an increment of loading in the Eshelby problem for an elastoplastic medium (EPM), the mechanical property is homogeneous, isotropic and incrementally linearized, and introduce a reference elastic medium (REM) with the identical configuration and elastic property of the EPM studied. For a purely traction boundary value problem, the distribution of the stress increment as well as the constrained elastic strain increment in the EPM can be approximated with that in the REM if both of them are subjected to exactly identical traction boundary condition. As the surface traction increment induced by the eigenstrain increment in an ellipsoidal subdomain Ω in the EPM is applied to the REM, the Eshelby tensor of the REM, Se, can be easily derived with the regular procedure of the traditional Eshelby problem. Then, the Eshelby tensor for the EPM can easily be obtained as S=[(Le)-1:L]-1:Se:[(Le)-1:L], where Le and L are the elastic and the tangent elastoplastic moduli of the EPM respectively. The developed Eshelby tensor is embedded in the conventional Mori–Tanaka scheme to predict the responses of particulate composites subjected respectively to tensile, shear, combined biaxial tensile and shear, and cyclic tensile-compressive, and non-proportional tensile and shear loadings. The comparison with the results obtained with the approaches using isotropic approximation of the tangent elastic modulus, and with the reference ones obtained with full-field FE analyses showed satisfactory agreement, demonstrating the validity of the proposed approach. The approach to determine the Eshelby tensor for elastoplastic media has the following distinct advantages: (1) it employs the regular anisotropic tangent modulus and has a unified form in both elastic and elastoplastic cases; (2) it can easily be embedded in the conventional mean-field homogenization schemes (MFHs) and used for the analyses of effective properties of composites subjected to complex loading histories; (3) it possesses high computational efficiency, since the Eshelby tensor can be simply computed using the elastic and elastoplastic properties of composites with no need of time-consuming numerical ellipsoidal integral in each increment.

Smeared-Bar Model for Viscoelastic Analysis of Uncracked Reinforced Concrete Structures

This paper presents a technique for computing the time-dependent behavior of reinforced and prestressed concrete as a composite material. This technique, when implemented in a finite-element model and assuming that the concrete and steel reinforcement act as a composite material, is computationally advantageous compared with explicitly modeling the concrete and steel materials separately. The method is developed assuming linear viscoelasticity and uncracked sections. The approach starts by first approximating the creep compliance functions for the viscoelastic concrete as a Kelvin chain model. This approximation allows the viscoelastic behavior to be framed as a rate-type creep law, which converts the analysis to an equivalent elastic problem, simplifying the computations. This approach, originally developed for plain concrete, is extended in this paper to account for the effects of linear elastic reinforcement. Several implementation examples are provided documenting the viability of the method for problems of uniaxial, multiaxial, and bending behaviors. For the presented cases, the composite method is shown to provide similar results compared with models containing explicitly modeled reinforcement. The paper concludes with a discussion regarding how to extend the methodology to the general case with linear viscoelastic reinforcement and matrix materials.

Micromechanical modelling for wood–fibre reinforced plastics in which the fibres are neither stiff nor rod-like

Plant fibres distort to curved or kinked shapes during injection moulding, while glass fibres are relatively stiff and remain rod-like. The consequences of these differences were investigated for an example of wood fibre prepared by thermomechanical pulping to reinforce polypropylene in tensile test specimens. Krenchel’s orientation factor increased with distance from the gate, reaching values similar to those published for glass-reinforced plastic. Halpin–Tsai and Mori–Tanaka micromechanical models predicted the tensile modulus within±7% at low strain, despite implicit and incorrect assumptions of rod-like shape. Both models assumed elastic reinforcement with perfect fibre–matrix bonding, and therefore overestimated the tensile stress at higher strains.

Effect of high-energy X-ray irradiation on creep mechanisms in bone and dentin

Under long-term loading creep conditions, mineralized biological tissues like bone are expected to behave in a similar manner to synthetic composites where the creeping matrix sheds load to the elastic reinforcement as creep deformation progresses. To study this mechanism in biological composites, creep experiments were performed at 37°C on bovine compact bone and dentin. Static compressive stresses were applied to the samples, while wide- and small-angle scattering patterns from high energy synchrotron X-rays were used to determine, respectively, the elastic strain in the hydroxyapatite (HAP) platelets and the strain in the mineralized collagen fibril, as a function of creep time. In these highly irradiated biological composites, the reinforcing hydroxyapatite platelets progressively transfer some of their stress back to the softer protein matrix during creep. While such behavior can be explained by damage at the interface between the two phases, it is not consistent with measurements of the apparent moduli – the ratio of applied stress to elastic HAP strain measured throughout the creep experiments by elastic unload/load segments – which remained constant throughout the experiment and thus indicated good HAP/protein bonding. A possible explanation is a combination of X-ray and load induced interfacial damage explaining the shedding of load from the HAP during long term creep, coupled with interfacial re-bonding of the load-disrupted reversible bonds upon unloading, explaining the unaffected elastic load partitioning during unload/load segments. This hypothesis is further supported by finite element modeling which shows results mirroring the experimental strain measurements when considering interfacial delamination and a compliant interstitial space at the ends of the HAP platelets.

An Implicit to Explicit FEA Solving of Tire F&amp;M with Detailed Tread Blocks

ABSTRACT A detailed tire-rolling model (185/75R14), using the implicit to explicit FEA solving strategy, was constructed to provide a reliable, dynamic simulation with several modeling features, including mesh, material modeling, and a solving strategy that could contribute to the consideration of the serious numerical noises. High-quality hexahedral meshes of tread blocks were obtained with a combined mapping method. The actual rubber distributing and nonlinear, stress-strain relationship of the rubber and bilinear elastic reinforcement were modeled for realism. In addition, a tread-rubber friction model obtained from the Laboratory Abrasion and Skid Tester (LAT 100) was applied to simulate the interaction of the tire with the road. The force and moment (F&amp;) behaviors of tire cornering when subjected to a slip-angle sweep of −10 to 10° were studied with that model. To demonstrate the efficiency of the proposed simulation, the computed F&amp;M were compared with experimental results from an MTS Flat-Trac Tire Test System. The computed cornering F&amp;M agreed well with the experimental results, so the footprint shape and contact pressure distribution of several cornering conditions were investigated. Furthermore, the longitudinal forces in response to braking/driving torque application in a slip-ratio range of −100% to 100% were computed. The proposed FEA solution confines the numerical noise within a smaller range and can serve as a valid tool in tire design.

Representative Volume Element Size of Elastoplastic and Elastoviscoplastic Particle-Reinforced Composites with Random Microstructure

With the progress of miniaturization, in many modern applications the characteristic dimensions of the physical volume occupied by particle-reinforced composites are getting comparable with the reinforcement size and many of those composite materials undergo plastic deformations. In both experimental and modelling contexts, it is therefore very important to know whether, and up to which characteristic size, the description of the composites in terms of effective, homogenized properties is sufficiently accurate to represent their response in the actual geometry. Herein, the case of particle-reinforced composites with elastoviscoplastic matrix materials and polyhedral randomly arranged linear elastic reinforcement is considered since it is representative of many metal matrix composites of technical interests. A large parametric study based on 3D finite element microstructural models is carried out to study the dependence of the Representative Volume Element (RVE) size on the mechanical properties of the constituents, the reinforcement volume fraction and the average strain level. The results show that RVE size mainly depends on the reinforcement volume fraction and on the macroscopic strain level. The estimated RVE size for elastoplastic composites with 5% to 10% volume fraction of reinforcements is found in the range of 5-6 times the average size of reinforcement particles, while for higher volume fraction, e.g. 15% to 25%vol., the RVE size increases rapidly to 10 to 20 times the reinforcement size. Moreover insights on the influence of mesh refinement and boundary conditions on finite element homogenization analysis are obtained.

Nanoplastic Interactions of Surface-Grafted Single-Walled Carbon Nanotubes with Glassy Polymer Chains in Nanocomposites

The nanoscopic interactions between glassy macromolecules and the dispersed single-walled carbon nanotubes (SWCNTs) in a nanocomposite during very large local elongations were revealed. The results also unveiled a unique mode of molecular motions followed by glassy chains during brittle nanoplastic flows. Based on detailed nanomechanical calculations on results from atomic force and electron microscopy, the molecular motions of the “strain-softened” glassy polymer chains were found highly dependent on chain entanglement density (νe), in sharp contrast to the νe-independent elastic reinforcement. Particularly, in the loosely entangled chains the SWCNTs behaved like “phantom tubes”, manifesting no effects on strain hardening of the chain network during plastic flow. This indicates that the “glassy” chains had undergone entanglement clustering, a new and unique mode of nonaffine molecular motions. The results bear important significance in revealing the fundamental behavior of glassy polymer chains and the r...

Tunnel reinforcement with rockbolts

Closed-form solutions are presented for a tunnel supported with Discretely Mechanically or Frictionally Coupled (DMFC) and with Continuously Mechanically Coupled (CMC) or Continuously Frictionally Coupled (CFC) rockbolts. The formulation is based on the following assumptions: (1) circular cross section; (2) deep tunnel; (3) K o = 1, i.e. axisymmetric problem; (4) homogeneous and isotropic ground; (5) elasto-plastic ground, with brittle failure governed by the Coulomb criterion and non-associated flow rule; (6) elastic reinforcement and (7) construction effects approximated with the β-method (reduction of internally applied stresses). The analytical solutions are compared with results obtained with a Finite Element Method. The comparisons show that the analytical solutions provide reasonable results for DMFC rockbolts and for CMC/CFC rockbolts with low to moderate spacing. For the same rock properties, tunnel geometry and construction, and reinforcement characteristics, CMC/CFC rockbolts result in slightly smaller convergence but somewhat larger rockbolt stresses than DMFC rockbolts. The behavior of DMFC rockbolts and rock response depends on “average” response of the rock between the two end points, while for CMC/CFC rockbolts the maximum stress in the rockbolt occurs at the location of maximum radial strain in the rock. In both cases the solution strongly depends on the relative stiffness between the rockbolt and the deformed rock. Practically speaking, placement of the reinforcement while the rock undergoes elastic deformations may not result in a substantial reduction of tunnel convergence. Instead, it appears that best results are obtained by placing the rockbolts while the rock undergoes plastic deformations. It has also been observed that when the distribution of rockbolts around the tunnel perimeter is linked to the far-field stresses, smaller convergence and reduced reinforcement stresses are possible.