Interface Constitutive Law Research Articles

Modeling of the Nonlinear Interface in Reinforced Concrete

This article presents a novel scheme for modeling of reinforced concrete. The strategy takes into account the nonlinear behavior of the concrete as well as the debonding in the interface. The proposed technique solves the kinematic and kinetic jump in the interface by performing sub-cycles over the constituents—reinforcing bar and concrete—jointly with an innovative interface constitutive law. Application to pull-out problems is performed to show the capabilities of the proposed methodology by means of comparison with available experimental data.

Theoretical Solution for Fatigue Debonding Growth and Fatigue Life Prediction of FRP-Concrete Interfaces

This paper presents an analytical solution for the evolution and distribution of shear stresses along the entire bond length of FRP-concrete interfaces due to mode-II fatigue loading. The creep-fatigue interaction and fatigue crack growth after debonding initiation are incorporated into a nonlinear interfacial constitutive law. While the creep-fatigue interaction is represented by the degradation of the interfacial stiffness, the debond growth is governed by a form of the Paris equation and the fracture energy ratio, Gmax/Gc. Furthermore, a new form of energy ratio is adopted to be debond-dependent. Through a series of experimental double-lap shear specimens, the results showed that the debond growth rate ( da/dN) along the FRP-concrete interfaces diminishes with fatigue cycles and that 30% of the static bond capacity of the FRP-concrete interface can be considered as the endurance limit of fatigue loading for FRP-strengthened beams. The agreement between the theoretical predictions and experimental results is valid, with a good degree of accuracy.

Minimum bond length and size effects in FRP–substrate bonded joints

The load transfer mechanism between the fibre-reinforced polymer (FRP) materials and the substrate plays a crucial role in the overall response of retrofitted structural members. The FRP–support material interface can be studied by using pull tests in which a reinforcement plate is bonded to a prism and subjected to a tensile force. The experimental results obtained regard the assembly (FRP strip-support block), then a central problem is how to carry out the interface constitutive laws and the related parameters. The principal objective of the present paper is to contrive a procedure which, for a fixed interface constitutive law, permits to derive the interface mechanical parameters from the pull tests experimental data. This procedure has its basis on the size effect phenomena which the experimental tests evidence. Furthermore, the size effect laws show that the effective or minimum bond length coincides with the internal length of the interface and permits to distinguish small and large specimens in the sense of fracture mechanics.

Interfacial stress analysis and prediction of debonding for a thin plate bonded to a curved substrate

This paper focuses on the analytical and numerical modeling of the interface between a rigid substrate with simple constant curvature and a thin bonded plate. The interfacial behavior is modeled by independent cohesive laws in the normal and tangential directions, coupled with a mixed-mode fracture criterion. The newly developed analytical model determines the interfacial shear and normal stress distributions as functions of the substrate curvature, during the various behavioral stages of the interface prior to the initiation of debonding. The model is also able to predict the debonding load and the effective bond length. In the numerical model the interface is modeled by zero-thickness node-to-segment contact elements, in which both the geometrical relationships between the nodes of the discretized problem and the interface constitutive laws are suitably defined. Numerical results and comparisons between the predictions of the two models are presented.

Modeling of mixed-mode debonding in the peel test applied to superficial reinforcements

This paper focuses on modeling of the interface between a rigid substrate and a thin elastic adherend subjected to mixed-mode loading in the peel test configuration. The context in which the investigation is situated is the study of bond between fiber-reinforced polymer (FRP) sheets and quasi-brittle substrates, where FRP sheets are used as a strengthening system for existing structures. The problem is approached both analytically and numerically. The analytical model is based on the linear-elastic fracture mechanics energy approach. In the numerical model, the interface is discretized with zero-thickness contact elements which account for both debonding and contact within a unified framework, using the node-to-segment contact strategy. Uncoupled cohesive interface constitutive laws are adopted in the normal and tangential directions. The formulation is implemented and tested using the finite element code FEAP. The models are able to predict the response of the bonded joint as a function of the main parameters, which are identified through dimensional analysis. The main objective is to compute the debonding load and the effective bond length of the adherend, i.e., the value of bond length beyond which a further increase has no effect on the debonding load, as functions of the peel angle. The detailed distributions of interfacial shear and normal stresses are also found. Numerical results and analytical predictions are shown to be in excellent agreement.

An Experimental and Numerical Study of the Static and Fatigue Performance of a Composite Adhesive Repair

Experimental static and fatigue tension-tension tests were carried out on 5HS/RTM6 composite intact coupons and coupons incorporating adhesively-bonded (FM300-2) stepped flush joints. The results show that the adhesive joint, which is widely used in repairs, significantly reduces the static strength as well as the fatigue life of the composite. Both, the static and the fatigue failure of the ‘repaired’ coupons occur at the adhesive joint and involve crack initiation and propagation. The latter is modelled using interface finite elements based on the decohezive zone approach. The material degradation in the interface constitutive law is described by a damage variable, which can evolve due to the applied loads as well as the number of fatigue cycles. The fatigue formulation, based on a published model, is adapted to fit the framework of the pseudotransient formulation that is used as a numerical tool to overcome convergence difficulties. The fatigue model requires three material parameters. Numerical tests show that a single set of these parameters can be used to recover, very accurately, the experimental S-N relationship. Sensitivity studies show that the results are not mesh dependent.

Schwarz method for earthquake source dynamics

Dynamic faulting under slip-dependent friction in a linear elastic domain (in-plane and 3D configurations) is considered. The use of an implicit time-stepping scheme (Newmark method) allows much larger values of the time step than the critical CFL time step, and higher accuracy to handle the non-smoothness of the interface constitutive law (slip weakening friction). The finite element form of the quasi-variational inequality is solved by a Schwarz domain decomposition method, by separating the inner nodes of the domain from the nodes on the fault. In this way, the quasi-variational inequality splits into two subproblems. The first one is a large linear system of equations, and its unknowns are related to the mesh nodes of the first subdomain (i.e. lying inside the domain). The unknowns of the second subproblem are the degrees of freedom of the mesh nodes of the second subdomain (i.e. lying on the domain boundary where the conditions of contact and friction are imposed). This nonlinear subproblem is solved by the same Schwarz algorithm, leading to some local nonlinear subproblems of a very small size. Numerical experiments are performed to illustrate convergence in time and space, instability capturing, energy dissipation and the influence of normal stress variations. We have used the proposed numerical method to compute source dynamics phenomena on complex and realistic 2D fault models (branched fault systems).

The effect of contact on the decohesion of laminated beams with multiple microcracks

The problem of interface decohesion in laminated beams is addressed with reference to the debonding double cantilever beam test geometry (DCB). The paper deals with the analysis of the influence of nonuniform bonding properties or interfacial defects on the crack propagation process and its stability. To this aim, the classical analytical approach based on the Euler–Bernoulli beam on an elastic foundation is extended to the presence of a general distribution of microcracks ahead of the macrocrack tip. The main features and limitations of this approach are carefully analyzed. In particular, it is shown that this simplified approach does not consider the unilateral contact condition along the interface, thus admitting a penetration between the two arms of the beam. A comparison with a finite element formulation is proposed to assess if this violation of the constraints inequalities, usually adopted in the case of uniform bonding, is still acceptable when interfacial defects are present. In order to fully describe the whole nonlinear behavior of the interface, a generalized interface constitutive law is used. The models comparison shows that, in the presence of interfacial defects, the effect of contact plays a crucial role in the description of the mechanical response of the joint.

Structural interfaces in linear elasticity. Part I: Nonlocality and gradient approximations

Many biological and optimal materials, at multiple scales, consist of what can be idealized as continuous bodies joined by structural interfaces. Mechanical characterization of the microstructure defining the interface can nowadays be accurately done; however, such interfaces are usually analyzed employing models where those properties are overly simplified. To introduce into the analysis the microstructure properties, a new model of structural interfaces is proposed and developed: a true structure is introduced in the transition zone, joining continuous bodies, with geometrical and material properties directly obtained from those of the interfacial microstructure. First, the case of an elliptical inclusion connected by a structural interface to an infinite matrix is solved analytically, showing that nonlocal effects follow directly from the introduction of the structure, related to the inclination of the connecting elements. Second, starting from a discrete structure, a continuous model of a structural interface is derived. The usual zero-thickness linear interface model is shown to be a special case of this more general continuous structural interface model. Then, a gradient approximation of the interface constitutive law is rigorously derived: it is the first example of the analytical derivation of a nonlocal interface model from the microstructure properties. The effects introduced in the mechanical behavior by both the continuous model and its gradient approximation are illustrated by solving, for the first time, the problem of a circular inclusion connected to an infinite matrix by a structural interface and subject to remote uniform stress.

A concise interface constitutive law for analysis of delamination and splitting in composite materials and its application to scaled notched tensile specimens

AbstractA concise constitutive law for cohesive interfaces is proposed in this paper. A new state variable is introduced to track the extent of damage accumulated at the interface. The constitutive equations not only account for mixed‐mode delamination propagation in composite materials, but also satisfactorily deal with mode ratio change during the debonding process. The interface model is implemented in the LS‐DYNA explicit finite element code. The model has been applied to scaled open hole tension tests on laminated composite material. Comparison between numerical results and experiments shows good correlation for failure modes and strengths for a range of different specimen sizes. Copyright © 2006 John Wiley & Sons, Ltd.

Analysis of shear capacity of lightweight concrete beams

In this paper, the failure mechanisms of lightweight concrete beams without shear reinforcement are examined by means of non-linear finite element analyses and experimental observations. For the 2-D computational simulations, discrete inter- and intra-element crack models based on zero-thickness interface constitutive laws are used within the format of discrete and embedded crack approaches. The objective is to capture the brittle failure behavior of lightweight concrete beams under mixed-mode fracture conditions.

Mixed mode failure analysis of bonded joints with rate‐dependent interface models

AbstractThe recent developments in joining technologies and the increasing use of composites materials in structural design justify the wide interest of structural mechanics researchers in bonded joints. Joints often represent the weakness zone of the structure and appropriate and rigorous mechanical models are required in order to describe deformation, durability and failure. The present work is devoted to the theoretical formulation and numerical implementation of an interface model suitable to simulate the time‐dependent behaviour of bonded joints. The interface laws are formulated in the framework of viscoplasticity for generalized standard materials and describe the softening response of the joint along its decohesion process in presence of shear and tensile normal tractions. These laws are derived in a thermodynamic consistent manner and take into account the rate dependency modifications of the fracture process zone making use of a sort of non‐local instantaneous dissipation. The interface constitutive laws are expressed both in rate and discrete incremental form for the purpose of numerical implementation. The consistent tangent matrix is derived. Finally, the problem of model parameters identification is approached making use of the finite element method for the experiments simulation and of an evolution strategy to solve the constrained optimization problem which mathematically represents the parameter identification inverse problem. Copyright © 2006 John Wiley & Sons, Ltd.

Crack patterns in thin layers under temperature loading. Part I: Monotonic loading

The analysis of cracking and delamination of a plate bonded to a substrate is presented in the paper. The plate is subjected to a monotonic temperature loading. Several types of interface constitutive laws are used in order to obtain analytical solutions specifying the maximum number of plate fragments and the description of fragmentation process. The segmentation cracking model is further used to measure the ultimate shear strength of a thin film–substrate interface.

Energy release rate and mode partition for interlaminar crack in circular laminated beams

This work describes an improved technique for the analysis of interlaminar crack growth in laminated circular beams subjected to mixed-mode loading conditions. By adopting a multi-layer curved beam model and curved interface elements leads to model the structure as a succession of first-order shear deformable beams joined by adhesive interfaces. The interface containing the crack is simulated by means of a cracking linear interfacial constitutive law which provides normal and shear interlaminar stresses. At the perfectly bonded interfaces the connection between beam elements is imposed by the Lagrange multiplier method. The total energy release rate and its individual mode components are obtained when the stiffnesses, considered as penalty parameters, tend to infinity thus reproducing the results of the linear elastic fracture mechanics theory. Results are obtained by adopting an accurate numerical integration procedure able to deal with stress singularities at the crack tip. Comparisons with results available from literature obtained by using the elasticity theory and solid finite elements show that the model is able to capture accurately both the total and the individual mode components of energy release rate. Numerical examples demonstrate the capability of the proposed method to provide a complete description of the problem of mixed-mode crack growth in curved interfaces, which takes into account the influence of curvature and of transverse shear deformability.

Non-local separation constitutive laws for interfaces and their relation to nanoscale simulations

A framework is proposed to characterize fracture through continuum interface separation constitutive laws that are motivated by molecular dynamics (MD) simulations using embedded-atom method potentials. These laws are distinguished from previous continuum models in that discrete atomistics are used to determine a set of nanoscale effects, accounting for the influence of atomic structure and imperfections on interface separation or fracture. This conceptual framework utilizes internal state variable (ISV) theory to embed a set of interface attributes into cohesive interface separation constitutive relations. Structural rearrangement of the interface region during separation can be explicitly tracked through a set of differential equations for the ISVs. To guide forms for the interface constitutive laws, MD simulations are presented for a planar, tilt nanograin boundary interface subjected to tension and shear deformations. The proposed list of ISVs accounts for geometry, composition, defect density, and damage within the interface region. Continuum calculations motivated by discrete nanoscale computations facilitate a more complete description of real material separation processes.

A continuum damage model for delaminations in laminated composites

Delamination, a typical mode of interfacial damage in laminated composites, has been considered in the context of continuum damage mechanics in this paper. Interfaces where delaminations could occur are introduced between the constituent layers. A simple but appropriate continuum damage representation is proposed. A single scalar damage parameter is employed and the degradation of the interface stiffness is established. Use has been made of the concept of a damage surface to derive the damage evolution law. The damage surface is constructed so that it combines the conventional stress-based and fracture-mechanics-based failure criteria which take account of mode interaction in mixed-mode delamination problems. The damage surface shrinks as damage develops and leads to a softening interfacial constitutive law. By adjusting the shrinkage rate of the damage surface, various interfacial constitutive laws found in the literature can be reproduced. An incremental interfacial constitutive law is also derived for use in damage analysis of laminated composites, which is a non-linear problem in nature. Numerical predictions for problems involving a DCB specimen under pure mode I delamination and mixed-mode delamination in a split beam are in good agreement with available experimental data or analytical solutions. The model has also been applied to the prediction of the failure strength of overlap ply-blocking specimens. The results have been compared with available experimental and alternative theoretical ones and discussed fully.

Stress Transfer and Fracture Propagation in Different Kinds of Adhesive Joints

To effectively and efficiently utilize fiber-reinforced plastic (FRP) laminates in strengthening civil infrastructure, a design strategy integrating the properties of FRP reinforcement and composite structural behavior must be adopted. The interfacial stress transfer behavior including debonding should be considered to be one of the most important effects on composite structural behavior. In this paper, 2 kinds of nonlinear interfacial constitutive laws describing the pre- and postinterfacial microdebonding behavior are introduced to solve the nonlinear interfacial stress transfer and fracture propagation problems for different kinds of adhesive joints in FRP/steel-strengthened concrete or steel structures. Expressions for the maximum transferable load, interfacial shear stress distribution, and initiation and propagation of interfacial cracks are derived analytically. In addition, numerical simulations are performed to discuss the factors influencing the interfacial behavior, and the theoretical derivations are validated by finite element analysis.

An asymptotic analysis of two-phase fluid mixing

We study the motion of the slightly compressible multi-phase flow model proposed by Chen, Glimm, Sharp and Zhang. The interface velocity and constitutive law are analyzed by derivation of the exact quantity. Using singular perturbation theory, a formal asymptotic expansion is derived for the solution of the compressible equations. An asymptotic analysis in the incompressible limit, for slightly compressible flows supplies important new information to resolve nonuniqueness of the pressure difference between the two fluid species of the incompressible flow equations.

THEORETICAL SOLUTIONS ON INTERFACIAL STRESS TRANSFER OF EXTERNALLY BONDED STEEL/COMPOSITE LAMINATES

連続繊維シート等の補強材とコンクリートの接着界面の応力伝達特性は, それらにより補強された構造物全体の構造性能に大きな影響を与える. 特に, 接着界面の剥離進展により, 補強された構造物の耐荷力や変形性能を大きく低下させることがあるため, 接着界面のせん断変形挙動および剥離現象の解明は重要な問題となっている. 本研究では, 幾かの簡易な線形・非線型式を想定した場合の接着界面の局所せん断応力τと相対変位δの関係に対して, 接着界面のせん断応力分布および補強材のひずみ分布に関する理論式を剥離破壊エネルギーの概念を用いて系統的に導いた. また, 最大剥離荷重, せん断応力の有効伝達長さ, 剥離の生成・進展に関する検討を行い, 界面せん断伝達メカニズムを解明した.

Optimal design of interfaces in a femoral head surface replacement prosthesis considering nonlinear behaviour

Shape optimization problems applied in the field of biomechanics are presented. Particularly the shape optimization of interfaces separating the bone tissue from the orthopaedic implant are considered. Nonlinear interface behaviour is included in the computational models: a nonlinear elastic model and a damage based model. For the two nonlinear interface constitutive laws an analytical shape sensitivity formulation has been developed. The objective functions included both the effect of the interface stresses and of the interface micromotions. The optimization procedure provided optimal designs, which display better mechanical performance in terms of interface stresses and damage diffusion.