Finite element modeling of dynamic frictional rupture with rate and state friction

Numerous laboratory experiments have demonstrated the dependence of the friction coefficient on the interfacial slip rate and the contact history, a behavior generically called rate and state friction. Although numerical models have been widely used for analyzing rate and state friction, in general they consider infinite elastic domains surrounding the sliding interface and rely on boundary integral formulations. Much less work has been dedicated to modeling finite size systems to account for interactions with boundaries. This paper investigates rate and state frictional interfaces in the context of finite size systems with the finite element method in explicit dynamics. It is shown that due to the highly non-linear nature of rate and state friction and its sensitivity to numerical noise, the time integration step to achieve an accurate steady state solution is orders of magnitude smaller compared to the stable time step required in boundary integral formulations. We provide evidence that the noise, which is source of instability in the finite element solution, originates from internal discretization nodes. We then investigate the long term behavior of the sliding interface for two different friction laws: a velocity weakening law, for which the friction monotonously decreases with increasing sliding velocity, and a velocity weakening-strengthening law, for which the friction coefficient first decreases but then increases above a critical velocity. We show that for both friction laws at finite times, that is before wave reflections from the boundaries come back to the sliding interface, a temporary steady state sliding is reached, with a well-defined stress drop at the interface. This stress drop gives rise to a stress concentration and leads to an analogy between friction and fracture. However, at longer times, that is after multiple wave reflections, the stress drop is essentially zero, resulting in losing the analogy with fracture mechanics. Finally, the simulations with applied constant traction boundary conditions reveal that velocity weakening is unstable at long time scales, as it results in an acceleration of the sliding blocks. On the other hand, velocity weakening-strengthening reaches a steady state sliding configuration. (C) 2020 Elsevier Ltd. All rights reserved.

Modèle numérique du comportement non-linéaire d'ouvrages massifs en béton non armé

Patrice Droz

Linear Elastic Fracture Mechanics (LEFM) are used to study crack propagation in unreinforced concrete of massive structures. This approach is well suited to the nonlinear analysis of structures of large dimensions, taking into account the size effect, i.e., the influence of the dimension of the structure on its behaviour at rupture. The Finite Element method is used to calculate the structure and the hypothesis of plane strain is made. The use of a criterion of crack propagation, based on LEFM requires the calculation of stress intensity factors. The evaluation of the latter is performed by the mean of a surface integral defined around the tip of the crack studied. It has been shown in this work that this integral is derived from the path integral J. The use of the surface integral has also been extended to the cases where body forces (gravity, inertie) act, or when the edges of the crack are subjected to pressure. This method is precise and numerically efficient. A smeared crack model is used in order to avoid continuous remeshing during crack propagation. But, as it has been shown in this research, classical smeared crack elements do not give satisfactory results when the crack is submitted to shear loading, a new finite element, using smeared cracking but with discontinuous shape functions has been developed. The model which combines LEFM and the smeared crack approach has been applied to different classical problems of fracture mechanics. It leads to good results under static or dynamic loading. As an example, the nonlinear behaviour of the vertical cross section of a gravity dam during an earthquake has been calculated and the crack pattern identified. Many further developments could be done starting from this original approach, in order to simulate more closely the real behaviour of structures, taking into account friction in the cracks and the three-dimensional development of then.

EPFL1987

Connections by Adhesion, Interlocking and Friction for Steel-Concrete Composite Bridges under Static and Cyclic Loading

Dimitrios Papastergiou

Steel-concrete composite bridges with twin-I steel girders and prefabricated slabs constitute an economical and competitive solution for small and medium bridge spans. In recent years they have started to gain their share in the construction market. However, the current slab-to-girder connection with groups of headed shear stud connectors is not well adapted for prefabrication and fast erection, and does not respond successfully to the durability of the construction. New types of connections by adhesion, interlocking and friction constitute a conception that aims to answer these demands. The resistance of these connections is based on the development of longitudinal shear stresses in the interfaces which form the connection. The goals of this study are to complete the existing research in this field by proposing scientific tools in order to predict the connection's structural performance, i.e. prediction of the connection's ultimate resistance and deformation capacity, including the post-failure behaviour. In addition, the behaviour of the connection under cyclic loading is also investigated to assess the connection's resistance to fatigue and to propose a design method for composite bridges under fatigue loading. To fulfill theses goals a combinational methodology was applied which included: study of the state of the art: a) in composite bridges so as to define the requirements and b) in interface behaviour in order to emphasize the parameters which are responsible for the resistance and obtain information for the nature of cyclic loading damage mechanisms, experimental investigations: a) to reveal the laws describing the interfaces and the connection's behaviour for static and cyclic loading, and provide data for development of analytical expressions and model validation and b) demonstrate the capacity of a composite beam under cyclic loading and the extent of its remaining resistance at ultimate limit state, analytical studies: a) to produce the laws describing the interface behaviour under static and cyclic loading and b) to evaluate the impact of the cyclic loading to the slip in the interfaces and in the connection and thus propose a damage factor for cyclic loading, finite element analysis in order to enable an analytical description of the confinement effect, caused by the reinforced concrete slab, which contributes to the resistance, the development of a numerical model to predict the connection's structural performance and to propose a design method for composite bridges fabricated with the new connection. Application of the mentioned methodology resulted in several useful conclusions: The interface behaviour can be described by analytical laws. The post failure behaviour of the interfaces was explained by accounting for the kinematics of the failed surface and basic notions of fracture mechanics. The damage due to cyclic loading on the interfaces and on the connection is expressed by the accumulation of a residual slip. Provided that the shear stresses remain lower than an elastic limit and the accumulated slip does not exceed the failure slip for static loading, fatigue failure is avoided. The confinement effect was incorporated, analytically, together with the laws of the interface behaviour in a numerical model to predict the connection's structural performance and allow a parametrical study. A design method for the verification of composite beams under static and cyclic loading was developed.

EPFL2012

Mixed-Mode Static and Fatigue Failure Criteria for Adhesively-Bonded FRP Joints

Moslem Shahverdi

Fiber-reinforced polymer (FRP) composites are increasingly used in many load-bearing structures. Joints are the most critical structural elements as they often become the weak links in engineering structures. Bonding and bolting are two of the main joining techniques used for composite elements but, although bolted and bonded joints have their advantages and disadvantages, adhesively-bonded joints are often preferred. This is thanks to their better performance in terms of cost-effective structures with uniformly distributed stresses without the need for cutting fastener holes that result in high stress concentrations in the FRP adherends at the edges of the holes. In addition, due to the absence of stress concentrations, adhesively-bonded joints exhibit better fatigue behavior. However, the efficient and reliable use of adhesively-bonded joints requires a thorough understanding of their failure mechanisms under mixed-mode quasi-static and fatigue loading conditions. In real structural applications, failure of adhesively-bonded joints occurs due to crack initiation and propagation under varying mixed-mode ratios. Since it is difficult to describe this progressive fracture in a structural joint, fracture joints with constant mode-mixity ratios are used to determine the strain energy release rates for crack initiation and propagation. Subsequently, mixed-mode failure criteria based on the determined strain energy release rates can be established and used to model/predict the fatigue and fracture behaviors of structural joints. The main objectives of this thesis were to understand the fracture and fatigue behaviors of adhesively-bonded FRP fracture joints under Mode I, Mode II, and mixed-Mode I/II loading conditions and, consequently, develop mixed-mode static and fatigue failure criteria applicable to structural joints. To fulfill these objectives a combined experimental-analytical-numerical study was undertaken. Double cantilever beam (DCB-Mode I), end-load split (ELS-Mode II), and mixed-mode bending (MMB-Mode I/II) specimens were examined under quasi-static and constant amplitude fatigue loading. Analytical approaches were used to determine the strain energy release rates under quasi-static and fatigue loading, whereas phenomenological models were developed to characterize the fatigue and fracture behaviors of the joints. A new approach designated the “extended global method” was established and applied for the analysis of the quasi-static and fatigue experimental data and the fracture mode partitioning in the mixed-mode experiments. In parallel, non-linear finite element models were developed to simulate the quasi-static fracture behavior and investigate the effects of both the existing asymmetry and the observed fiber bridging on the fracture behavior of the examined joints. The bridging zone was modeled by zero-thickness cohesive elements. An exponential traction-separation description of the cohesive zone model was shown to appropriately model the fiber bridging and calculate its contribution to the fracture energy under quasi-static loading. The FE models were successfully employed for the separation of the fracture parameters, i.e. strain energy released at the crack tip (Gtip) and the amount of energy released along the crack-bridging zone (Gbr), in the quasi-static mixed-mode failure criterion for crack propagation. In addition to the studies on the quasi-static fracture behavior of the joints, a new phenomenological fatigue crack growth formulation for the modeling and prediction of Rratio effects on the Mode I fatigue behavior of adhesively-bonded joints was also derived. The model was used for prediction of the fatigue behavior of the examined joints under different R-ratios. The results proved that the model could accurately simulate the fatigue behavior of the examined joints and was also capable of predicting behavior exhibited under unseen loading conditions, i.e. the R-ratios used for estimating the model parameters were different from those used for validating its prediction capability. The experimental results and numerical analyses combined with the phenomenological models were used to establish mixed-mode static and fatigue failure criteria for crack initiation and crack propagation for the adhesively-bonded joints. The derived mixed-mode failure criteria can be used for simulating/predicting the crack initiation and progressive crack propagation in structural joints comprising the same adhesive and adherends.

EPFL2013