Jean-François Destrebecq

Incremental analysis of time-dependent effects in composite structures

Abstract An efficient numerical method is presented, to account for time effects in composite structures. The method is based on the theory of linear viscoelasticity and on the finite element method. The global behaviour of structural elements made of several viscoelastic materials (composite beams, layered plates or shells) is expressed in terms of the generalized variables of the structure mechanics. The incremental nature of the formulation results from the choice of a Dirichlet’s series to express the constitutive law of the materials. A specific algorithm which allows for a process of construction by phases is implemented in a finite element program. The use of the method is illustrated through two computation examples: a prestressed concrete beam previously tested over a 5-year period of creeping, and an existing cooling tower which is a thin reinforced concrete shell. The method provides valuable information about time effects that may be used either while designing new structures, or for the diagnosis of existing structures.

The transfer length in concrete structures repaired with composite materials: a survey of some analytical models and simplified approaches

This work focuses on the closed-form solutions for the shear distribution that takes place in the adhesive between composite and concrete in RC structures repaired with composite plates. Three different loading cases are studied. It is shown that the exact shear stress distributions, which are rather complicated, can be simplified to provide very similar expressions in the three studied cases. The main parameters that govern the shear distribution are then clearly highlighted. This leads to an easy understanding of the influence of some geometrical and material parameters on the shear distribution, as illustrated through a parametric study.

TWIG: A model to simulate the gravitropic response of a tree axis in the frame of elasticity and viscoelasticity, at intra-annual time scale

Trees are able to maintain or modify the orientation of their axes (trunks or branches) by tropic movements. For axes in which elongation is achieved but cambial growth active, the tropic movements are due to the production of a particular wood, called reaction wood which is prestressed within the growing tree. Several models have been developed to simulate the gravitropic response of axes in trees due to the formation of reaction wood, all within the frame of linear elasticity and considering the wood maturation as instantaneous. The effect viscoelasticity of wood has, to our knowledge, never been considered. The TWIG model presented in this paper aims at simulating the gravitropic movement of a tree axis at the intra-annual scale. In this work we studied both the effect of a non-instantaneous maturation process and of viscoelasticity. For this purpose, we considered the elastic case with maturation considered as an instantaneous process as the reference. The introduction of viscoelasticity in TWIG has been done by coupling TWIG to a model developed for bridges. Indeed from a purely mechanical point of view, bridges and trees are very similar: they are structures which are built in stages, they are made of several materials (composite structures), their materials are prestressed (wood is prestressed during the maturation process as a result of polymerisation of lignin and cellulose to form the secondary cell wall and concrete is prestressed during drying). Simulations gave evidence that the reorientation process of axes can be significantly influenced by the kinetics of maturation. Moreover the model has now to be tested with more experimental data of wood viscoelasticity but it appears that in the range of a relaxation time from 0 to 50 days, viscoelasticity has an important effect on the evolution of tree shape as well as on the values of prestresses.

A numerical method for the analysis of rheologic effects in concrete bridges

Strains and deflections, rheologic properties, in concrete bridges usually increase over time because of creep and shrinkage. Efficient methods are required to consider rheologic effects while designing concrete bridges. The authors propose a practical, but efficient method suitable for time analysis of creep, shrinkage, and relaxation in concrete bridges. The approach is based on an incremental analysis of the behavior of a viscoelastic composite member and on the use of a classic finite beam element. One of the main advantages of the method is its ability to take the structure constitution and the material behaviors into account in a very precise manner for low calculation cost, that is limited numbers of finite elements and calculation steps. In addition, the processes of construction, prestressing, and free strain development are easily taken into account. The method is compared with test results for two prestressed concrete beams. Finally, the method is applied to the time analysis of a cable-stayed footbridge.

Interaction Between Concrete Cylinders and Shape-Memory Wires in the Achievement of Active Confinement

This study deals with the use of shape memory alloys (SMAs) to create confinement stresses in concrete cylinders. A nickel-titanium SMA wire with suitable transformation temperatures is stretched in the martensite state before wrapping with a constant pitch around the cylinders. A thermal cycle is applied to transform the martensite to austenite, in order to activate the shape memory effect in the wires. The strain evolutions in the concrete cylinders are measured during the thermal cycle. An active confinement effect is clearly observed in the cylinders during the procedure until cooling down to ambient temperature. The ‘effective confinement stress’ in the cylinders as well as the ‘recovery stress’ in the SMA wires are determined. The influence of the initial stretch of the wires on the final confinement is evidenced. It is observed that the confinement level is the highest for low-stretched wires; it decreases when the amplitude of the wire stretch is increased. A complex interaction between cylinder and wire responses can explain this result. It is shown that a non-stretched wire leads also to an active confinement. So an effect of the curvature due to the wrapping of the wire around the cylinders is evidenced.

Experimental study of the mechanosorptive behaviour of softwood in relaxation

In softwood material, the coupling between mechanical loading and hydric state is known as the mechanosorptive effect. However, the coupling with viscoelastic effect remains unclear so far, especially when the loading is controlled by strain. In this context, the present paper is focused on the process of creation and recovery of ‘hygrolock’ behaviour, i.e. a stress locking effect which occurs in a phase of drying under load. For this purpose, several relaxation tests were first performed on small-scale silver fir specimens in order to express the relaxation function in terms of the ambient humidity. Then, two mechanosorptive tests were carried out in order to induce hygrolock stresses in the same sample loaded in sustained strain condition, and subjected to cyclically varying humidity. Based on the assumption of stress partition, the analysis of the test results clearly shows the existence of a hygrolock stress. From these experimental evidences, a law is finally proposed to describe the evolution of the hygrolock stress in terms of the hydric state of the softwood material.

Fully-Coupled Closed-Form Solution for Stresses in Adhesively Bonded Joints in Slender Reinforced Structures Subjected to Bending and Buckling

An improved method is presented for the analysis of the stresses in adhesively bonded joints in slender reinforced structures subjected to bending and buckling. The method is based on a precise description of the kinematic equations in a reinforced beam cross-section under the assumption of isotropy and linear elasticity for both the adherends and adhesive. Second-order effects due to the member slenderness, as well as transverse deformation in the adhesive layer due to differential curvature between the two adherends, are taken into account. Governing equations for the shear and peel stresses in the adhesive layer are established in the form of two coupled differential equations. Here we take this interaction into account and propose a general solution for these two equations, which yields two fully-coupled closed-form equations for the stresses in the adhesive. These general equations can be adapted to any geometry and loading with appropriate boundary conditions. Exemplary calculations are worked out for a slender reinforced beam subjected to two different loadings. The theoretical results are found to be in good agreement with reference values obtained by means of a Finite Element Method analysis, especially at the adhesive edges where the stresses reach their critical values. It is concluded that the closed-form solution presented in this paper is suitable for a precise prediction of the adhesive stresses in bonded structural members subjected to bending and buckling.

Long Term Serviceability of Concrete Structures with Regards to Material Behaviors and Cyclic Loading

A method is presented that accounts in a precise way for the effects of creep, shrinkage and relaxation of materials in the time analysis of prestressed concrete structures under variable loading conditions. The method is applied to a prestressed concrete bridge built as a balanced cantilever. The influence of time related effects on its long term serviceability is discussed.

Influence of Thermal Boundary Effects on the Process of Creating Recovery Stresses in a SMA Wire Activated by Joule Heating

The study deals with the influence of thermal boundary effects on the process of creating recovery stresses in a SMA wire activated by Joule heating, during a thermal cycle (up to the return to ambient temperature). First, a thermal characterization is performed using infrared thermography for temperature profile measurements along the wire in a steady-state regime. Second, recovery stress tests are performed using a uniaxial testing machine. Finally, tests are analyzed using a thermomechanical model, taking the inhomogeneous temperature distribution along the wire into account. The influence of the initial distribution of martensite (before thermal activation of the memory effect) is discussed, as well as the influence of the wire length. It is shown that the thermal boundary effects at the contact with the grips of the testing machine significantly influence the response of the wire. For instance, during the heating of the wire, an austenite-to-martensite transformation may occur in the zones near the wire ends (where the temperature remains close to ambient) due to the increased stress. A length of influence of the thermal boundary effects on the overall wire response is defined, and a condition to neglect this influence is proposed. The study highlights the importance of taking thermal boundary effects into account for practical applications of SMAs based on Joule heating.

An Incremental Constituve Law for Damaging Viscoelastic Materials

An incremental formulation suitable for modelling of materials with damaging viscoelastic behaviours is proposed in this work. A constitutive law based on linear viscoelasticity coupled with strain dependent damage is developed. The viscoelastic model is represented by a generalized Maxwell’s chain. It is governed by a set of internal stress variables attached to the branches of the Maxwell’s chain. The damage evolution is governed by values gained by a pseudo strain. The coupled law is turned into an incremental form suitable for the numerical analysis of damaging time dependent structures. Taking advantage of the incremental form, the coupled damaging viscoelastic law is implemented as a step-by-step procedure. The calculation procedure consists of a damaging elastic step followed by a number of damaging viscoelastic steps. The damage variable is adjusted at each step, according to the value gained by the pseudo strain. Exemplary calculations are worked out for two cases of uniaxial and biaxial variable or cyclic loadings. The results show the efficiency of the incremental model. It is worth noticing that the time increment used for the calculations is not necessarily small. As a consequence, precise analysis of damaging time dependent structures can be performed for low calculation cost.