Evelyne Toussaint

The Virtual Fields Method

The Virtual Fields Method (VFM) is one of the techniques developed to identify the parameters governing constitutive equations, the experimental data processed for this purpose being displacement or strain fields. It will be shown in this chapter that one of its main advantages is the fact that, in several cases, the sought parameters can be directly found from the measurements, without the need of calculating the stress with a numerical tool such as a finite element programme.

Special virtual fields for the direct determination of material parameters with the virtual fields method. 1–Principle and definition

This paper deals with the direct and simultaneous estimation of parameters used in some constitutive laws. Whole-field data captured in mechanical configurations which give rise to heterogeneous stress fields are processed. Since no analytical relationship is available between measured data and unknown parameters, a specific procedure based on a relevant use of the principle of virtual work is proposed. The main advantage is to provide directly the unknown parameters. The main features of the method are described in the paper.

Special virtual fields for the direct determination of material parameters with the virtual fields method. 2-Application to in-plane properties

This paper deals with the direct identification of mechanical parameters that govern the in-plane constitutive law of orthotropic materials. Those parameters are extracted from heterogeneous strain fields that occur in a short beam specimen tested in a Iosipescu fixture. The procedure used is the virtual fields method with special virtual fields. The case of linear elasticity is first addressed. It is shown that the parameters are directly extracted with this method: no iterative calculations are required. The stability is also discussed in different cases. A non-linear shear response is then considered. The parameter that governs this non-linearity is also directly identified with the special virtual fields.

Special virtual fields for the direct determination of material parameters with the virtual fields method. 3. Application to the bending rigidities of anisotropic plates

This paper deals with the direct identification of bending rigidities of thin anisotropic plates. These parameters are extracted from an heterogeneous strain field which takes place onto the top surface of a bent plate. The loading conditions are such that no closed-form solution is available for the deflection/slope/curvature fields. The procedure presently used is the virtual fields method with “special” virtual fields. It is shown that the unknown parameters are directly extracted with this method since no iterative calculations are required. The parameters are in fact directly equal to the virtual work of the applied loading with the special virtual displacement fields. The headlines of the method are recalled in the first part of the paper. They are then applied in the case of anisotropic bent plates. The accuracy and the stability of the procedure are finally discussed through some relevant examples.

Investigation of the Hydric Transfer Phenomenon in Wood at the Ring Scale with the Grid Method

The water diffusion phenomenon and its effect on the deformation of wood samples are studied here. A suitable experimental device is designed to impose a direct contact on one side of the specimen with water. Strain maps are measured over time on the other side. The grid method is used for this purpose. White fir of Massif Central (Abies alba Mill) is studied here. During the experiments, strain gradients clearly appear between early and late woods, highlighting the different diffusion properties at the scale of the rings. The results also show changes in the moisture diffusivity of the material during the test. A cycle of adsorption/desorption is also studied. Results highlight the existence of residual strains at the wood ring scale.

Inverse identification of early- and latewood hydric properties using full-field measurements

ABSTRACT The study and identification of the water diffusion properties of Abies alba Mill at the growth ring scale are investigated in this paper. A full-field measurement technique, the grid method, is used in the experimental tests in order to observe heterogeneities and to measure strain fields in the annual growth rings. In this case, the mechanical behaviour of latewood (LW) and earlywood (EW) is studied under the effect of water stress. This technique is coupled to an inverse method for parameter identification. It enables us to assess the diffusivity of EW and LW in the tangential diffusion direction (T) and their expansion coefficients in the radial direction (R) from strain maps obtained using the grid method. Thus the water diffusion phenomenon and its effect on the deformation of wood specimens are studied. A suitable experimental device is designed to provide direct contact with water on one side of the specimen, and strain maps are obtained over time on the other side. During the experiments, strain gradients that appear are clearly different between EW and LW, highlighting the different diffusion properties at the ring scale level. The results also show changes in the kinetics of the hydric deformation of the material.

Experimental study of the mechanical behaviour of thin slices of maturating green poplar wood using cyclic tensile tests

In this study, longitudinal cyclic tensile tests were performed on green wood samples of Populus cv I4551. Complex mechanical behaviour, such as permanent set in terms of displacement and strain-dependent stiffness, was found. A linear relationship between stiffness and strain enabled each sample to be characterized. A large-scale experimental campaign led to the observation of the evolution of temporal and spatial intra-ring mechanical behaviour of intra-ring sliced specimens during wood maturation and tree gravitropic response. The results showed that tension wood lamellas exhibit strain hardening behaviour whereas normal wood lamellas exhibit strain softening behaviour. Temporal variations in the strain hardening behaviour of tension wood lamellas occurred once cell wall deposition was achieved. Moreover, no correlation was found between infradensity and mechanical behaviour of lamellas. These results show that cells undergo temporal variations in their properties due to a complex maturation process.

Studying the Influence of the Reclaimed Asphalt Pavement (RAP) on Local Deformation Properties of Asphalt Mixtures

The present study focuses on the experimental investigation of the mechanical response of recycled asphalt mixtures (RAP) using a full-field measurement technique: the grid method. Four hot mixture asphalt (HMA) specimens containing 0, 20, 40, and 100 % of RAP were prepared. Aggregates of different colors were selected in order to distinguish RAP and virgin aggregates. Compression tests were then carried out during which the displacement and strain fields were measured. It was found that the 100 % RAP specimen exhibits highly concentrated strain distributions around the aggregates. Strain is more homogeneously distributed over the specimen surface of virgin mixes. The analysis of the local behavior of RAP showed a local stiffening of the binder along the border of the RAP aggregates. The obtained results highlight the difference in behavior between specimens both at the micro- and the macro-scales.

Experimental Fracture Analysis of Tropical Species Using the Grid Method

The fracture processes of three tropical species: Aucoumea klaineana, Malicia excelsa and Pterocarpus soyauxii, are investigated with the grid method. These species are widely used in many sub-tropical countries, in timber building construction, as well as in semi-finished products and paper fabrication. However their fracture behaviour must still be investigated, data being scarcely available on this subject. Modified Mixed Mode Crack Growth specimens are used in order to obtain a stable crack growth evolution in opening, shear and mixed mode ratios. The images of the grid are analysed to provide the crack opening displacement and the crack tip location. The stress intensity factors and the critical energy release rates for each species are then obtained by using the compliance method in imposed displacement. The semi-experimental energetic method is also applied in order to show the efficiency of the proposed technique to characterize the fracture properties of the tropical species under study.

Investigating wood under thermo-hydromechanical loading at the ring scale using full-field measurements

The thermo-visco-hydromechanical properties of Abies alba Mills (white fir of Massif Central) are investigated in this paper. These properties are generally complex to study and model because of various couplings that exist between underlying phenomena. In addition, wood is heterogeneous by species, but these properties are generally studied at the macroscopic scale, thus without having the possibility of discerning the contribution of the various levels of organization which exist in wood. In this context, the main contribution of this paper is to experimentally evidence that earlywood and latewood exhibit each a different visco-hydromechanical response and, more specifically, that humidity directly governs their viscoelastic properties. Three suitable experiments were carried out on three different specimens to highlight this phenomenon. These experiments consist of mechanically testing the specimens under natural drying conditions. The difference in response was observed at the scale of the annual ring by using a full-field measurement technique, namely the grid method. This technique provides the strain fields occurring on the surface of the specimens during the different steps of their hydromechanical loading. Its spatial resolution is such that the strain level in latewood and earlywood can be accurately measured, thus evidencing the significant difference in response of the rings. This measurement technique as well as the three experiments carried out during this study is first briefly described in this paper. The obtained results are then presented and discussed, with a special emphasis on the different responses observed in earlywood and latewood.