Elsevier

Computers & Structures

Volume 177, December 2016, Pages 83-90
Computers & Structures

Multi-scale model updating for the mechanical properties of cross-laminated timber

https://doi.org/10.1016/j.compstruc.2016.08.009Get rights and content

Highlights

  • A homogenisation-based four-scale model is proposed for cross-laminated timber.

  • An optimisation strategy is adopted to calibrate the micro-mechanical parameters.

  • The influence of wood density is investigated on the mechanical properties of CLT.

  • Variations of the longitudinal and rolling shear moduli are also investigated.

  • Our numerical predictions are compared successfully with experimental results.

Abstract

In this paper we propose a homogenisation-based four-scale model for the mechanical properties of cross-laminated timber. The spatial scales considered in this study are the wood cell-wall, the wood fibres, growth rings and the structural scale. The computational homogenisation scheme is solved sequently from the lowest to the highest level in order to determine the effective mechanical properties of each material scale. As we are interested in improving the predictions of our computational simulations, we propose an optimisation strategy to calibrate the micro-mechanical parameters. Our numerical predictions are compared with experimental results and are validated successfully.

Introduction

Over the last two decades or so, cross-laminated timber (CLT) has been gaining popularity in residential applications, mainly in Europe and North America. CLT is a relatively new building system based on structural panels made of several layers of boards stacked crosswise and glued together on their faces (Fig. 1).

As CLT panels are light-weight structural elements with high stiffness and strength to bending, compression and shear, they are an economically competitive building system when compared to traditional options and therefore, are a suitable candidate for some applications which currently use concrete, masonry and steel [2]. CLT has multiple advantages including its favourable seismic performance, its ability to self-protect against fire, its lessened environmental impact and its renewable material source [3].

In spite of the advantages of building with CLT, and the considerable growth that the total production is experiencing in the world market [4], the benefits of using CLT and in general timber, in the construction industry are still far from maximised. This is mainly due to the fact that dimensioning practices and many existing structural design rules are still based on an empirical background [5]. Different methods have been adopted for the determination of the basic mechanical properties of CLT. However, to date no method has been universally accepted by CLT manufacturers and designers [6].

The reason for the slow progress in the development of timber design codes, and in particular, in the difficulties to fully understand the mechanics of timber materials, lies mainly in the highly complex and intricate nature of wood microstructure [7]. At very small scales, wood shows a complicated hierarchical nature distributed across multiple spatial scales, from submicrometer dimensions to macroscopic scales. This important feature has been a subject of intensive research over the last few years by means of multi-scale homogenisation techniques. Initial investigations were carried out by Holmberg et al. [8] on the mechanical behaviour of wood from a micro up to a macro level. They obtained numerically stiffness and shrinkage properties and compared them with experimental data. Hofstetter et al. [9] suggested five elementary phases for the mechanical characterisation of wood. These were hemicellulose, lignin, cellulose, with its crystalline and amorphous portions, and water. Qing and Mishnaevsky [10] studied the effect of wood density, microfibril angle (MFA) and cell shape on the longitudinal tensile strength of softwood. Rafsanjani et al. [11], [12] investigated experimentally and numerically the hygroscopic swelling and shrinkage properties of softwood. Saavedra Flores and Friswell [13] investigated the deformation and failure mechanisms of wood at the ultrastructural scale. They also studied the development of a new material inspired by the mechanics and structure of wood cell-walls [14]. In the context of multi-scale modelling of CLT structures, Saavedra Flores et al. [15], [7] investigated the structural behaviour of CLT by linking three different scales. We note, however, that despite the increasing interest in this subject, the complete understanding of the mechanical properties of wood, and in particular cross-laminated timber, is still an issue which remains open at present.

In this new paper, we continue with the line of development started in the above references [15], [7] by introducing the following new features:

  • 1.

    The explicit modelling of growth rings as a new material scale.

  • 2.

    Multi-scale model updating by means of a Genetic Algorithm (GA).

  • 3.

    Investigation of the influence of wood density on the mechanical properties of CLT.

  • 4.

    New experimental results.

This paper is organised as follows. Section 2 describes briefly the mathematical foundations of the multi-scale constitutive theory. Section 3 presents the strategy adopted for the multi-scale modelling of timber structures. The experimental works are described in detail in Section 4. Section 5 introduces the use of the GA technique to improve our numerical predictions. The validation of our (updated) model along with some numerical predictions are presented in Section 6. Finally, Section 7 summarises our main conclusions.

Section snippets

Multi-scale constitutive theory

Multi-scale models enable specifying the relationships between physical variables observed at different length scales. These are of particular importance in the study of heterogeneous materials with hierarchical microstructures in which the macroscopic response of the material can be predicted from the information coming from the microscopic (or lower) level.

In the present type of homogenisation-based multi-scale constitutive theory, each material scale is associated with a microstructure whose

Multi-scale modelling strategy for timber

In this section, we describe the multi-scale finite element modelling of timber. The type of wood chosen for this study is radiata pine, which has several applications in building and engineering structures. As commented in the previous section, the class of multi-scale model adopted here corresponds to the Periodic boundary displacement fluctuations model.

The procedure described in the following consists of modelling the mechanical response of the CLT structure by means of four fundamental

Experimental works

The type of wood chosen for this study was Chilean radiata pine and the adhesive used to manufacture the specimens was EPI (Emulsion Polymer Isocyanate) system PREFERE 6151/6651 [25]. Budget constraints allowed us to perform only a limited number of experiments. In the following we described these tests.

  • 1.

    Preliminary experimental tests on individual timber pieces.

    We conducted experimental tests to measure density and moisture content in 103 individual timber pieces employed for the manufacture of

Multi-scale model updating

As we are interested in improving the predictions of our numerical model, we propose an optimisation strategy based on a GA technique [28] to calibrate the micromechanical parameters which are either not well-known, or susceptible to considerable variations when measured experimentally. Such parameters are considered to be random and are listed in Table 1 with their corresponding intervals of variation.

We must note that the term multi-scale finite element model updating refers here to the

Numerical simulations

In this section we compare our numerical predictions with the experimental data and we perform additional simulations in order to investigate the structural response. Table 2 shows the comparison between experimental results and their numerical counterparts obtained from the present model. As expected, a very small difference is found between the numerical and experimental densities, with a relative error of 1.8%. Similarly, a small relative error of 1% is found for the values of the

Conclusion

In this paper we have investigated the mechanical properties of CLT by means of a homogenisation-based four-scale model. The material scales considered in our analyses are represented by the wood cell-wall, the wood fibres, growth rings and the macroscopic or structural scale. In addition, as wood shows a large amount of uncertainty in its properties, we have proposed an optimisation strategy based on a GA technique to tune those micromechanical parameters which are either not well-known or

Acknowledgments

E.I. Saavedra Flores acknowledges the support from the Chilean National Commission for Scientific and Technological Research (CONICYT), FONDECYT research project No 1140245.

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