Regular Article

Cyclic virtual test on wood furniture by Monte Carlo simulation: from compression behavior to connection modeling

¹ Laboratoire Modélisation et Simulation Multi Echelle, Université Paris-Est, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France
² Institut technologique Forêt Cellulose Bois-Construction Ameublement, FCBA, 10 rue Galilée, 77420 Champs sur Marne, France

^* e-mail: luc.chevalier@univ-paris-est.fr

Received: 16 February 2019
Accepted: 15 May 2019

Abstract

Prediction of durability of wood product is a major challenge and an important goal for furniture industry. Numerical simulation based on approximation methods such as the finite element method (FEM) is an efficient and powerful tool to address this challenge while avoiding expensive experimental testing campaigns. Nevertheless, the strong heterogeneity of wood-based materials, the specific geometrical characteristics of wood-based structures (such as furniture that can often be represented as an assembly of beams, plates and/or shells) and the complex nonlinear 3D local behavior near the connections between structural parts may induce some difficulties in the numerical modeling and virtual testing of furniture for robust design purposes. Especially, when cyclic loading occurs, the behavior of junctions in furniture involves a local permanent strain that increases with the number of cycles and that can lead to an important gap potentially affecting the structural integrity of furniture. In this paper, we present an experimental campaign of cyclic compression tests carried out on spruce specimens. Theses specimens are cut out from a bunk bed and loaded under cyclic compression. The cyclic compression loading applied to the specimens leads to an evolution of the permanent strain during cycles that is modeled using a simple law describing the displacement gap as a function of the number of cycles. Considering the strong dispersion in the mechanical properties of wood-based materials and the variabilities induced by the experimental configuration, a stochastic modeling of the gap is proposed by having recourse to the maximum entropy (MaxEnt) principle in order to take into account the random uncertainties on the experimental setup and between the test specimens. The random mechanical response of a complex corner junction in a bunk bed under cyclic loading is then numerically simulated by using a Monte Carlo numerical simulation method as stochastic solver. This provides independent realizations of the random gap evolution (with respect to the number of cycles) in the bunk bed corner, allowing probabilistic quantities of interest related to the random gap, such as first- and second-order statistical moments (mean value, standard deviation) as well as confidence regions (with a given probability level), to be estimated.