A multi-linear material based FEM for nonlinear analysis of steel-reinforced glulam timber

The present paper deals with the development and application of an implicit nonlinear finite element model for analyzing glulam-laminated (glulam) timber beams, reinforced with steel bars. A generalized material model is built in a FEM code that can simulate the mechanical behavior of a solid under various type of loading and thermal history. The ability of the model is to schematize the nonlinear behavior, of the interacting materials: glulam timber, adhesive and steel bar, with a multi-linear, piecewise, stress-strain curve for each three-dimensional components of the stiffness tensor, without the need of plasticity theoretical function. This feature habilitate us to properly use this procedure for wood which shows an high anisotropy, affected by a complicate nonlinear behavior, difficult to introduce in a numerical simulation model. Thus, this more adequate representation of the material mechanical characteristics can improve the numerical simulation of material responses. A similar concept was used by other authors representing the stress-strain law, with power functions that fits the measured values from material tests. In the present study wood is schematized as orthotropic material, then the representation of the stress-strain curves is obtained by fitting the raw data measured from experimental tests. The numerical procedure has been applied to analyze a beam made of a wooden glulam, reinforced with steel bar, that is statically loaded in a four-point experimental set-up. The solution of the problem is obtained by an approximate Newton-Raphson iterative procedure, due to the nonlinear nature of the equations, in which load has been discretized into a finite number of steps. A software routine is developed for the material representation and implemented in a general FEM, which is capable to simulate the mechanical behavior of a solid undergoing large displacements and deformations. The numerical results have been compared with those of some experimental tests obtained in a previous work. The proposed methodology has demonstrated its adequateness to describe the mechanical behavior of steel reinforced glulam timber, under bending loads. This encourages us to extend the present approach to other more complex cases, in a future work. Furthermore, this model can contribute, when it is supported by experimental data, to improve current available techniques of timber reinforcement.