FINITE ELEMENT METHOD FOR NUMERICAL MODELING OF ELASTIC-PLASTIC DEFORMATION OF WOOD UNDER SHOCK LOADING

The 3D problem of wood deformation under shock loading is considered. The governing system of equations is formulated in Lagrange variables. A defining system of equations in a three-dimensional formulation is presented. The equation of motion is derived from the balance of the virtual powers of work. Wood is modeled as a unidirectionally reinforced material with a description of the descending branch of the deformation diagram. Deformations and stresses are determined in a local basis, the position of which in space is related to the direction of the wood grain. Wood material is represented as a combination of reinforcing fibers and a matrix, the elastoplastic deformation of which is described by the relations of the theory of flow with combined kinematic and isotropic strengthening. The deformation characteristics of the matrix and fibers are determined on the basis of a computational and experimental study of the mechanical properties of wood along and across the fibers. In numerical simulation, the moment scheme of the finite element method and an explicit time integration scheme of the “cross” type are used. Discretization of the computational domain is based on an eight-node isoparametric finite element adapted to the specifics of the problem under consideration. Software realization of the developed mathematical model and numerical methodology is implemented within the computing complex “Dynamics-3”. Computer simulation of compression of an experimental specimen of spruce along and across the fibers has been performed. The reliability of the calculation results is confirmed by good agreement with the experimental data.