Large deformation analysis of functionally graded thermoviscoplastic beams under ductile damage via finite elements

A large deformation model to predict ductile damage in functionally graded thermoviscoplastic beams is presented in this work. The novelty of the study is the finite element analysis of highly deformable beams considering plastic strains, porosity evolution, strain-rate hardening, thermal softening, heat generation by plastic work and gradual variation of material properties along the thickness direction. The constitutive model adopted is thermodynamically consistent and based on an extension of the Gurson-Tvergaard-Needleman yield criterion, which includes void growth and nucleation, as well as material degradation through cavitation. The finite element adopted is a 2D beam of any order of approximation, transversely enriched in order to reproduce shearing and variable transverse strain across the thickness. To numerically solve the resultant system of equations, the dual-phase procedure, involving elastic trial and internal variables update, is employed together with the backward-Euler integration scheme.Two numerical examples involving ductile damage under large deformation bending are studied: a cantilever beam and the buckling of a clamped column. Preliminary studies confirm that mesh refinement leads quickly to a converged solution, considering element orders from quadratic up to sixth degree. The concept of functionally graded variation is applied to the material parameters, following two sets extracted from metallic materials. The effect of the gradual variation on the beam response is investigated in detail, in terms of displacements, forces, plastic strains, stresses, temperature and ductile damage. Results show that the gradation of properties has a great influence regarding flexibility and ductility.