2017/10/18 by Michele Botti, Botti, Michele, Rita Riedlbeck +1
Engineering · #Elasticity and Material Modeling #Advanced Numerical Methods in Computational Mathematics #Fatigue and fracture mechanics
paper · pdf · doi:10.48550/arxiv.1710.06649
We consider hyperelastic problems and their numerical solution using a\nconforming finite element discretization and iterative linearization\nalgorithms. For these problems, we present equilibrated, weakly symmetric,\nH( rmdiv)-conforming stress tensor reconstructions, obtained from local\nproblems on patches around vertices using the Arnold--Falk--Winther finite\nelement spaces. We distinguish two stress reconstructions, one for the discrete\nstress and one representing the linearization error. The reconstructions are\nindependent of the mechanical behavior law. Based on these stress tensor\nreconstructions, we derive an a posteriori error estimate distinguishing the\ndiscretization, linearization, and quadrature error estimates, and propose an\nadaptive algorithm balancing these different error sources. We prove the\nefficiency of the estimate, and confirm it on a numerical test with analytical\nsolution for the linear elasticity problem. We then apply the adaptive\nalgorithm to a more application-oriented test, considering the Hencky--Mises\nand an isotropic damage models.\n