Constitutive relation error estimator for transient finite element analysis Original Research Article

The concept of error in the constitutive relation allows defining a consistent error measurement for dynamic finite element simulations. A solution which satisfies exactly the kinematic constraints, the initial conditions and the equilibrium equation is built from the solution to the discretised problem. This construction utilizes, as best as possible, the properties of the integration scheme used to obtain a satisfactory effectivity index. The quality of the numerical solution is assessed by the way in which the constitutive relations are satisfied. Results from various tests conducted on a one degree-of-freedom problem and on a 1D example display the estimatorʹs good behaviour. The effectivity index remains at a reasonable value and, on the basis of the first test, a comparison of the error in the constitutive relation with different estimators drawn from the literature, is presented.