Showing papers by "Stefan Hartmann published in 2021"

Material parameter identification using finite elements with time-adaptive higher-order time integration and experimental full-field strain information

Abstract: In this article, we follow a thorough matrix presentation of material parameter identification using a least-square approach, where the model is given by non-linear finite elements, and the experimental data is provided by both force data as well as full-field strain measurement data based on digital image correlation. First, the rigorous concept of semi-discretization for the direct problem is chosen, where—in the first step—the spatial discretization yields a large system of differential-algebraic equation (DAE-system). This is solved using a time-adaptive, high-order, singly diagonally-implicit Runge–Kutta method. Second, to study the fully analytical versus fully numerical determination of the sensitivities, required in a gradient-based optimization scheme, the force determination using the Lagrange-multiplier method and the strain computation must be provided explicitly. The consideration of the strains is necessary to circumvent the influence of rigid body motions occurring in the experimental data. This is done by applying an external strain determination tool which is based on the nodal displacements of the finite element program. Third, we apply the concept of local identifiability on the entire parameter identification procedure and show its influence on the choice of the parameters of the rate-type constitutive model. As a test example, a finite strain viscoelasticity model and biaxial tensile tests applied to a rubber-like material are chosen.

Material parameter identification of unidirectional fiber-reinforced composites

Abstract: In this article, several aspects of material parameter identification are addressed. We compare several methods to identify material parameters of a constitutive model for small strain, linear elastic transverse isotropy based on experimental data of specimens made from composite plates. These approaches range from identifying the five material parameters from purely analytical considerations to the fully numerical identification on the basis of finite elements and various data provided by digital image correlation (DIC). The underlying experimental tests range from purely uniaxial tensile tests with varying fiber orientation to shear and compression tests. A specific measuring instrument has been developed for the latter tests to obtain unique material parameters—motivated by the concept of local identifiability. Besides, we compare the numerical differentiation, which is the common procedure in parameter identification, with the fully analytical derivation of sensitivities within the DIC/FEM approach.

Measures describing curvilinear short fiber distributions

Abstract: In this article, we discuss measures for fibers having a curvilinear shape. This is the case, for example, for man-made cellulose fibers having a weak stiffness. The fibers are bent during the injection molding process of short fiber reinforced plastics. For this purpose, $$\mu $$ -CT data can be evaluated and several measures can be introduced defining the geometrical orientation of the fibers. These measures are the length, a mean curvature, and the mean torsion. Furthermore, a mean orientation of a fiber and a mean deviation to a straight line can be defined. Additionally, to these measures, which are based on a continuous interpolation of given data points, discretized quantities only considering the data points are compared. Finally, the distributions of these measures at real $$\mu $$ -CT data are provided.