A. Matzenmiller

A constitutive model for anisotropic damage in fiber-composites

Abstract A constitutive model for anisotropic damage is developed to describe the elastic-brittle behavior of fiber-reinforced composites. The main objective of the paper focuses on the relationship between damage of the material and the effective elastic properties for the purpose of stress analysis of structures. A homogenized continuum is adopted for the constitutive theory of anisotropic damage and elasticity. Internal variables are introduced to describe the evolution of the damage state under loading and as a subsequence the degradation of the material stiffness. The corresponding rate-equations are subjected to the laws of thermomechanics. Emphasis is placed on a suitable coupling among the equations for the rates of the damage variables with respect to different damage modes. Evolution equations for the progression of the passive damage variables complete the kinetic equations. Most material parameters are obtained from uniaxial and simple shear tests as demonstrated by the example.

On Damage Induced Anisotropy for Fiber Composites

A stress-strain relation on the basis of a homogenized continuum is devel oped from a potential energy function for an elastic material with anisotropic damage. It is assumed that the influence of the state of damage can be represented by a vector-valued function, resulting from an array of surface discontinuities with coinciding orientation such as disk-like, parallel cracks. Usually, only low-order polynomial expansions in terms of the damage variable have been considered in the literature, limiting the results to non- interacting microcracks. In this paper, a complete polynomial expansion of the potential function with respect to the damage variable is developed and the general form of the con stitutive tensor for the damaged material is derived. This allows account to be taken of nonlinear dependencies of the effective elastic properties on the damage variable in the case of interacting microcracks.

Consistent discretization of thickness strains in thin shells including 3D-material models

Following an idea by Buchter et al. (1994), the normal strain in the thickness direction of shells with inextensible directors is accounted for by the EAS-method, in order to enforce for arbitrary 3D-material models the zero normal stress-condition in the average sense. In the present paper a polynomial expansion of the normal strain interpolation in the thickness direction including the constant term is proposed. This extension is consistent with Simo and Rifai (1990). The proposed method is also suitable to analyse plane stress problems with arbitrary 3D-material models. Copyright

A Comparison of Micromechanical Models for the Homogenization of Microheterogeneous Elastic Composites

The structural analyses of stresses, strains and deformations by mathematical means and mechanical considerations demand for constitutive models, which set the mathematical mapping between the different physical fields. The constitutive properties of many materials like metals or plastics can be represented well by phenomenological models that do not explicitly concern about the underlying microscopical structure. Nevertheless, all solid matter shows a discrete texture if it is regarded on a sufficiently small lengthscale. In the vast field of composite materials solely phenomenological models need a sophisticated formulation and demand for elaborate experimental data in order to identify the rather high number of constituting parameters. Hence, micromechanical approaches have more and more moved into the focus of material modelling. Their central task is to deduce and obtain large scale properties from numerical analyses of the small scale structure followed by the application of averaging procedures to the computed small scale fields. Thereby, the level, on which the constitutive formulation is a purely phenomenological one, is pushed towards a lower scale. Since several years, the growth of computational power has lead to the propagation of micromechanically based constitutive approaches.

FE–Analysis of Simultaneous Hot/Cold Forging

A new, highly innovative manufacturing method is under development in research and industry, where the workpiece undergoes simultaneously a hot and a cold forging process followed by press hardening directly in the forging dies. Such a high complex forging technology is simulated by means of the finite element method, where the inductive electrical heating is modelled with substitute sources for the heat production besides the forming and the cooling process with thermal deformation and eigenstress evolution. The measured data for the temperature field and the final geometry of the forging test are compared to the results of the simulation, showing a very good agreement.

Parameter Identification of a Damage Model for the Lifetime Prediction of Adhesively Bonded Joints

A damage model for thin adhesively bonded joints is presented, which predicts the time to creep-fatigue failure of the joint subjected to combined static and cyclic sustained loadings with constant or variable amplitudes. The influences of particular model parameters on the predicted lifetime are elaborated suggesting the proposed stepwise parameter identification strategy by means of creep and Wöhler fatigue tests until rupture. The parameters are identified and computationally optimized. As a conclusion, the model prediction is verified and validated.

Mikromechanische Modellierung von dehnungsratenabhängigen Faserverbundwerkstoffen

In der vorliegenden Arbeit werden die effektiven Eigenschaften eines Faserverbundwerkstoffs mit einer viskoelastischen Matrix modelliert. Die Grundlagen der Modellierung sind ein mikromechanisches Modell basierend auf der Betrachtung einer Einheitszelle und die Anwendung des Korrespondenzprinzips der linearen Viskoelastizitat zum Auffinden der Relaxationsfunktion des Verbundes. Das verwendete Modell sowie die Anwendung des Korrespondenzprinzips in der Mikromechanik werden kurz erltautert und die Ergebnisse einer Simulationsrechung dargestellt.

Geklebte Strukturen im Fahrzeugbau – Simulation und Bewertung von Fertigungstoleranzen

Bisher blieb bei der Auslegung von Klebverbindungen im Automobilbau der Einfluss der Fertigungstoleranzen auf ihr Crashverhalten vollig unberucksichtigt. Um nun die Frage zu beantworten, in welcher Weise die Anderungen u. a. der Klebschichtdicke, des Fugenfullungsgrades und der Belastungsgeschwindigkeit infolge von Fertigungstoleranzen Wirkung auf das Verhalten geklebter Verbindungen zeigen, wurden entsprechende experimentelle und numerische Untersuchungen durchgefuhrt und analysiert.

Simulation und Bewertung von Fertigungstoleranzen

Bisher blieb bei der Auslegung von Klebverbindungen im Automobilbau der Einfluss der Fertigungstoleranzen auf ihr Crashverhalten völlig unberücksichtigt. Um nun die Frage zu beantworten, in welcher Weise die Änderungen u.a. der Klebschichtdicke, des Fugenfüllungsgrades und der Belastungsgeschwindigkeit infolge von Fertigungstoleranzen Wirkung auf das Verhalten geklebter Verbindungen zeigen, wurden entsprechende experimentelle und numerische Untersuchungen durchgeführt und analysiert.