# Zweiskalensimulation von mikroheterogenen Strukturen aus spröden Faserverbundwerkstoffen

kassel university press, ISBN: 978-3-89958-462-2, 2010, 230 Pages

(Berichte des Instituts für Mechanik 1/2010)

Zugl.: Kassel, Univ., Diss. 2009

Content: The thesis at hand deals with simultaneous two-scale analyses of micro-heterogeneous ﬁbre reinforced composite structures. The mechanical design calculation of components made of inhomogeneous media is esteemed as a multi-scale task. In contrast to state of the art approaches, which usually apply the idea of a homogeneous continuum, a methodology is pursued herein that explicitly takes the composition of different phase materials into account. The subject-matter of the thesis is given by the demand for a computationally effient approach, which will allow to describe the constitutive behaviour of composites in elastic and inelastic regimes as well as to determine initial and ﬁnal failure modes in laminate structures with increased physical accurateness than state of the art techniques. The design of ﬁbre-reinforced structures against failure represents a problem of simulation and modelling on different length-scales, for the stiﬀness and strength reducing processes, located on a level which is to be characterized in terms of micro-or even nanometers, are caused by loadings on the structural or lamina level. The propagation of inelastic, irreversible processes on the micro-scale might causally prelude the global loss of structural integrity and load bearing capacity on the macro-scale.

In this work, micromechanical material modelling is predicated upon the concept of the so-called Representative Volume Element (RVE). This means an adequately chosen sample of the heterogeneous material representing the microstructure as a whole. The RVE deﬁnes the subregion on which a micro-scale initial boundary value problem can be formulated. The appropriate Dirichlet boundary conditions are imposed in terms of either periodic or homogeneous conditions on surface displacements. In connection with two-scale simulations, the boundary values are derived from the macroscopical strain tensor at the integration points of the large-scale ﬁnite element discretization. The approximate solution of the boundary value problem imposed on the RVE domain is obtained by the numerically effcient Generalized Method of Cells or its more sophisticated descendant named High-Fidelity Generalized Method of Cells. The volume averages of the process dependent stress-ﬁelds inside the RVE are taken as the effective large-scale stresses. The constitutive mapping of the rate of the macro-strain tensor onto the rate of the macro-stress tensor states the eﬀective, mechanical behaviour of the computationally homogenized composite.

The mathematical representation of the several phases within the RVE is supplied by the theories of linear and physically nonlinear elasticity as wells as by linear viscoelasticity. The inﬂuence of the ﬁbre-matrix-bond on the effetive material properties is described by constitutive interface models based on elastic and viscoelastic assumptions. The damage of the bonding is described by formulations borrowed from fracture mechanics. The damage of the matrix phase is implemented by introducing microcracks along subcell boundaries of the discrete micromechanical model. Hence, damage is occurring localized at micro fracture surfaces such that the micro-scale boundary value problem remains mathematically well posed.