Zusammenfassung
Not only the classical geomaterials like sand, clay, stone and rock but also a number of engineering materials, for example concrete, can be classified as cohesive frictional materials. Their mechanical behavior is governed by their pronounced pressure-sensitivity manifesting itself in entirely different failure mechanisms under tensile and compressive loadings. Consequently, the tensile and compressive strength of these materials can vary by several orders of magnitude. During their failure process, the formation of highly localized zones of concentrated straining, such as microcracks, slip planes, macroscopic crack planes or shear bands, can be observed. In general, this phenomenon of strain localization induces a highly anisotropic material response.
The development of finite element-based numerical models which take into account the above mentioned failure characteristics is the basic concern of the present work. To set the stage, the classical, local isotropic models of elasto-plasticity and elasto-damage are briefly reviewed. In a second step, the basic features of these models will be transferred to an anisotropic material characterization embedded in the so-called microplane concept. Within the framework of microplane theory, the response of a material point can be understood as the volume integral of its behavior on all material planes in space integrated over the solid angle. A general, thermodynamically consistent concept of formulating microplane-based constitutive laws will be presented. Its basic features are illustrated by means of the constitutive equations of microplane elasticity, microplane elasto-plasticity and microplane elasto-damage.
Especially in the post-critical regime, the solution of classical local continuum approaches shows the tendency to form highly localized failure zones. In a numerical simulation, the width of these failure zones corresponds to the width of a single finite element and thus tends to zero with an infinite mesh refinement. This disability of classical continuum approaches to model correctly the material behavior in the softening regime is caused by the fact, that local continuum models disregard the effects of changes in the microstructure. From a mathematical point of view, the resulting mesh dependency of the numerical solution is caused by a change of type of the governing equations. Insufficient boundary conditions lead to an ill-posed problem, the result of which is primarily determined by the underlying discretization. In the literature, several strategies have been proposed to remedy this deficiency through the introduction of an internal length scale. By doing so, microstructural changes can be taken into account. Within the present work, the microstructural length scale will be introduced in terms of a gradient enhanced continuum approach. Through the incorporation of higher order gradients in the constitutive equations, the problem remains well-posed and a finite number of solutions can be guaranteed. The existing gradient enhanced damage approaches in the literature are generalized to capture not only the classical isotropic material models but also the new anisotropic microplane-based material formulation. The performance of the proposed models is demonstrated and discussed by means of several selected examples.
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