Based on a layered 3D-oriented shell formulation stmctural as well as niaterial modeis for reinforced concrete stnictures are developed. Fiuite element analyses of experiments taken from the literature are used for Validation. First tlie special properties of the layered 3D shell formulation which can be employed with C0- or C1-continuous displacement fields across the thickness direction will be pornted out. An overview of various possibilities to descnbe the füll tliree di-mensional constitutive relationship of cohesive frictional materials is given and discussed in view of tlie application in the structural model. It will be shown that the phenomenological description of the niaterial behaviour by advanced plasticity models in combination with a simple approach from damage theory is a suitable means for the numerical Simulation of concrete stnictures.
On the one hand an associated multi-surface plasticity-model for piain concrete which has beeil proposed by Menrath [121] for 2D-oriented stnictures obeymg the plane stress condition and which is based on two invariants of the stress tensor, is expanded for the 3D shell formulation. On the other hand the non-associated single-surface plasticity-niodel of Kang [84] which incorporates all tliree stress invariants is developed furtner. Aspects of the Urne discretization of the single-surface model and its implementation are extensively discussed since the required derivatives are extremely involved. Both models exlübit softening evolution laws based on the fracture energy approach. Tlie local unloading effects are taken into account through a simple scalar damage formulation. The main problem of softening materials in numerical investigations is the loss of ellipticity of the underlaying differential equation which comes along with undesired effects like dependencies on the mesh orientation and the mesh density. Using a mesh adjusted internal length paranieter is a common remedy of the problem, yet the results are slightly dependent on the mesh orientation.
The hierarchy of failure indicators is discussed using established model problems. Numeri-cal investigations of both concrete modeis show the expected loss of uniqueness already m the hardening regime of rhe non-associated model. The approack of viscoplastic regularisation is in-vestigated to mamraiii the well-posedness of the boundary value problem. Here regularising ef-fects can be shown for viscoplastic materials but for concrete material linder static loading this approach has been proven to be unsuitable.
The reinforcement is accounted for through an orthotropic constitutive model wlüch is also based on classical plasticity theory with nonlinear or multilinear evolution laws. Different evolu-tion laws are defined for steel and textile reinforcement and are discussed in view of the tension-stiffening-effect. The three dunensional load carrying behaviour of textile reinforcement struc-tiires (fabrics etc.) is accounted for vvitliin a shear defonnable approach.
All necessary model parameters are identified by means of model problems. Numerical si-mulations of appropriate experiments of plates. Shells and folded plates are used to verify the de-veloped constitutive modeis and to show their significance for practical applications.