N-directional approach to damage material laws

If N, evenly distributed, unit direction vectors are chosen properly in two- or three dimensional space, their components have some rather surprising ''uncoupling'' properties. By describing the strain state using the normal strain components, in these N directions, linear isotropic elasticity can be modelled exactly in an almost uncoupled and very elegant way. In fact, the continuum appears as being modelled by N loosely coupled uniaxial sub-continua each capable of transmitting in its direction a stress component, which is a function only of the corresponding normal strain and of the volumetric strain valid for all directions.

The main postulate of the N-Directional Approach lies in the assumption that this uncoupling property is also valid in the non-linear large-strain case. This is similar to a generalised spring model. For modelling irreversible, non-isotropic structural damage, constitutive laws based on this strain description are an attractive alternative. In the large-strain case the use of logarithmic uniaxial strain components is suggested.

Practical experience with real life problems is still, to a large extent, missing, so that a reliable assessment of the applicability of the N-Directional Approach is, so far, not possible. It can be said, however, that it appears to be quite attractive, mainly because the decomposition of a tensorial problem into N nearly-uncoupled uniaxial springmodels has a straightforward physical interpretation. This is expected to facilitate the derivation of constitutive laws for the large-strain damage case which are directly based on experimental evidence.

Among the several applications of this method, the modelling of reinforced concrete panels in plane stress (or other kinds of non-homogeneous composite materials) should be mentioned. Obviously, the panel forces can be obtained for an arbitrary deformation state by superimposing the concrete forces computed with an N-Directional plane stress damage model and the directional forces of the reinforcing bars. It also appears that tension stiffening effects can be treated.

Staff

Prof. Dr. Edoardo Anderheggen (Guidance)
Dr. Juan Renau