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An energy-based damage model of geomaterials. I: Formulation and numerical results. (English) Zbl 0973.74008
The proposed anisotropic model for geomaterials under dominantly compression resorts to a “fabric tensor” for damage in terms of radii and normals for a set of cracks which are described by an evolution law including a conjugate force and a fourth-order tensor, together with the associated damage elasticity. By distinguishing between the stress transmitted “across” the crack and the macroscopic equivalent ones, the authors assume identical strains for both associated states and for similar quantities. The free energy and the conjugate force for the equivalent state is used in order to obtain a correlation with the energy of the real state. It is assumed that the stress and damage tensors of the equivalent state are parallel, and that both are parallel to the real tensor. Consequently, the conjugate forces of both states are linearly dependent. Based on results presented in part II [see the following entry], the authors formulate in part I an evolution law for the equivalent state, which is analyzed and correlated with the elastic tensor for isotropic materials. Numerical results and diagrams illustrate the behaviour of the model (apparent Young modulus for different cracks and loading directions, and also for different angles between loading direction and damage vector), taking into account given constants which occur in the definition of effective or purely elastic damage tensor; other tests concern uni- and biaxial loading and conjugate forces versus strain. Performed structural analysis refers to dams.
The principal conclusion of this study consists in the observation that a microstructure damage variable employed in the paper furnishes a more essential characterization of distributed defects than does a phenomenological variable. This conclusion concerns especially geomaterials. We also attract attention of the reader to an introductive historical part.

MSC:
74A45 Theories of fracture and damage
74L05 Geophysical solid mechanics
74L10 Soil and rock mechanics
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