# FORMULATION OF ORTHOTROPIC DEGRADATION MODELS FROM DAMAGE- EFFECT TENSORS FOR PHYSICALLY NONLINEAR ANALYSIS

## Palavras-chave:

Orthotropic damage model, Damage-effect tensors, Physically nonlinear analysis## Resumo

In constitutive models based on the continuum damage mechanics, the process of material

degradation is described from damage variables that evaluate the nucleation and growth of micro voids

and microcracks in the medium. These variables can be expressed from tensorial entities called damage-

effect tensors, which is able to describe the material behavior considering, in the most general form,

anisotropic degradation. These entities are defined by a fourth-order tensor. This degradation approach

leads to a generalization of the deterioration process, since the secant tensor is obtained from a product

between the damage-effect tensor and the elastic tensor. This work presents a formulation of a continuum

damage model to deal with orthotropic material degradation, assuming different damage evolutions laws.

The degradation process is considered from damage-effect tensors for the physically nonlinear analysis

of concrete structures subjected to monotonic loadings. Different approaches of damage-effect tensors

presented on literature are discussed and implemented to validate this theory. The formulation was

implemented in the INSANE platform (INteractive Structural ANalysis Environment), a free computing

system developed in the Structural Engineering Department of Federal University of Minas Gerais.