International Journal for Numerical Methods in Engineering, 63 (2005), 77-102.


   Milan Jirásek
Czech Technical University in Prague, Czech Republic
Sonia Marfia
University of Cassino, Italy


Continuum damage models describe the changes of material stiffness and strength, caused by the evolution of defects, in the framework of continuum mechanics. In many materials, a fast evolution of defects leads to stress-strain laws with softening, which creates serious mathematical and numerical problems. To regularize the model behavior, various generalized continuum theories have been proposed. Integral-type nonlocal damage models are often based on weighted spatial averaging of a strain-like quantity. This paper explores an alternative formulation with averaging of the displacement field. Damage is assumed to be driven by the symmetric gradient of the nonlocal displacements. It is demonstrated that an exact equivalence between strain and displacement averaging can be achieved only in an unbounded medium. Around physical boundaries of the analyzed body, both formulations differ and the nonlocal displacement model generates spurious damage in the boundary layers. The paper shows that this undesirable effect can be suppressed by an appropriate adjustment of the nonlocal weight function. Alternatively, an implicit gradient formulation could be used. Issues of algorithmic implementation, computational efficiency and smoothness of the resolved stress fields are discussed.


The main results of the present study can be summarized as follows:

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CVUT / 16 May 2005 /