International Journal of Solids and Structures, 35 (1998), 4133-4145.


Milan Jirásek
Swiss Federal Institute of Technology
LSC -DGC, EPFL, 1015 Lausanne, Switzerland


The paper analyzes nonlocal constitutive models used in simulations of damage and fracture processes in quasibrittle materials. A number of nonlocal formulations found in the literature are classified according to the type of variable subjected to nonlocal averaging. Analytical and numerical solutions of a simple one-dimensional localization problem are presented. It is shown that some of the formulations inevitably lead to residual stresses at even very late stages of the deformation process and, consequently, they are not capable of modeling complete separation in a widely open macroscopic crack. The mechanisms leading to this specific type of stress locking are explained based on a theoretical analysis of the nonlocal constitutive equations. It is also pointed out that the nonlocal approach distorts the shape of the stress-strain diagram, which has to be taken into account when designing an appropriate local softening law.

Concluding Remarks

It has been shown that certain nonlocal formulations are inherently incapable of reproducing the entire material degradation process up to complete failure. Unless we are interested only in the response at the onset of localization, models that exhibit the special type of stress locking described in the paper should be avoided.

Load-displacement diagrams of concrete specimens tested under direct tension typically exhibit a relatively steep drop immediately after the peak load, followed by a long tail. The shape of diagrams obtained with a nonlocal model using a linear local softening law are not at all realistic. More reasonable response is produced by an exponential local softening law.

Due to its limited extent, the present study has dealt exclusively with damage-type models that unload to the origin. Another sound nonlocal approach can be developed in the context of plasticity. Comparison of nonlocal damage and plasticity theories and analysis of the structure and evolution of the process zone shall be presented in a separate paper.

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EPFL / 13 July 1998 /