NONLOCAL FRACTURE CHARACTERISTICS OF STRAIN-SOFTENING MATERIALS

Modeling the strain-softening properties of brittle heterogeneous materials requires a special attention since spurious strain-localization and physically unrealistic solutions are encountered with the usual continuum theory. The present dissertation addresses this problem by proposing a new type of continuum called "Nonlocal Continuum with Local Strain".; The key-idea is to use in the nonlocal continuum a local definition of the strain. Only the variable which controls strain-softening is subjected to spatial averaging. For this purpose, the continuum damage mechanics is convenient since the damage parameter controls the nonlinear behavior. Damage is averaged over a representative volume of size, the characteristic length {dollar}ell{dollar}.; Dynamic and static finite element calculations are presented and a proper convergence of the solution toward a constant non-zero energy dissipation at failure is obtained. Since the stresses which figure in the constitutive laws are subjected to the standard equations of equilibrium and boundary conditions, this model can be easily implemented in a finite element code. Its convergence properties are amply discussed.; An analytical solution of strain-localization instability analysis is also presented. It shows the influence of the characteristic length. This material parameter is proportional to the minimum size of the zone in which damage localizes. Static and dynamic stability limits are calculated, demonstrating the size effect on snapback instability.; Numerous localization limiters proposed in the literature are further compared to the nonlocal damage model. It is found that the nonlocal continuum describes adequately the transitional states in which continuum or fracture mechanics cannot be applied.; Finally, an experimental method is proposed for the measurement of the characteristic length. By identifying the material parameters from test data on uniformly strained specimens and matching the model with fracture test results, the characteristic length is estimated to be of the order of the maximum aggregate size.; This model bears considerable promise for the analysis of concrete structures and geotechnical problems up to complete failure.