Probabilistic Nonlocal Damage Model for Continua with Random Field Properties

Abstract

Nonlocal continuum damage mechanics and random field theory are used to model the stochastic damage behavior of a strain‐softening material with random field properties. The randomness in the damage process is introduced by considering the initial damage threshold and the local strain‐softening behavior as a bivariate random Nataf field, defined by the marginal distributions and correlation matrix. A key component of the model is the introduction of two different length parameters: the characteristic length of the nonlocal damage model and the correlation distance for the random field. The probabilistic nonlocal damage model is illustrated by presenting finite‐element analyses of direct‐tension tests. It is found that the specimen exhibits a structural behavior representing a nonsymmetrical deformation and nonlinear stress‐displacement curve. The influence of the cross‐correlation coefficient between the initial damage and the strain‐softening behavior is discussed. The probabilistic nonlocal damage model is also capable of describing the deterministic and probabilistic size effect of structures.