Relationship between probabilistic characteristics of microscopic and macroscopic strength within the stochastic phase-field model

Abstract

Stochastic phase-field models can reproduce the nonlinearity and randomness of the mechanical behavior of quasi-brittle materials within a unified macroscopic continuum framework. To study the probabilistic characteristics of microscopic and macroscopic strength within the stochastic phase-field model and their relationship, a series of numerical results of a specimen subjected to uniaxial tension using a stochastic phase-field model is presented. The probabilistic characteristics of the macroscopic responses and the underlying mechanisms are discussed. Based on the numerical results, a probabilistic model is developed, which can effectively determine the probability information of the macroscopic structural strength of quasi-brittle uniaxial tensile specimens. In particular, the interaction of several characteristic scales involved in the stochastic phase-field model can be demonstrated.