Elastic-plastic-brittle transitions using anti-plane elastic spring lattice model

Elastic-plastic-brittle transitions;Damage localization;Strain localization;Spring lattice model;Fractals;Random media

Kale, Sohan ; Ostoja-Starzewski ; Martin

关键词: Elastic-plastic-brittle transitions;    Damage localization;    Strain localization;    Spring lattice model;    Fractals;    Random media;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/42130/Sohan_Kale.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The experimentally observed behavior in materials such as the size effect in failure strength, crack surface roughness and acoustic emission activity are directly related to the spatial material disorder present at the macroscopic and/or microscopic length scales. The classical continuum based theories fail to effectively address such issues and, therefore, spring-lattice models that can explicitly account for disorder are extensively used in statistical solid mechanics. The spring-lattice models reported in the literature over the past few decades have been used to study elastic-brittle and elastic-perfectly plastic transitions. The elastic-plastic-brittle spring lattice model proposed in this thesis is an extension of the existing spring lattice models that is more generalized and can simulate a wide range of material responses. The advantages of this model are demonstrated in this thesis by a thorough parametric study focusing on elastic-plastic transitions to understand the effects of the plastic hardening ratio and strength of disorder. The difference between elastic-plastic hardening and elastic-perfectly plastic behavior in anti-plane elasto-plastic medium is confirmed in terms of weak/strong nature of neighboring interactions and their implications in describing the problem as an uncorrelated/correlated percolation. Next, the damage localization in elastic-brittle transition is demonstrated and the roughness coefficient of the crack surface is estimated to be 0.7, which matches well with the previous studies. Absence of localization in the elastic-plastic transitions is attributed to the absence of stress concentrations near the yielded sites, as opposed to elastic-brittle transitions. Finally, usefulness of the proposed model is proved through a range of material responses that can be simulated controlled by the strength of disorder distribution in yield and failure limits of the given material.