期刊
THIN-WALLED STRUCTURES
卷 159, 期 -, 页码 -出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.tws.2020.107234
关键词
Fracture mechanics; Gamma-convergence; Phase field; Functionally Graded Materials; Finite element method
资金
- Consejeria de Economia y Conocimiento of the Junta de Andalucia (Spain) [US-1265577]
- Italian Ministry of Education, University and Research [CUP: D68D19001260001]
This study proposes a phase field approximation of fracture for functionally graded materials, incorporating the characteristic length scale as a material parameter, and conducts a comprehensive sensitivity analysis on various model parameters. The research demonstrates the Gamma-convergence of the model, as well as the limitation of fracture energy and elastic energy by homogeneous constituents.
A phase field (PF) approximation of fracture for functionally graded materials (FGM) using a diffusive crack approach incorporating the characteristic length scale as a material parameter is herein proposed. A rule of mixture is employed to estimate the material properties, according to the volume fractions of the constituent materials, which have been varied according to given grading profiles. In addition to the previous aspects, the current formulation includes the internal length scale of the phase field approach variable from point to point, to model a spatial variation of the material strength. Based on the ideas stemming from the study of size-scale effects, Gamma-convergence for the proposed model is proved when the internal length scale is either constant or a bounded function. In a comprehensive sensitivity analysis, the effects of various model parameters for different grading profiles are analyzed. We first prove that the fracture energy and the elastic energy of FGM is bounded by their homogeneous constituents. Constitutive examples of boundary value problems solved using the BFGS solver are provided to bolster this claim. Finally, crack propagation events in conjunction with the differences with respect to their homogeneous surrogates are discussed through several representative applications, providing equivalence relationships for size-scale effects and demonstrating the applicability of the current model for structural analysis of FGMs.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据