We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite element modelling with a mixed micromechanics formulation. The latter is used to estimate the constitutive properties of CNT-based composites, including the elastic tensor, fracture energy, electrical conductivity, and linear piezoresistive coefficients. These properties are inputted into a coupled electro-structural finite element model, which simulates the evolution of cracks based upon phase-field fracture. The coupled physical problem is solved in a monolithic manner, exploiting the robustness and efficiency of a quasi-Newton algorithm. 2D and 3D boundary value problems are simulated to illustrate the potential of the modelling framework in assessing the influence of defects on the electromechanical response of meso- and macro-scale smart structures. Case studies aim at shedding light into the interplay between fracture and the electromechanical material response and include parametric analyses, validation against experiments and the simulation of complex cracking conditions (multiple defects, crack merging). The presented numerical results showcase the efficiency and robustness of the computational framework, as well as its ability to model a large variety of structural configurations and damage patterns. The deformation-electrical-fracture finite element code developed is made freely available to download.

翻译：我们提出了一种新颖的计算框架，用于模拟含断裂的自感知碳纳米管基复合材料的力电响应。该计算框架将电-变形-断裂有限元建模与混合细观力学公式相结合，后者用于估算碳纳米管基复合材料的本构特性，包括弹性张量、断裂能、电导率及线性压阻系数。这些特性作为输入参数，输入至耦合电-结构有限元模型中，该模型基于相场断裂模拟裂纹的演化过程。通过采用拟牛顿算法的鲁棒性与高效性，以整体求解方式处理耦合物理问题。通过模拟二维和三维边值问题，展示了该建模框架在评估缺陷对细观及宏观智能结构力电响应影响方面的潜力。案例研究旨在揭示断裂与力电材料响应之间的相互作用，包括参数分析、实验验证以及复杂开裂条件（多缺陷、裂纹合并）的模拟。所呈现的数值结果展示了该计算框架的高效性与鲁棒性，以及其对多种结构构型和损伤模式的建模能力。本文开发的变形-电-断裂有限元代码已免费提供下载。