Solving the CEM forward model. from Full-field mechanics imaging by direct inversion of electrical data

Self-sensing materials with deformation-dependent electrical conductivity have been studied in diverse applications. A limitation of self-sensing materials is that they do not directly report on the underlying condition of the material. That is, it would be much more useful to know the actual stresses, strains or damages that give rise to observed conductivity changes. The process of deducing material condition from electrical data is called the <i>self-sensing inverse problem</i> (SSIP). Previous work has required electrical impedance tomography (EIT) as an intermediate step to estimate the conductivity distribution prior to estimating the spatially varying mechanics. But this is undesirable because EIT is an ill-posed inverse problem and is highly dependent on regularization, which renders the SSIP as subject to the same assumptions and limitations of EIT. The contribution of this manuscript is the development of a <i>direct</i> SSIP formulation that omits the EIT step such that mechanics are predicted directly from voltage–current data. The effects of regularization type, regularization norm and formulation (difference versus absolute imaging) are also explored. The direct SSIP formulation is experimentally validated on a soft carbon nanofibre-modified polyurethane pressure sensor and compared to ANSYS-solved mechanics with good agreement.

具备形变依赖性导电性的自感知材料（Self-sensing materials）已在诸多应用场景中得到研究。自感知材料存在一项核心局限：其无法直接反映材料的内在状态。换言之，若能精准知晓引发观测到的导电性变化的实际应力、应变或损伤，将具备更高的实用价值。从电学数据中推导材料状态的过程被称为**自感知逆问题（self-sensing inverse problem，SSIP）**。过往相关研究需以电阻抗断层成像（electrical impedance tomography, EIT）作为中间步骤，先估算导电性分布，再进一步求解空间变化的力学状态。但该方案并不理想：电阻抗断层成像（EIT）属于不适定逆问题，且高度依赖正则化操作，这使得自感知逆问题（SSIP）同样受到EIT的固有假设与局限的制约。本研究的核心贡献在于提出了一种**直接型**自感知逆问题建模框架，该框架省略了EIT步骤，可直接从电压-电流数据中预测材料的力学状态。本研究还探讨了正则化类型、正则化范数以及建模方案（差分成像与绝对成像）对结果的影响。该直接型自感知逆问题建模框架已在软质碳纳米纤维改性聚氨酯压力传感器上完成实验验证，并与ANSYS求解得到的力学结果进行对比，二者吻合度良好。