# Electrical Resistance Response to Strain in 3D-Printed Conductive Thermoplastic Polyurethane (TPU)
## 1 Introduction  
Soft robots are flexible actuators designed to adapt, deform, and comply to complex environments, conforming to surfaces and the environment while avoiding rigidity and stiffness [1, 2, 3]. Soft technologies have gained significant attention due to their potential applications in a variety of fields, including medical devices, human interacting robotics, and industrial applications [4, 5]. The main actuation technologies are pneumatic, shape memory materials, electroactive, magnetic, and chemical [2, 6, 7]. Pneumatic soft actuators, made of compliant materials, require complex geometries to transfer pressure into actuation and stiffening [8, 9, 10, 11]. Actuators are often casted in complex procedures combining several components with multi-stage casting to create the required geometrical structures [8, 10, 12, 13, 14, 15, 16, 17, 18]. Additive manufacturing (AM) and fused filament fabrication (FFF) allows for the fabrication of components by extruding thermoplastic filament into a solidifying geometry [19, 20, 21]. Availability, simplicity, design flexibility, and affordability have made AM a common soft robotics mold fabrication method for elastomer casting [8, 10, 12, 13, 14, 16, 17, 18]. However, AM and FFF also introduces design freedom compared to casting processes, allowing for single-step fabrication with internal structures, thin walls, minimal volumecompartments, and complex geometries [3; 5; 22]. Multimaterial printing with conductive materials allows for new innovative smart products with embedded sensors that allows for strain, pressure, temperature, and humidity detection [23]. In addition, FFF offers the option to fabricate complex, all-in-one, and low-cost actuators out of TPE and TPU in a single step process [22; 24; 25; 26; 27; 28]. In biomechanical applications, recent studies show sensors capable of measuring body movements, joint bending motions, phonations, and cardiac activities [29]. There has also been a development in 3D-printed nanostructures that allow for the mechanical sensing of products [30]. Sensors embedded into products with different functionalities and using different materials is a promising research direction [29], and we suggest that the next step is to embed sensors into any material or product. The layer-by-layer building process in additive manufacturing (Figure 1A) allows for the implementation of embedded sensors within the products that are capable of in situ monitoring. Implementing sensors by conductive filament is applicable to any product if it is capable of accurately sensing. Examples of sensor-embedded products can be soft robotics with large deformations, products with structural integrity for end-of-life monitoring, and digital twins where the product can provide live feedback. Due to the process of multi-material printing, the embedded sensor may be implemented independently of component complexity and can be designed in the X, Y, and Z dimensions. The embedding of the sensor by FFF can be seen in Figure 1A, and a hypothetical example of a sensor embedded in a soft robotic gripper arm gripping a strawberry is shown in Figure 1B. AM also introduces the possibility to easily manipulate compliance by fabricating multi-material and meta-material components or by integrating other features such as self-healing in the structure [2; 25; 31; 32]. NinjaTek Eel [33] is a commercially available TPU 3D-printing filament with carbon additives, resulting in both conductive and flexible properties [34]. The material can be integrated in the component to create integrated PCBs and three-dimensional meshes of flexible conductive wires. To ensure the suitable and autonomous behavior of an actuator, it is important to be aware of the surrounding environment and gather information [35]. Soft sensors can accurately capture information about the environment while also maintaining compliance [36; 37]. Typically, flexible sensors are fabricated by reducing the geometric dimension in one or more axes, allowing for compliance [38].