Overloading, which is one of the factors contributing to bone resorption around an implant body, can lead to complications because force is applied beyond the prosthodontic or biological tolerance [23]. It is believed that when stress of a certain magnitude is applied to the bone, microscopic bone destruction occurs resulting in bone resorption [24, 25]. Because implants do not have buffering mechanisms like a periodontal ligament, occlusal force propagates directly to the surrounding bone via the implant body. Therefore, overloading is considered to be deeply involved in bone resorption after the beginning of functional loading [26]. In addition, since it has been reported that bone resorption by overloading is facilitated by infection, a design that does not place excessive stress on the surrounding bone is ideal [27]. Using a strain gauge is a popular method to evaluate stress in vivo. However, since the implant body is embedded in bone, it is impossible to evaluate the stress within the implant body noninvasively using the strain gauge method. Also, because the sensor is large, it may not be suitable for capturing the stress distribution to each part of the tissue. However, FEA is a method of capturing the entire behavior by dividing an object having a complicated shape or property into simple small parts and performing a numerical calculation. It is advantageous that an appropriate analysis model can represent the stress distribution within a structure noninvasively.

There are various types of stress that can be measured, and this must be selected according to the material and the item under evaluation. In this study, the implant body was either cpTi or TiZr, and this was evaluated using the von Mises stress, which is proportionally equivalent to the “shear strain energy theory”. Fracture occurs when the principal stress, which is the maximum generated stress, exceeds the strength of the material. Brittle materials are generally evaluated using the “maximum principal stress theory”; therefore, the maximum principal stress was used for evaluating the cortical bone in this study. It has been reported that the bone is strongly resistant to compressive stress, and the bone resorption threshold of tensile stress is lower than that of compressive stress by about 30% [28]. However, one study reported that tensile stress promotes bone deposition and compressive stress promotes bone resorption [29]. Therefore, the maximum absolute value of the maximum principal stress was measured, and the stress type (tensile or compressive) that had the greater maximum principal stress was then evaluated.