Thanks for the question. Wood and concrete typically have fibrous or porous surfaces that are best handled with a liquid adhesive. Also, wood expands a lot with temperature and humidity changes compared to metal and concrete. Because of this, a flexible adhesive is often a good choice.
The specific adhesive and surface prep depend on the details of the application including joint design, surface area, flatness/fit of substrates, application temperature, ability to fixture, and other factors. Because of this, testing the design is always an important part of creating an adhesive bond. I would suggest starting your testing with either a two-part structural urethane adhesive, a one-part flexible urethane adhesive sealant, or a two-part structural flexible epoxy. The epoxy should only be considered if the substrates are unpainted. More information on each option can be found below:
Please note that these products (like many adhesives sold by the 3M Industrial Adhesives and Tapes Division) are for industrial/occupational use only. They are not intended for consumer sale or use.