Logistic Regression - General concepts

I am relatively new to predictive modeling techniques and would like to get a few concepts cleared/discussed. I am currently in the process of building a logistic regression model using Weight of Evidence (WOE) technique. I understand that the log odds and WOEs tend to have a linear relationship - a pre-requisite for the model. In case of categorical variables, WOEs can be used to make them continuous. But what if, the Log odds have a U-shaped relationship with the independent variable.