LCA for damage pattern analysis?

I have a dataset that deals with damage to various/random parts of a structure and how it will break. Basically, I have a categorical dataset with binary entries for whether specific areas of the structure is affected "yes=1" or "not=0" and its association with how severe was the end-result (shatter) when subjected to specific stress. The problem is that multiple areas of the structure are often affected. But interestingly, Chi-Squared tests show that some areas more frequently correlate with specific type of breakage as compared to the no breakage situation (which btw also has damage patterns). I would like to reveal hidden patterns (linkages between perhaps multiple sensitive areas) in the data-set or even better allow me to see how unique the initial pattern of damage is between cases that broke versus the ones that did not. Since I am totally new to multivariate stats I am not sure how to handle this problem. I considered factor analysis for a while but now after having read up a bit on Latent Class Analysis, it seems to make more sense. I will really appreciate it if anyone interested in such problems can advice me. Thanks a lot in advance for any info.