I think that one should retain "assume" in English, as one does generally use the term "to assume responsibility". As a general rule, one should retain the scope of the source text, particularly in the case of a legal contract. It is possible that the source text is intended to cover not just safekeeping of the materials, but also any liability arising from their storage, e.g. the materials might conceivably cause corrosion, poisoning, pollution etc., or responsibility to safely dispose of unused materials at the end of the job.