elastic modulus : stress/strain. why it could not be strain / stress? My answer is the amount of stress depends on the amount of strain. So we must write stress is proportional to strain and the modulus will be stress/strain. Is my answer correct? If it is then is it just a convention to write relations like this or it has a particular reason?
It's completely up to us to choose what the proportionality constant is. We could write:
Strain = k * stress
So now when we interpret what k is, it's the ratio of the resulting strain to the applied stress and we can just work with it, no problem at all, as long as we agree on this definition. But there are just lots of inconvenient things about this, first; the values of strain are very small compared to the stress, thus the values for the constant k for every material would be very small and look very bad, secondly; it's just more natural to define k as the ratio of the applied stress to the resulting strain. It's just a matter of convenience.
Another famous example is Ohm's law, the voltage V is directly proportional to the current I. Based on the predefined units for voltage and current (that is, the values for voltage in Volts are larger than the values of current in Amperes, so the ratio V/I will usually be greater than 1 based on this) , we find from experiments that the relation is usually V = (number greater than 1) * I , or that I = (number greater than 1) / V, that's the relation we get based on the units of V and I, so, now we observe that the larger this number, for the same voltage, the smaller the current will be, so we decide to call it resistance.