This is all known. What I really wanted to know is if there is a mathematical model to estimate the difference in terms of force required to break the egg, at any point, say from inside as well as outside. Suppose we are applying force 'F1' over a pointed area 'A' from outside, or alternatively force 'F2' from inside over the same area 'A'. F2 will certainly be always less than 'F1' due to the shape of egg. But is there a way to find out the function relation between F1 and F2 at all the points on the surface of egg.

Two kinds of things are being talked about here. One is a static pressure and the other a dynamic or shock pressure (blow of a hammer etc.). These are different in comparison,

But an answer to your question of inside and outside pressure perhaps lies in a tensile or compressive strength difference. While pressurized from inside you are exploiting tensile modulus. And it is now a question we need to address why tensile modulus is small and the breaking point or limit is reached at much lower pressures. It seems the curvature (+ve or -ve) will matter. Hope there is no excess pressure inside an egg?

Vijay you got it right. Let us take the case of static pressure first. Also assume that there is no excess pressure inside egg. Then, what will be the effect of +ve and -ve curvature in creating the difference between outside and inside force, required to break the egg.

It seems that the force F applied from out side will face reaction from the curved surface (now convex) as Fcos(theta) where theta is an angle F makes to tangent of surface inside. This reaction will be F cos(pi-theta) from inside. When added from all points around, we may talk of this as pressure. But this reaction is either inward or outward depending upon F applied from outside or inside. Thus it either tends to compress (if F is outside) or elongate as in case of inside. Elongation is easy as is evident from microscopic interaction point of view. Any interaction between to atoms results in a hardened compression - atoms dislike to be compressed closer due to so called Pauli exclusion principle in addition to other Coulombic interactions. Any typical potential energy curve has this asymmetry - it is not harmonic always. So it is tensile and compressive difference that results in this behavior.

It seems true that the most important factor in eggshell penetrability is its shape, a sphere being the most impenetrable convex surface, at least from the outside. Concave interior of eggshell can be from spherical to a more planar surface. It seems that the impact force needed to break through from inside the egg should relate to shell thickness and the radius of curvature. The difference between the breakthrough force at the same thickness and curvature ("the same point", or place) should be greater for the external approach owing to shape. However, the reasoning of comparable internal break through for being less than external is less sure, as far as deriving formulae. Nature has already done this via selective protective optimization for shell design, as some fowl eggs are much harder than others but shaped much the same (for various reasons). Shells are porous and keep bacteria away. During deposition onto the basement membrane the grains or 'chunks' of calcification are smaller and/or more compact. As the thickness builds pore space increases. Thus, impact crack propagation tendency is greater from the inside out. Mother Nature, you don't mess with!