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I am working on a project where I must find the maximum principal stresses on an object subjected to impact loading condition. I know the velocity of the object (the one which will hit the test object) and its weight. My questions are:
Your problem is ill-posed as stated.
However, a zeroth-order estimate of the impact force can be calculated using a one-dimensional balance of energy. The kinetic energy of the projectile is $$ \text{KE} = \tfrac{1}{2} m v^2 $$ where $m$ is the mass of the projectile and $v$ is its velocity.
The strain energy of the target, assuming linear elasticity, is $$ \text{U} = \tfrac{1}{2} \sigma \varepsilon V $$ where $\sigma$ is the stress in the target, $\varepsilon$ is the strain in the target, and $V$ is the volume of the target.
Equation the two, we have $$ m v^2 = \sigma \varepsilon V = \frac{F}{A} \varepsilon A L = F \varepsilon L $$ where $F$ is the impact force, $A$ is the impact area and $L$ is the length of the target normal to the impact direction.
The impact force estimate is, therefore, $$ F = \frac{m v^2}{\varepsilon L} = \frac{m v^2}{d} $$ where $d$ is the depth of penetration.
If, instead, you would like to use the pressure, $$ p = \sigma = \frac{m v^2}{\varepsilon A L} = \frac{m v^2}{A d} $$ Either can be used, but note that the force has to be applied over the contact area.
The problem is ill-posed because, even if you know $A$, you don't know $\varepsilon$ and $L$. People usually assume that $L$ is the thickness of the object (which may be infinite in some cases) and that $\varepsilon$ is small (e.g., 0.001). On the other hand, you may know a value of $d$ and get a reasonable estimate that way.
The only accurate way to compute the impact forces is to do a full-physics dynamic simulation.
