In static, the equilibrium equation is f = K u, where f is the force vector, u is the displacement vector for all nodes, and K is the stiffness matrix of the whole system.

In impact loading (dynamic), the equilibrium equation is f = K u + c u_dot + m u_doubledot where u_dot is the velocities and u_double dot is the acceleration vector, c is damping factor, and m is the mass. In this case, m u_doubledot is the inertial terms due to the acceleration.

For rate-dependent material, in both cases, the term K is function of strain rate. So clearly, inertia effect and rate-dependent effect are totally different.

For some cases, the rate-dependent effect can be large, even if you load in quasi-static loading (in this case, quasi static means inertial term is negligible).

In aluminum, it is normally rate-independent means K is not function of strain rate... but under dynamic loading, the inertia term (m u_doubledot) can be comparable to (K u) term.

So the 30% different can comes from (m u_doubledot) term and (c u_dot) terms.

Hope this helps.

Dear Kumar Ap,

if possible please elabotrate on the method you have used for static and impact loading

In static, the equilibrium equation is f = K u, where f is the force vector, u is the displacement vector for all nodes, and K is the stiffness matrix of the whole system.

In impact loading (dynamic), the equilibrium equation is f = K u + c u_dot + m u_doubledot where u_dot is the velocities and u_double dot is the acceleration vector, c is damping factor, and m is the mass. In this case, m u_doubledot is the inertial terms due to the acceleration.

For rate-dependent material, in both cases, the term K is function of strain rate. So clearly, inertia effect and rate-dependent effect are totally different.

For some cases, the rate-dependent effect can be large, even if you load in quasi-static loading (in this case, quasi static means inertial term is negligible).

In aluminum, it is normally rate-independent means K is not function of strain rate... but under dynamic loading, the inertia term (m u_doubledot) can be comparable to (K u) term.

So the 30% different can comes from (m u_doubledot) term and (c u_dot) terms.

Hope this helps.

Some answers to your different questions:

- All metals, deforming plastically through dislocation glide, in the end are strain rate sensitive. Nevertheless, depending on the strain rate interval you are looking at, you might sometimes consider a specific material to be strain rate insensitive.

- The latter might explain why certain people consider AA6061 to be strain rate insensitive. Nevertheless, AA6061 is definitely strain rate sensitive as shown by the results of several research groups. To name just one:

Characterization of Dynamic Tensile Testing Using Aluminum Alloy 6061-T6 at Intermediate Strain Rates Deju Zhu, Ph.D.1 ; Barzin Mobasher, Ph.D., P.E., M.ASCE2 ; S. D. Rajan, Ph.D., M.ASCE3 ; and Pedro Peralta, Ph.D.4.

- Basically the question comes down to what strain rates your material is experiencing during respectively static and dynamic testing, and if these strain rates are different enough to have significant influence on the outcome (especially if you only look at results from crushable structures, that generally tend to show relatively strain rate insensitive behaviour, the opposite from what you have been experiencing).

- Metals, as all materials, have mass and strength. Mass leads to inertia effects, strength is influenced by strain rate. For experimental results, it is not always easy to distinguish between respectively inertia effects and strain rate effects on the material strength, as both effects are 'superposed' and both increase with increasing strain rate leading to a perceived higher-strength response. Although there exist experimental and analytical approaches to separate the two of them, finite element modeling is often a more easy tool to determine the relative importance of both effects, as it allows you to 'test' the material without mass or without strain rate effects.

Hope this helps!