Drop Impact Test Simulation

Theory and Physics

Mechanics of Free Fall

For example, dropping a smartphone from a height of 1.2 m (about the height when taking it out of a pocket):

Giving this velocity as the "initial velocity" to the product is the basic setup method for drop FEM. The mass $m$ cancels out as if by promise, but of course it affects the deformation and stress after impact.

About 2,400 N of force on a 200 g object means an acceleration of about 1,200 G. This is what destroys solder joints on electronic components.

Contact Mechanics of Impact

Here $K_H$ is the Hertzian contact stiffness, determined from the elastic modulus, Poisson's ratio, and radius of curvature of both objects. However, in drop testing, plastic deformation and fracture occur, so Hertz theory alone is insufficient. In FEM, the nonlinear contact force is directly calculated by solving the elastoplastic constitutive law at the element level.

$k_p$ is the penalty stiffness, $g_n$ is the gap (negative means penetration amount). If $k_p$ is too small, the product "passes through" the floor; if too large, the time step becomes extremely small and computational cost explodes. Running with default values first and then fine-tuning is the practical approach.

Energy Balance and Absorption Mechanisms

• Elastic strain energy $E_{elastic}$ — The part that returns after deformation. Source of bounce energy.
• Plastic dissipation energy $E_{plastic}$ — Consumed in permanent deformation. Dents or cracks in the housing.
• Friction energy $E_{friction}$ — Consumed by sliding on the contact surface.
• Damping energy $E_{damping}$ — Absorbed by material viscosity.
• Rebound energy $E_{rebound}$ — Kinetic energy after bouncing.

Expressed by the coefficient of restitution (COR) $e$, $E_{rebound} = e^2 \cdot E_k$. When a smartphone glass surface hits tile, $e \approx 0.2\text{~}0.4$, and most of the energy is consumed by plastic deformation and internal damping.

Drop Orientation and Stress Concentration

IEC 60068-2-31 requires drops from a total of 26 directions: 6 faces, 12 edges, 8 corners. In FEM, at least the three representative orientations (face, edge, corner) are essential, and ideally all 26 directions should be run to see design margins.

Strain Rate Effect

$\sigma_0$ is the quasi-static yield stress, $D$ and $q$ are material constants. For example, for polycarbonate (PC), $D = 10$ /s, $q = 2$ approximately, and at a strain rate of 100 /s, the yield stress jumps to about 3 times the quasi-static value. Ignoring this risks the simulation deforming more than in reality and misjudging it as "broken".

Numerical Methods and Implementation

Explicit Method Time Integration

If the mass matrix $M$ is diagonalized (lumped mass), there is no need to solve simultaneous equations. Since the acceleration of each node can be calculated independently, it progresses stably even for problems with strong nonlinearity. However, it is conditionally stable, and the stable time step is:

For a 1 mm hexahedral steel element, $\Delta t \approx 0.2$ μs. Simulating a 5 ms collision phenomenon requires about 25,000 steps.

Contact Algorithm

• Product vs. Floor surface — External contact. Defining the floor as a rigid surface is efficient as it requires no elements. Very hard surfaces like concrete or tile are sufficiently approximated as rigid.
• Self-contact inside the product — Cases where the housing deforms and contacts internal substrates or batteries. Often overlooked but important for electronic devices.

In LS-DYNA, *CONTACT_AUTOMATIC_SINGLE_SURFACE is standard, automatically detecting all outer surfaces as one contact group. For the penalty stiffness scale factor (SFS/SFM), running first with the default 1.0 and then increasing to 2.0~5.0 if penetration is observed is practical.

LS-DYNA Input Example

$ --- Initial velocity (apply downward velocity to entire product set) ---
*INITIAL_VELOCITY_SET
$  nsid    vx      vy      vz
   1,      0.0,    0.0,    -4.43

$ --- Gravity (only needed for tracking bounce) ---
*LOAD_BODY_Z
$  lcid    sf
   1,      1,      9.81e-3   $ mm/ms^2

$ --- Rigid wall (infinitely hard floor surface) ---
*RIGIDWALL_PLANAR
$  xt  yt  zt  xh  yh  zh
   0., 0., 0., 0., 0., 1.

$ --- Contact (automatic single surface) ---
*CONTACT_AUTOMATIC_SINGLE_SURFACE
$  ssid  msid  sstyp  mstyp  sboxid  mboxid  spr  mpr
   1,    0,    3,     0,     0,      0,      1,   1
$ fs    fd    dc     vc
  0.3,  0.2,  0.,    0.

$ --- Time control ---
*CONTROL_TIMESTEP
$  dtinit  tssfac
   0.,     0.9

The key point is using TSSFAC=0.9, which uses 90% of the stable time step. The default 0.9 is usually OK, but for severe contact, it might be reduced to 0.67.

Abaqus/Explicit Input Example

** --- Initial velocity ---
*INITIAL CONDITIONS, TYPE=VELOCITY
product_set, 3, -4.43

** --- Gravity ---
*DLOAD
product_set, GRAV, 9.81, 0., 0., -1.

** --- Rigid floor (analytical rigid surface) ---
*RIGID BODY, REF NODE=floor_rp,
  ANALYTICAL SURFACE=floor_surf
*SURFACE, TYPE=PLANAR, NAME=floor_surf
  DATA LINE: 0., 0., 0., 0., 0., 1.

** --- General contact (recommended) ---
*CONTACT, OP=NEW
*CONTACT INCLUSIONS, ALL EXTERIOR

** --- Step (5 ms analysis) ---
*DYNAMIC, EXPLICIT
  , 0.005

Abaqus's General Contact is very convenient, automatically registering all outer surfaces as contact candidates. It's a similar concept to LS-DYNA's AUTOMATIC_SINGLE_SURFACE. Defining the floor as an analytical rigid surface eliminates the need for floor meshing and improves computational efficiency.

Element Selection and Mesh Strategy

Mesh size must be sufficiently fine relative to the impact wave wavelength. As a rule of thumb, near contact surfaces, element size 0.5~1.0 mm, elsewhere 2~5 mm, with at least 5 integration points for shells or 3 layers for solids in the thickness direction.