Because $\Delta t$ depends on density and element size, analysts often manipulate the material density to increase the time step. This is known as .
That’s where takes center stage.
In structural mechanics, dynamic problems are governed by Newton’s Second Law: $$ M \ddotu + C \dotu + Ku = F(t) $$ Where: explicit dynamics
You should reach for an explicit solver when the event happens faster than the natural frequency of the structure. Specifically:
Explicit dynamics forces you to think differently. You stop asking, "Is this part strong enough?" and start asking, "How long does it take for the load to travel from the point of contact to the bolt hole?" Because $\Delta t$ depends on density and element
The velocity and acceleration are approximated using finite difference formulas:
To understand explicit dynamics, we first have to look at its counterpart: Implicit analysis. In structural mechanics, dynamic problems are governed by
Have you struggled with convergence issues in implicit codes for high-speed events? Or are you just getting started with explicit analysis? Let me know in the comments below.
Because there is no matrix inversion, explicit methods are incredibly robust at handling severe non-linearities—provided you use a very small, stable time step.
Used for processes that are technically static but involve severe nonlinearity (buckling, complex contact) that prevents Implicit solvers from converging.
. While standard "implicit" analysis is great for steady loads, it struggles when the clock is measured in milliseconds and the forces are chaotic. Why the "Explicit" Approach? The term comes from the way the math is handled. In these simulations, the state of the system at the next tiny increment of time is calculated "explicitly" based on what is happening right now. It doesn't try to balance the whole equation at once; it simply marches forward in time, step by incredibly small step. This makes it the perfect tool for three specific scenarios: High Velocity: Impacts, crashes, and explosions. Extreme Deformation: When metal tears, rubber stretches to its limit, or glass shatters. Complex Contact: When different parts of a machine slam into each other and bounce off in fractions of a second. Real-World Impact You encounter the results of explicit dynamics every day, likely without realizing it. Automotive Safety: Engineers run thousands of virtual crash tests to design "crumple zones" that absorb energy, keeping the passenger cabin intact. Consumer Electronics: Before a new smartphone is manufactured, "drop tests" are simulated to ensure the screen won't crack from a pocket-height fall. Aerospace: It is used to simulate bird strikes on jet engines or the deployment of landing gear. The Trade-off The catch is computational power. Because the time steps must be so small to remain accurate—often a millionth of a second or less—these simulations are "expensive." They require high-performance computers to crunch the numbers. However, the payoff is a digital laboratory where engineers can test the limits of safety and durability without destroying a single physical prototype. Explicit dynamics is essentially the physics of "the bang." It allows us to slow down time, peer into the chaos of an impact, and build a world that is safer and more resilient. Would you like to dive deeper into the