INTERSPACE

Engineering problem

INTERSPACE investigates how a deployable hemispherical structural network responds to mechanical impact. The model combines structural dynamics, contact mechanics, wave propagation, adaptive damping, electromechanical energy recovery and deployment feasibility analysis.

The simulated structure is a triangulated network of nodes, elastic elements, damping components and boundary constraints interacting with projectiles. Impact produces deformation, momentum transfer, stored elastic energy, mechanical dissipation and, in selected models, electrical energy recovery. It is a computational mechanics investigation, not a demonstrated physical energy shield.

Mathematical foundations

Particle and lattice dynamics

Early models use the Morse potential

$$U(r)=D_e\left(1-e^{-a(r-r_e)}\right)^2,$$

with forces obtained from the potential gradient and trajectories advanced using velocity-Verlet integration.

Three-dimensional structural dynamics

The network model follows

$$m_i\ddot{\mathbf{x}}_i=\sum_j\mathbf{F}^{elastic}_{ij}+\sum_j\mathbf{F}^{damping}_{ij}+\mathbf{F}^{contact}_i+\mathbf{F}^{actuation}_i,$$

with elastic energy

$$U=\frac12\sum_{(i,j)}k_{ij}(\ell_{ij}-\ell_{ij}^{0})^2.$$

Geometry, element stiffness, damping, boundary constraints and impact location determine the structural response and the propagation of mechanical energy through the lattice.

Contact mechanics

Projectile interaction is represented with penalty-based contact forces against triangular surface geometry. The numerical studies track penetration, contact force, impulse, rebound and energy transfer rather than assuming a perfectly rigid collision.

Adaptive damping

Controlled damping fields are used to investigate how localized or time-dependent dissipation changes wave propagation and structural response. They are numerical control studies, not experimentally validated adaptive-material behavior.

Electromechanical recovery

A representative coupled model is

$$m\ddot{x}+c\dot{x}+kx+\theta V=F,$$ $$C\dot V+\frac VR=\theta\dot x.$$

The equations couple mechanical deformation to piezoelectric voltage, electrical loading and energy accounting. They make it possible to compare stored, dissipated, transferred and electrically recovered energy within the model.

Deployment feasibility

Deployment studies move the network from a flat-ring geometry toward a hemisphere. Inverse-dynamics calculations estimate actuator forces, mechanical work and peak power. The tested rapid-deployment configurations exceeded the illustrative actuator force and power constraints, an important feasibility limitation rather than a hidden negative result.

Numerical methods

The project uses velocity-Verlet integration, mass-spring dynamics, penalty contact, explicit energy accounting, parameter perturbations and sensitivity studies. It developed through twelve computational stages; the individual standard numerical methods are established techniques rather than claimed inventions.

Case-study library

1. Normal impact
2. Oblique impact
3. Multiple impacts
4. Geometry comparisons
5. Stiffness and damping optimization
6. Structural defects
7. Piezoelectric energy harvesting
8. Adaptive damping
9. Deployment feasibility
10. Multiobjective optimization
11. Robustness and uncertainty
12. Numerical fidelity and convergence

The interface distinguishes completed archived numerical studies from proposed research protocols.

Verification and limitations

Numerical checks include energy and momentum accounting, time-step studies, parameter perturbations and comparisons across geometric and material assumptions. Results depend on reduced constitutive, damping, contact and actuation models. The project does not establish commercial protection performance or experimentally validated deployment hardware.

Engineering applications

INTERSPACE demonstrates computational mechanics, structural dynamics, numerical solver development, multiphysics coupling, engineering feasibility analysis and scientific visualization.

Technical resources

• Live demonstration
• Public source repository