In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element exterior calculus and domain decomposition to interconnect two systems with dual input-output behavior. The spatial domain is split into two parts by introducing an arbitrary interface. Each subdomain is discretized with a mixed finite element formulation that introduces a uniform boundary condition in a natural way as the input. In each subdomain the finite element spaces are selected from a finite element subcomplex to obtain a stable discretization. The two systems are then interconnected together by making use of a feedback interconnection. This is achieved by discretizing the boundary inputs using appropriate spaces that couple the two formulations. The final systems include all boundary conditions explicitly and do not contain any Lagrange multiplier. Time integration is performed using the implicit midpoint or Störmer-Verlet scheme. The method can also be applied to semilinear systems containing algebraic nonlinearities. The proposed strategy is tested on different examples: geometrically exact intrinsic beam model, the wave equation, membrane elastodynamics and the Mindlin plate. Numerical tests assess the conservation properties of the scheme, the effectiveness of the methodology and its robustness against shear locking phenomena.

Organ-on-Chip (OoC) devices enable controlled replication of physiological microenvironments and are increasingly used in biomedical engineering and drug discovery. This study presents a comprehensive 3D simulation-based characterization of mass transport and mechanical properties of a silicon-based Barrier-on-Chip (BoC) device comprising two stacked microfluidic channels separated by a porous Si3N4 membrane. Steady-state laminar flow simulations are performed to obtain the velocity field, after which transient convection-diffusion simulations are conducted to evaluate species transport toward and across the membrane. The mechanical performance of the membrane is analyzed using coupled Fluid-Structure Interaction (FSI) simulations with effective material properties accounting for porosity. Three flow configurations namely coflow, counter-flow, and single-channel flow are investigated across four volumetric flow rates. The results show that both flow configuration and flow rate strongly influence concentration distributions along the membrane. Counter-flow produces the strongest axial concentration gradient, which becomes more spatially uniform at higher flow rates as convection-dominated transport increasingly governs the system. Higher flow rates also result in larger membrane deflections, with counter-flow producing deflections approximately two orders of magnitude greater than co-flow at low flow rates for both configurations. Wall shear stress increases linearly with flow rate, spanning the physiologically relevant ranges for intestinal epithelial and blood-brain barrier endothelial cells. These findings provide quantitative design guidelines for selecting flow configurations and rates based on target concentration gradients, shear stress levels, and mechanical constraints in BoC applications.

A meshless method is used to simulate the Fluid-Structure Interaction (FSI) in a micropump intended to treat nerve injury. Conventional meshbased methods can suffer from mesh deformation and quality issues, and find it difficult to track the fluid-structure interface. The Material Point Method (MPM) combines Lagrangian material points with an Eulerian computational grid, thereby avoiding any mesh related problems. To simulate the valve dynamics in the micropump, MPM was used to analyze the effect of the valve length on the behaviour of the pump. A longer valve length takes longer to open, as it sticks to the valve seat, meaning the pump needs to generate more pressure to open the valve. This contribution shows that MPM simulations can be used to optimize the valve design for implantable micropumps.