One area of research we actively explore at Mondaic is the non-destructive testing (finding flaws) and evaluation (estimation of properties) of objects made out of Carbon-Fibre Reinforced Polymers (CFRP). These are highly anisotropy materials (typically orthotropic) that layered in such a way to make lightweight but very strong objects - you might know these from your daily life if you own a fancy bike, Formula 1 car or nice racket for ball sports.
Inspecting these can be done with classical ultrasound pitch-and-catch or C-Scans style acquisition, but at Mondaic we'd like to offer an alternative: guided wave inspection. Our value proposition is that once we integrate inspection methods based on guided waves with accurate numerical modelling and digital twin creation, any complex, heterogeneous and anisotropic object can be inspected.
At JEC World 2025 (conference website) we demonstrated our recent advancements on modelling arbitrarily complex CFRP objects. Although our core simulation engine Salvus has supported heterogeneous anisotropic (and attenuating) materials for some years, we have recently integrated this with advanced digital twin creation that accounts for complex CFRP geometry and varying layups and ply orientations.
These developments culminate in the work we presented at JEC: a digital twin of a reinforced CFRP panel with varying layup between the base plate and all stringers. We have created this digital twin with a reference frequency for the guided waves at 100 kHz.
The digital twin we created does not exists on its own. In the context of our collaboration in an Innosuisse-funded project, João Francisco and Christian Brauner at Fachhochschule Nordwestschweiz FHNW have fabricated this exact panel, and Henrik Rasmus Thomsen and Dirk-Jan van Manen at ETH Zürich have captured vibration data of the panel's response to a 100 kHz transducer using a robotized 3D Laser Doppler Vibrometer (LDV) at the "Centre for Immersive Wave Experimentation" at Switzerland Innovation Park Zurich.
Although the individual materials making up the CFRP in each ply are orthotropic, their layering and ply curvature make the final object have a space varying stiffness tensor, that in all its generality turns out to need the freedom of triclinic materials. In other words, to accurately simulate guided waves (as well as static load simulations) while accounting for layup, any numerical solver needs to be able to handle spatially varying stiffnesses for 21 independent components!
A technical challenged we hadn't considered during Mondaic's typical operation in Earth Sciences was the accounting of local orientation of each of the elements in our produced hexahedral mesh. Although we have a lot of expertise creating layered meshes needed to resolve every ply in a CFRP stackup, assigning ply id's to all elements proved non-trivial. We found that tracing plies through a mesh using graph-based algorithms was the best approach, and using the expertise João and Christian we managed to obtain spatially varying local rosettes that also account for the ply angle.
This high-fidelity wave equation-compatible discretisation (a hexahedral mesh) has 682'890 elements, each with 8 GLL nodes. This results in us accounting for more than 5 million orientations of the stiffness tensor, each having 21 independent components. All that comes together when we run our digital twin in our (gpu-accelerated) simulation engine: Salvus. The final high-fidelity wavefields that Salvus resolved are annotated below.
This digital twin, its simulations and the experimental work done with the LDV will be the basis of further collaboration between the teams at FHNW, ETH and Mondaic for flaw-finding and material property estimation using guided waves. For technical questions on the digital twin or our simulation engine, feel free to reach out.
