Modelling fourth-order hyperelasticity in soft solids using physics informed neural networks without labelled data.

Area of Science:

• Biomechanics
• Computational mechanics
• Neuroscience

Background:

• Mild traumatic brain injury (mTBI) results from shear shock waves during head impacts.
• Higher-order hyperelastic models, like Landau, better capture brain deformation than simpler models.
• Traditional finite element solvers are too computationally expensive for real-time mTBI prediction.

Purpose of the Study:

• To develop a real-time prediction model for brain deformation under impact.
• To model the nonlinear mechanical response of higher-order hyperelastic materials.
• To introduce a physics-informed neural network (PINN) approach for brain injury simulation.

Main Methods:

• Proposed a causal marching physics-informed neural network (CMPINN) model.
• Implemented a novel adaptive training scheme with incremental weight updates.
• Incorporated domain-specific loss terms (material, boundary, internal) for total loss minimization.

Main Results:

• The CMPINN framework accurately captures nonlinear mechanical responses of higher-order hyperelastic materials.
• Validated the model for canonical deformations (uniaxial, biaxial, shear) in a cube.
• Demonstrated effectiveness in scenarios with spatially varying material properties and inhomogeneous deformations.

Conclusions:

• The CMPINN offers a computationally efficient alternative for real-time brain deformation prediction.
• This physics-informed neural network approach advances modeling capabilities for traumatic brain injury.
• The study provides a robust framework for simulating complex hyperelastic material behaviors.