  Data-driven methods are becoming an essential part of computational mechanics
due to their unique advantages over traditional material modeling. Deep neural
networks are able to learn complex material response without the constraints of
closed-form approximations. However, imposing the physics-based mathematical
requirements that any material model must comply with is not straightforward
for data-driven approaches. In this study, we use a novel class of neural
networks, known as neural ordinary differential equations (N-ODEs), to develop
data-driven material models that automatically satisfy polyconvexity of the
strain energy function with respect to the deformation gradient, a condition
needed for the existence of minimizers for boundary value problems in
elasticity. We take advantage of the properties of ordinary differential
equations to create monotonic functions that approximate the derivatives of the
strain energy function with respect to the invariants of the right Cauchy-Green
deformation tensor. The monotonicity of the derivatives guarantees the
convexity of the energy. The N-ODE material model is able to capture synthetic
data generated from closed-form material models, and it outperforms
conventional models when tested against experimental data on skin, a highly
nonlinear and anisotropic material. We also showcase the use of the N-ODE
material model in finite element simulations. The framework is general and can
be used to model a large class of materials. Here we focus on hyperelasticity,
but polyconvex strain energies are a core building block for other problems in
elasticity such as viscous and plastic deformations. We therefore expect our
methodology to further enable data-driven methods in computational mechanics
