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We describe the SOniCS (SOFA + FEniCS) plugin to help develop an intuitive understanding of complex biomechanics systems. This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise. Constitutive models can be modified by one line of code only. This ease in building new models makes SOniCS ideal to develop surrogate, reduced order models and to train machine-learning algorithms for enabling real-time patient-specific simulations. SOniCS is thus not only a tool that facilitates the development of surgical training simulations but also, and perhaps more importantly, paves the way to increase the intuition of users or otherwise non-intuitive behaviors of (bio)mechanical systems. The plugin uses new developments of the FEniCSx project enabling automatic generation with FFCx of finite-element tensors, such as the local residual vector and Jacobian matrix. We verify our approach with numerical simulations, such as manufactured solutions, cantilever beams, and benchmarks provided by FEBio. We reach machine precision accuracy and demonstrate the use of the plugin for a real-time haptic simulation involving a surgical tool controlled by the user in contact with a hyperelastic liver. We include complete examples showing the use of our plugin for simulations involving Saint Venant–Kirchhoff, Neo-Hookean, Mooney–Rivlin, and Holzapfel Ogden anisotropic models as supplementary material.

In this paper we develop a framework for solving inverse deformation problems using the FEniCS Project finite-element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In contrast with inverse iterative algorithms that require multiple solutions of a standard elasticity problem, the proposed method can compute the undeformed configuration by solving only one modified elasticity problem. This modified problem has a complexity comparable to the standard one. The framework is implemented within an open-source pipeline enabling the direct and inverse deformation simulation directly from imaging data. We use the high-level unified form language (UFL) of the FEniCS Project to express the finite-element model in variational form and to automatically derive the consistent Jacobian. Consequently, the design of the pipeline is flexible: for example, it allows the modification of the constitutive models by changing a single line of code. We include a complete working example showing the inverse deformation of a beam deformed by gravity as supplementary material.