Real-time Error Control for Surgical Simulation

Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local $h$-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations.Comment: 12 pages, 16 figures, change of the title, submitted to IEEE TBM

Real-time Error Control for Surgical Simulation

International audienceObjective: To present the first real-time a poste-riori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA 1. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local h-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations. Index Terms—Finite element method, real-time error estimate, adaptive refinement, constraint-based interaction

Explicit Topology Optimization of Conforming Voronoi Foams

Topology optimization is able to maximally leverage the high DOFs and mechanical potentiality of porous foams but faces three fundamental challenges: conforming to free-form outer shapes, maintaining geometric connectivity between adjacent cells, and achieving high simulation accuracy. To resolve the issues, borrowing the concept from Voronoi tessellation, we propose to use the site (or seed) positions and radii of the beams as the DOFs for open-cell foam design. Such DOFs cover extensive design space and have clear geometrical meaning, which makes it easy to provide explicit controls (e.g. granularity). During the gradient-based optimization, the foam topology can change freely, and some seeds may even be pushed out of the shape, which greatly alleviates the challenges of prescribing a fixed underlying grid. The mechanical property of our foam is computed from its highly heterogeneous density field counterpart discretized on a background mesh, with a much improved accuracy via a new material-aware numerical coarsening method. We also explore the differentiability of the open-cell Voronoi foams w.r.t. its seed locations, and propose a local finite difference method to estimate the derivatives efficiently. We do not only show the improved foam performance of our Voronoi foam in comparison with classical topology optimization approaches, but also demonstrate its advantages in various settings, especially when the target volume fraction is extremely low

Integrated Experimental, Atomistic, and Microstructurally Based Finite Element Investigation of the Dynamic Compressive Behavior of 2139 Aluminum

The objective of this study was to identify the microstructural mechanisms related to the high strength and ductile behavior of 2139-Al, and how dynamic conditions would affect the overall behavior of this alloy. Three interrelated approaches, which span a spectrum of spatial and temporal scales, were used: (i) The mechanical response was obtained using the split Hopkinson pressure bar, for strain-rates ranging from 1.0×10^(−3) s to 1.0×10^4 s^(−1). (ii) First principles density functional theory calculations were undertaken to characterize the structure of the interface and to better understand the role played by Ag in promoting the formation of the Ω phase for several Ω-Al interface structures. (iii) A specialized microstructurally based finite element analysis and a dislocation-density based multiple-slip formulation that accounts for an explicit crystallographic and morphological representation of Ω and Θ' precipitates and their rational orientation relations were conducted. The predictions from the microstructural finite element model indicated that the precipitates continue to harden and also act as physical barriers that impede the matrix from forming large connected zones of intense plastic strain. As the microstructural FE predictions indicated, and consistent with the experimental observations, the combined effects of Θ' and Ω, acting on different crystallographic orientations, enhance the strength and ductility, and reduce the susceptibility of 2139-Al to shear strain localization due to dynamic compressive loads

Mechanics of Materials

All up-to-date engineering applications of advanced multi-phase materials necessitate a concurrent design of materials (including composition, processing routes, microstructures and properties) with structural components. Simulation-based material design requires an intensive interaction of solid state physics, material physics and chemistry, mathematics and information technology. Since mechanics of materials fuses many of the above fields, there is a pressing need for well founded quantitative analytical and numerical approaches to predict microstructure-process-property relationships taking into account hierarchical stationary or evolving microstructures. Owing to this hierarchy of length and time scales, novel approaches for describing/ modelling non-equilibrium material evolution with various degrees of resolution are crucial to linking solid mechanics with realistic material behavior. For example, approaches such as atomistic to continuum transitions (scale coupling), multiresolution numerics, and handshaking algorithms that pass information to models with different degrees of freedom are highly relevant in this context. Many of the topics addressed were dealt with in depth in this workshop

Real-time simulation and visualisation of cloth using edge-based adaptive meshes

Real-time rendering and the animation of realistic virtual environments and characters has progressed at a great pace, following advances in computer graphics hardware in the last decade. The role of cloth simulation is becoming ever more important in the quest to improve the realism of virtual environments. The real-time simulation of cloth and clothing is important for many applications such as virtual reality, crowd simulation, games and software for online clothes shopping. A large number of polygons are necessary to depict the highly exible nature of cloth with wrinkling and frequent changes in its curvature. In combination with the physical calculations which model the deformations, the effort required to simulate cloth in detail is very computationally expensive resulting in much diffculty for its realistic simulation at interactive frame rates. Real-time cloth simulations can lack quality and realism compared to their offline counterparts, since coarse meshes must often be employed for performance reasons. The focus of this thesis is to develop techniques to allow the real-time simulation of realistic cloth and clothing. Adaptive meshes have previously been developed to act as a bridge between low and high polygon meshes, aiming to adaptively exploit variations in the shape of the cloth. The mesh complexity is dynamically increased or refined to balance quality against computational cost during a simulation. A limitation of many approaches is they do not often consider the decimation or coarsening of previously refined areas, or otherwise are not fast enough for real-time applications. A novel edge-based adaptive mesh is developed for the fast incremental refinement and coarsening of a triangular mesh. A mass-spring network is integrated into the mesh permitting the real-time adaptive simulation of cloth, and techniques are developed for the simulation of clothing on an animated character

Preserving Topology and Elasticity for Embedded Deformable Models

International audienceIn this paper we introduce a new approach for the embedding of linear elastic deformable models. Our technique results in significant improvements in the efficient physically based simulation of highly detailed objects. First, our embedding takes into account topological details, that is, disconnected parts that fall into the same coarse element are simulated independently. Second, we account for the varying material properties by computing stiffness and interpolation functions for coarse elements which accurately approximate the behaviour of the embedded material. Finally, we also take into account empty space in the coarse embeddings, which provides a better simulation of the boundary. The result is a straightforward approach to simulating complex deformable models with the ease and speed associated with a coarse regular embedding, and with a quality of detail that would only be possible at much finer resolution