In this paper a novel strategy is presented for the real-time simulation of contact between non-linear deformable solids at haptic feedback rates. The proposed method is somehow related to the Voxmap Pointshell method for two deformable solids. Its novelty and crucial advantages over existing implementations of this algorithm come from the intensive use of computational vademecums. These are in essence a pre-computed solution of a parametric model in which every possible situation during the on-line phase of the method has been considered through the introduction of the appropriate parameters. Such a high-dimensional parametric model is efficiently solved by using Proper Generalized Decompositions (PGD) and stored in memory as a set of vectors. The paper presents a thorough description of the developed algorithm together with some examples of its performance.
Summary A new method for the real‐time simulation of surgical cutting in haptic environments is presented. It is based on the intensive use of computational vademecums, that is, a sort of computational parametric meta‐model, which is computed offline and only evaluated online. Therefore, the necessary time savings are obtained, allowing for feedback responses on the order of kilohertz. Such a high‐dimensional, parametric solution of the problem is computed by employing proper generalized decomposition for the offline phase of the method, along with X‐FEM techniques for the incorporation of the discontinuities in the displacement field after cutting, in the online phase. A thorough description of the proposed method, along with examples of its performance in the simulation of corneal surgery, are provided. Copyright © 2016 John Wiley & Sons, Ltd.
In this paper we present the basics of a novel methodology for the development of simulation-based and augmented learning tools in the context of applied science and engineering. It is based on the extensive use of model order reduction, and particularly, of the so-called Proper Generalized Decomposition (PGD) method. This method provides a sort of meta-modeling tool without the need for prior computer experiments that allows the user to obtain real-time response in the solution of complex engineering or physical problems. This real-time capability also allows for its implementation in deployed, touch-screen, handheld devices or even to be immersed into electronic textbooks. We explore here the basics of the proposed methodology and give examples on a few challenging applications never until now explored, up to our knowledge.Peer ReviewedPostprint (author's final draft
We present a method for the real-time, interactive simulation of tissue tearing during laparoscopic surgery. The method is designed to work at haptic feedback rates (ie, around 1 kHz). Tissue tearing is simulated under the general framework of continuum damage mechanics. The problem is stated as a general, multidimensional parametric problem, which is solved by means of proper generalized decomposition methods. One of the main novelties is the reduction of history-dependent problems, such as damage mechanics, by resorting to an approach in which a reduced-order field of initial damage values is considered as a parameter of the formulation. We focus on the laparoscopic cholecystectomy procedure as a general example of the performance of the method.
A novel data-driven real-time procedure based on diffuse approximation is proposed to characterize the mechanical behavior of liquid-core microcapsules from their deformed shape and identify the mechanical properties of the submicron-thick membrane that protects the inner core through inverse analysis. The method first involves experimentally acquiring the deformed shape that a given microcapsule takes at steady state when it flows through a microfluidic microchannel of comparable cross-sectional size. From the mid-plane capsule profile, we deduce two characteristic geometric quantities that uniquely characterize the shape taken by the microcapsule under external hydrodynamic stresses. To identify the values of the unknown rigidity of the membrane and of the size of the capsule, we compare the geometric quantities with the values predicted numerically using a fluid-structure-interaction model by solving the three-dimensional capsule-flow interactions. The complete numerical data set is obtained off-line by systematically varying the governing parameters of the problem, i.e. the capsule-to-tube confinement ratio, and the capillary number, which is the ratio of the viscous to elastic forces. We show that diffuse approximation efficiently estimates the unknown mechanical resistance of the capsule membrane. We validate the data-driven procedure by applying it to the geometric and mechanical characterization of ovalbumin microcapsules (diameter of the order of a few tens of microns). As soon as the capsule is sufficiently deformed to exhibit a parachute shape at the rear, the capsule size and surface shear modulus are determined with an accuracy of 0.2% and 2.7%, respectively, as compared with 2–3% and 25% without it, in the best cases (Hu et al. Characterizing the membrane properties of capsules flowing in a square-section microfluidic channel: Effects of the membrane constitutive law. Phys Rev E 2013; 87(6): 063008). Diffuse approximation thus allows the capsule size and membrane elastic resistance to be provided quasi-instantly with very high precision. This opens interesting perspectives for industrial applications that require tight control of the capsule mechanical properties in order to secure their behavior when they transport active material.
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