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Abstract:
We provide an optimization framework that is capable of identifying the material parameters and contact traction field from two measured deformed geometries of a soft body in contact. The novelty of the framework is the idea of parametrizing the missing contact traction field and incorporating it into the inverse+forward hyper-elasticity formulation. We provide the continuum- and finite element formulation of the framework, as well as the direct differentiation method of sensitivity analysis to efficiently obtain necessary gradients for the BFGS optimizer. The correctness of the formulation and the excellent performance of the framework are confirmed by a series of benchmark numerical examples.

Keywords:
Hyper-elasticity, Inverse form, Large strains, Contact, Calibration, Soft bodies

Abstract:
Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use remains a significant challenge when dealing with real-world complex examples. In this work, we demonstrate three types of neural network architectures for efficient learning of highly non-linear deformations of solid bodies. The first two architectures are based on the recently proposed CNN U-NET and MAgNET (graph U-NET) frameworks which have shown promising performance for learning on mesh-based data. The third architecture is Perceiver IO, a very recent architecture that belongs to the family of attention-based neural networks–a class that has revolutionised diverse engineering fields and is still unexplored in computational mechanics. We study and compare the performance of all three networks on two benchmark examples, and show their capabilities to accurately predict the non-linear mechanical responses of soft bodies.

Keywords:
surrogate modeling, deep learning-artificial neural network, CNN U-NET, graph U-net, perceiver IO, finite element method

Abstract:
For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can we be about their predictions. In the present work, we propose a highly efficient deep-learning surrogate framework that is able to accurately predict the response of bodies undergoing large deformations in real-time. The surrogate model has a convolutional neural network architecture, called U-Net, which is trained with force–displacement data obtained with the finite element method. We propose deterministic and probabilistic versions of the framework. The probabilistic framework utilizes the Variational Bayes Inference approach and is able to capture all the uncertainties present in the data as well as in the deep-learning model. Based on several benchmark examples, we show the predictive capabilities of the framework and discuss its possible limitations.

Keywords:
convolutional neural network, Bayesian inference, Bayesian deep learning, large deformations, finite element method, real-time simulations

Abstract:
Being able to reposition tumors from prone imaging to supine surgery stances is key for bypassing current invasive marking used for conservative breast surgery. This study aims to demonstrate the feasibility of using Digital Volume Correlation (DVC) to measure the deformation of a female quarter thorax between two different body positioning when subjected to gravity. A segmented multipart mesh (bones, cartilage and tissue) was constructed and a three-step FE-based DVC procedure with heterogeneous elastic regularization was implemented. With the proposed framework, the large displacement field of a hard/soft breast sample was recovered with low registration residuals and small error between the measured and manually determined deformations of phase interfaces. The present study showed the capacity of FE-based DVC to faithfully capture large deformations of hard/soft tissues.

Keywords:
Digital Volume Correlation, Elastic regularization, Hard/soft tissues, Large displacements, Kinematic fields, X-ray tomography

Abstract:
We present a distributed framework for predicting whether a planned reconfiguration step of a modular robot will mechanically overload the structure, causing it to break or lose stability under its own weight. The algorithm is executed by the modular robot itself and based on a distributed iterative solution of mechanical equilibrium equations derived from a simplified model of the robot. The model treats intermodular connections as beams and assumes no-sliding contact between the modules and the ground. We also provide a procedure for simplified instability detection. The algorithm is verified in the Programmable Matter simulator VisibleSim, and in real-life experiments on the modular robotic system Blinky Blocks.

Keywords:
distributed algorithms, modular robots, mechanical constraints, programmable matter, self-reconfiguration

Abstract:
Large-scale 3D autonomous self-reconfigurable modular robots are made of numerous interconnected robotic modules that operate in a close packing. The modules are assumed to have their own CPU and memory, and are only able to communicate with their direct neighbors. As such, the robots embody a special computing architecture: a distributed memory and distributed CPU system with a local messagepassing interface. The modules can move and rearrange themselves changing the robot's connection topology. This may potentially cause mechanical failures (e.g., overloading of some inter-modular connections), which are irreversible and need to be detected in advance. In the present contribution, we further develop the idea of performing model-based detection of mechanical failures, posed in the form of balance equations solved by the modular robot itself in a distributed manner. A special implementation of the Conjugate Gradient iterative solution method is proposed and shown to greatly reduce the required number of iterations compared with the weighted Jacobi method used previously. The algorithm is verified in a virtual test bed—the VisibleSim emulator of the modular robot. The assessments of time-, CPU-, communication- and memory complexities of the proposed scheme are provided.

Abstract:
Summary We present a computational scheme for predicting whether addition of new modules to an existing modular robotic structure will mechanically overload the system, causing it to break or lose stability. The algorithm is executed by the modular robot itself in a distributed way, and relies on the iterative solution of mechanical equilibrium equations derived from a simple Finite Element model of the robot. In the model, inter-modular connections are represented as beams and the contact between modules and external supports is accounted for by a predictor-corrector scheme. The algorithm is verified through simulations in the Programmable Matter simulator VisibleSim and real-life experiments on the modular robotic system Blinky Blocks.