Hyperelastic modelling of nonlinear running surfaces

Accurate, 3-D analyses of running impact require a constitutive model of the running surface that includes the material nonlinearity shown by many modern surfaces. This paper describes a hyperelastic continuum that mimics the experimentally measured response of a particular treadmill surface. The material model sacrifices a little accuracy to admit a robust, low-order hyperelastic strain-energy functional. This helps prevent the premature termination of finite element simulations, due to numerical or material instabilities, that can occur with higher-order functionals. With only two free constants, it is also a more practical design tool. The best fit to the quasi-static response of the treadmill was achieved with an initial shear modulus =2 MPa and a power-stiffening index =25. The paper outlines the method used to derive the material constants for the treadmill, a device that is not amenable to the usual materials laboratory tests and must be reverse-engineered. Finite element analyses were then performed to ensure that the treadmill model interacts with the other components of the multibody running system in a numerically stable and physically realistic manner. The model surface was struck by a rigid heel, cushioned by a hyperfoam material that represents a shoe midsole. The results show that, while the ground reaction force is similar to that obtained with a rigid surface, the maximum principal stress in the shoe is reduced by 15%. Such a reduction, particularly when endured over many load cycles, may have a significant effect on comfort and damage to nearby tissue

Simulation of hyperelastic materials in real-time using Deep Learning

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition, parallel computing, adaptive meshing, and model order reduction. In this paper we present U-Mesh: a data-driven method based on a U-Net architecture that approximates the non-linear relation between a contact force and the displacement field computed by a FEM algorithm. We show that deep learning, one of the latest machine learning methods based on artificial neural networks, can enhance computational mechanics through its ability to encode highly non-linear models in a compact form. Our method is applied to two benchmark examples: a cantilever beam and an L-shape subject to moving punctual loads. A comparison between our method and proper orthogonal decomposition (POD) is done through the paper. The results show that U-Mesh can perform very fast simulations on various geometries, mesh resolutions and number of input forces with very small errors

Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity

The aim of this paper is to compare a hyperelastic with a hypoelastic model describing the Eulerian dynamics of solids in the context of non-linear elastoplastic deformations. Specifically, we consider the well-known hypoelastic Wilkins model, which is compared against a hyperelastic model based on the work of Godunov and Romenski. First, we discuss some general conceptual differences between the two approaches. Second, a detailed study of both models is proposed, where differences are made evident at the aid of deriving a hypoelastic-type model corresponding to the hyperelastic model and a particular equation of state used in this paper. Third, using the same high order ADER Finite Volume and Discontinuous Galerkin methods on fixed and moving unstructured meshes for both models, a wide range of numerical benchmark test problems has been solved. The numerical solutions obtained for the two different models are directly compared with each other. For small elastic deformations, the two models produce very similar solutions that are close to each other. However, if large elastic or elastoplastic deformations occur, the solutions present larger differences.Comment: 14 figure

Anisotropic microsphere-based approach to damage in soft fibered tissue

The final publication is available at Springer via http://dx.doi.org/10.1007/s10237-011-0336-9An anisotropic damage model for soft fibered tissue is presented in this paper, using a multi-scale scheme and focusing on the directionally dependent behavior of these materials. For this purpose, a micro-structural or, more precisely, a microsphere-based approach is used to model the contribution of the fibers. The link between micro-structural contribution and macroscopic response is achieved by means of computational homogenization, involving numerical integration over the surface of the unit sphere. In order to deal with the distribution of the fibrils within the fiber, a von Mises probability function is incorporated, and the mechanical (phenomenological) behavior of the fibrils is defined by an exponential-type model. We will restrict ourselves to affine deformations of the network, neglecting any cross-link between fibrils and sliding between fibers and the surrounding ground matrix. Damage in the fiber bundles is introduced through a thermodynamic formulation, which is directly included in the hyperelastic model. When the fibers are stretched far from their natural state, they become damaged. The damage increases gradually due to the progressive failure of the fibrils that make up such a structure. This model has been implemented in a finite element code, and different boundary value problems are solved and discussed herein in order to test the model features. Finally, a clinical application with the material behavior obtained from actual experimental data is also presented.Peer ReviewedPostprint (author's final draft

Computational modelling of the behaviour of biomarker particles of colorectal cancer in fecal matter

Colorectal adenocarcinoma is one of the carcinogenic diseases that is increasing the morbidity and mortality rates worldwide. The disease initially occurs through the segregation of biomarker substances in the human system without manifesting symptoms that affect the health of the carrier. Early detection would allow the application of more effective treatments, less invasive procedures and reduce the development of cancer. The purpose of this investigation was the elaboration of a mathematical model and the development of computational simulations to visualize the behavior of biomarker particles in transit through the colon. The flow conditions, properties of the viscous medium and biological regions of interest were established. Constitutive models, numerical conditions and solution strategies were determined. A numerical grid was used to represent the model of the colon and the human feces that carry the bioparticles (biomarkers). The results indicated the trajectories of the bioparticles in the fecal mass and the interactive movement with the natural contractions of the colon. The analysis of the movement of the biomarker particles can provide future less invasive alternatives for the detection in real time of the cancer by means of the implantation of biosensors in the walls of the colon

Nonlinear effects in finite elements analysis of colorectal surgical clamping

Minimal Invasive Surgery (MIS) is a procedure that has increased its applications in past few years in different types of surgeries. As number of application fields are increasing day by day, new issues have been arising. In particular, instruments must be inserted through a trocar to access the abdominal cavity without capability of direct manipulation of tissues, so a loss of sensitivity occurs. Generally speaking, the student of medicine or junior surgeons need a lot of practice hours before starting any surgical procedure, since they have to difficulty in acquiring specific skills (hand–eye coordination among others) for this type of surgery. Here is what the surgical simulator present a promising training method using an approach based on Finite Element Method (FEM). The use of continuum mechanics, especially Finite Element Analysis (FEA) has gained an extensive application in medical field in order to simulate soft tissues. In particular, colorectal simulations can be used to understand the interaction between colon and the surrounding tissues and also between colon and instruments. Although several works have been introduced considering small displacements, FEA applied to colorectal surgical procedures with large displacements is a topic that asks for more investigations. This work aims to investigate how FEA can describe non-linear effects induced by material properties and different approximating geometries, focusing as test-case application colorectal surgery. More in detail, it shows a comparison between simulations that are performed using both linear and hyperelastic models. These different mechanical behaviours are applied on different geometrical models (planar, cylindrical, 3D-SS and a real model from digital acquisitions 3D-S) with the aim of evaluating the effects of geometric non-linearity. Final aim of the research is to provide a preliminary contribution to the simulation of the interaction between surgical instrument and colon tissues with multi-purpose FEA in order to help the preliminary set-up of different bioengineering tasks like force-contact evaluation or approximated modelling for virtual reality (surgical simulations). In particular, the contribution of this work is focused on the sensitivity analysis of the nonlinearities by FEA in the tissue-tool interaction through an explicit FEA solver. By doing in this way, we aim to demonstrate that the set-up of FEA computational surgical tools may be simplified in order to provide assistance to non-expert FEA engineers or medicians in more precise way of using FEA tools