A generalized orthotropic hyperelastic material model with application to incompressible shells

In the present paper a new orthotropic hyperelastic constitutive model is proposed which can be applied to the numerical simulation of a wide range of anisotropic materials and particularly biological soft tissues. The model represents a non‐linear extension of the orthotropic St. Venant–Kirchhoff material and is described in each principal material direction by an arbitrary isotropic tensor function coupled with the corresponding structural tensor. In the special case of isotropy this constitutive formulation reduces to the Valanis–Landel hypothesis and may therefore be considered as its generalization to the case of orthotropy. Constitutive relations and tangent moduli of the model are expressed in terms of eigenvalue bases of the right Cauchy–Green tensor C and obtained for the case of distinct and coinciding eigenvalues as well. For the analysis of shells the model is then coupled with a six (five in incompressible case) parametric shell kinematics able to deal with large strains as well as finite rotations. The application of the developed finite shell element is finally illustrated by a number of numerical examples. Copyright © 2001 John Wiley & Sons, Ltd.     

High performance computing of discrete nonsmooth contact dynamics with domain decomposition

We investigate two algorithms for solving large‐scale granular problems using DD methods. These numerical schemes can be connected to classical DDs, with and without overlapping, developed in continuum mechanics. The two algorithms are compared in terms of implementation and parallel performance. We focus the numerical study on communication procedures between processors, load balancing, and scalability, topics particularly crucial in nonlinear evolutive problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Fast reconstruction of optical properties for complex segmentations in near infrared imaging

The intrinsic ill-posed nature of the inverse problem in near infrared imaging makes the reconstruction of fine details of objects deeply embedded in turbid media challenging even for the large amounts of data provided by time-resolved cameras. In addition, most reconstruction algorithms for this type of measurements are only suitable for highly symmetric geometries and rely on a linear approximation to the diffusion equation since a numerical solution of the fully non-linear problem is computationally too expensive. In this paper, we will show that a problem of practical interest can be successfully addressed making efficient use of the totality of the information supplied by time-resolved cameras. We set aside the goal of achieving high spatial resolution for deep structures and focus on the reconstruction of complex arrangements of large regions. We show numerical results based on a combined approach of wavelength-normalized data and prior geometrical information, defining a fully parallelizable problem in arbitrary geometries for time-resolved measurements. Fast reconstructions are obtained using a diffusion approximation and Monte-Carlo simulations, parallelized in a multicore computer and a GPU respectively.     

Inexact FETI‐DP methods

Inexact FETI‐DP domain decomposition methods are considered. Preconditioners based on formulations of FETI‐DP as a saddle point problem are used which allow for an inexact solution of the coarse problem. A positive definite reformulation of the preconditioned saddle point problem, which also allows for approximate solvers, is considered as well. In the formulation that iterates on the original FETI‐DP saddle point system, it is also possible to solve the local Neumann subdomain problems inexactly. Given good approximate solvers for the local and coarse problems, convergence bounds of the same quality as for the standard FETI‐DP methods are obtained. Numerical experiments which compare the convergence of the inexact methods with that of standard FETI‐DP are shown for 2D and 3D elasticity using GMRES and CG as Krylov space methods. Based on parallel computations, a comparison of one variant of the inexact FETI‐DP algorithms and the standard FETI‐DP method is carried out and similar parallel performance is achieved. Parallel scalability of the inexact variant is also demonstrated. It is shown that for a very large number of subdomains and a very large coarse problem, the inexact method can be superior. Copyright © 2006 John Wiley & Sons, Ltd.     

A Comparative Study of Several Material Models for Prediction of Hyperelastic Properties: Application to Silicone-Rubber and Soft Tissues

Abstract:  The correct modelling of constitutive laws is of critical importance for the analysis of mechanical behaviour of solids and structures. For example, the understanding of soft tissue mechanics, because of the nonlinear behaviour commonly displayed by the mechanical properties of such materials, makes common place the use of hyperelastic constitutive models. Hyperelastic models however, depend on sets of variables that must be obtained experimentally. In this study the authors use a computational/experimental scheme, for the study of the nonlinear mechanical behaviour of biological soft tissues under uniaxial tension. The material constants for seven different hyperelastic material models are obtained via inverse methods. The use of Martins's model to fit experimental data is presented in this paper for the first time. The search for an optimal value for each set of material parameters is performed by a Levenberg–Marquardt algorithm. As a control measure, the process is fully applied to silicone-rubber samples subjected to uniaxial tension tests. The fitting accuracy of the experimental stress–strain relation to the theoretical one, for both soft tissues and silicone-rubber (typically nonlinear) is evaluated. This study intents also to select which material models (or model types), the authors will employ in future works, for the analysis of human soft biological tissues.