Experimental and numerical study of the relaxation behavior of facial soft tissue

Challenges in computational simulation of the mechanical behavior of soft tissues and organs for clinical applications are related to the reliability of the models with respect to the anatomy, the mechanical interactions between different tissues, and the non linear (time dependent) force deformation characteristics of soft biological materials. In this paper a 3D finite element model of the face and neck, which has applications in surgical devices optimization and surgery planning, is presented. Bones, muscles, skin, fat, and superficial muscoloaponeurotic system (SMAS) were reconstructed from magnetic resonance images and their shape, constraints and interactions have been modeled according to anatomical, plastic and reconstructive surgery literature. Non linear time dependent constitutive equations are implemented in the numerical model, based on the Rubin-Bodner model. For the present calculations a simplified hyperelastic formulation has been used. The corresponding model parameters were selected according to previous work with mechanical measurements ex vivo on facial soft tissue. For determination of model parameters, in particular the ones corresponding to the time dependent behavior, an instrument for measuring the relaxation behavior of the face tissue in vivo was developed. The experimental set-up is described and results are presented for tests performed on different locations of the face (jaw, mid-face, parotid regions) and neck. The measured “long term” reaction force of the facial soft tissue is compared to numerical results. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A polygonal finite element formulation for modeling nearly incompressible materials

The objective of the present paper is to develop a finite element formulation for modeling nearly incompressible materials at large strains using polygonal elements. The present finite element formulation is a simplified version of the three-field mixed formulation and, in particular, it reduces the functional of the internal potential energy by expressing the field of the average volume-change in terms of the displacement field, where the latter is discretized using the Wachspress shape functions. The reduced mixed formulation eliminates the volumetric locking in nearly incompressible materials and enhances the computational efficiency as the static condensation is circumvented. A detailed implementation of the finite element formulation is presented in this study. Also, different example problems, including eigenvalue analysis, nonlinear patch test and other benchmark problems are presented for demonstrating the accuracy and the reliability of the developed formulation for polygonal elements.

     

Intraoperative mechanical characterization of human liver

The tissue aspiration experiment, the instrumentation for intraoperative measurements and the procedure for quantitative evaluation of the measurement results are presented. This experiment is currently used in a clinical study on the correlation between the mechanical properties of liver tissue and its histopathologic state. To date the liver of 25 patients has been tested. The results indicate a difference of 40% in the initial stiffness between peritumoral normal liver tissue and liver tumor. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Physically Based Invariants for Nonlinear Elastic Orthotropic Solids

Hydrostatic loading causes an isotropic elastic solid to be in a state of pure dilatation with no distortion relative to its unstressed reference configuration. Similarly, hydrostatic loading causes a general orthotropic solid to be distorted relative to its unstressed reference configuration. This paper introduces physically based invariants for orthotropic nonlinear elastic solids which are measures of distortions that cause deviatoric Cauchy stress. Specifically, these invariants allow for the modeling of the distortion in a hydrostatic state of stress independently of the form of the strain energy function. Consequently, use of these invariants may lead to simpler forms of the strain energy function which adequately model specific orthotropic solids.      

Modeling of skin anisotropy directions for identifying stress free reference configuration of the female breast

Biomechanical simulations of the female breast are important for surgical applications such as implants augmentation, tumorectomy and reconstruction after the tumor removal. One of the main challenges for such breast simulations is to define its reference configuration which can be considered as a stress free state. Indeed, MRI (Magnetic Resonance Imaging) scans of the breast can be obtained only under gravitational load which introduces a considerable stress and strains level for any position of the patient. Moreover, realistic material properties especially anisotropy of skin should be taken into account. This anisotropy can play an important role but has not so far been considered in biomechanical simulations of the breast. In the current contribution, we implement an iterative method to define the reference configuration of the breast model according to MRI data of certain individuals in the prone position by taking into account the anisotropy directions of skin. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On non-physical response in models for fiber-reinforced hyperelastic materials

Soft biological tissues are sometimes composed of thin and stiff collagen fibers in a soft matrix leading to a strong anisotropy. Commonly, constitutive models for quasi-incompressible materials, as for soft biological tissues, make use of an additive split of the Helmholz free-energy into a volumetric and a deviatoric part that is applied to the matrix and fiber contribution. This split offers conceptual and numerical advantages. The purpose of this paper is to investigate a non-physical effect that arises thereof. In fact, simulations involving uniaxial stress configurations reveal volume growth at rather small stretches. Numerical methods such as the Augmented Lagrangian method might be used to suppress this behavior. An alternative approach, proposed here, solves this problem on the constitutive level.     

Stability of imperfect stiffened conical shells

A general procedure is developed for stability of stiffened conical shells. It is used for studying the sensitivity behavior with respect to the stiffener configurations. The effect of the pre-buckling nonlinearity on the bifurcation point, as well as the limit-point load level, is examined. The unique algorithm presented by the authors is an extended version of an earlier one, adapted for determination of the limit-point load level of imperfect conical shells. The eigenvalue problem is iteratively solved with respect to the nonlinear equilibrium state up to the bifurcation point or to the limit-point load level.A general symbolic code (using MAPLE) was programmed to create the differential operators based on Donnell’s type shell theory. Then the code uses the Galerkin procedure, the Newton–Raphson procedure, and a finite difference scheme for automatic development of an efficient FORTRAN code which is used for the parametric study.     

Further Developments of Physically Based Invariants for?Nonlinear Elastic Orthotropic Solids

Recently, Rubin and Jabareen (J.?Elast. 90:1?C18, 2008) introduced six physically based invariants for nonlinear elastic orthotropic solids which are measures of distortions that cause deviatoric Cauchy stress. Three of these invariants include three dependent functions that characterize the distortion in a hydrostatic state of stress. In particular, these invariants can be used without the need to place additional restrictions on the strain energy function to model the distortion in a hydrostatic state of stress. The objective of this research note is to modify the definitions of the remaining three invariants. These new invariants have clear physical interpretations that can be measured in experiments.     

A general finite plasticity model with a smooth elastic-plastic transition and isotropic hardening. A finite element formulation and numerical verification

A number of approaches for finite deformation elastoplasticity with different classes of kinematic decomposition have been published in the literature (e.g. additive split of the Lagrange strain, multiplicative split of the deformation gradient, additive split of the rate of deformation, etc.). In the present work, a general theoretical framework for modeling a smooth elastic inelastic transition for large deformations of rate independent elastic-plastic and rate dependent elastic-viscoplastic materials has been proposed. It is well known that in classical rate independent elastic-plastic models the transition from the elastic regime to the plastic regime is rather sharp, while in the present model this transition is smooth and both rate independent and rate dependent models are characterized by overstress. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)