Efficient isogeometric thin shell formulations for soft biological materials

Abstract

This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches do not need any numerical integration and so they are computationally more efficient. The formulation is designed for large deformations and allows for geometrical and material nonlinearities, which makes it very suitable for the modeling of soft tissues. Furthermore, six different isotropic and anisotropic material models, which are commonly used to model soft biological materials, are examined for the three proposed constitutive approaches. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the shell surface. Several numerical examples are investigated to demonstrate the capabilities of the formulation. Those include the contact simulation during balloon angioplasty.

Isogeometric analysis of ice accretion on wind turbine blades

“…It has since been used to solve the most challenging science and engineering applications [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. For thin structures, isogeometric shells [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] have been previously demonstrated as an effective method for the analysis of complex problems , including the analysis of composites [83][84][85][86][87][88][89][90][91][92]. Isogeometric shells have also been effectively applied to wind turbine structural [93][94][95][96]…”

A nonlinear thermomechanical formulation for anisotropic volume and surface continua

“…Tepole et al [40] and Roohbakhshan et al [41] utilize a projection method to extract a membrane constitutive law from the anisotropic three-dimensional biomaterial model of Gasser et al [42]. This projection method is extended to extract a shell formulation for composite materials and biological tissues by Roohbakhshan and Sauer [43, 44]. Here, the projection method of Roohbakhshan and Sauer [44] is extended to finite-temperature material models.…”

Simulation of angioplasty using isogoemetric laminated composite shell elements

“…Here, the isogeometric shell formulation of [2][3][4] is used to model an artery. The formulation allows for the modeling of laminated composite shells constructed from different materials, like the adventitia, media and intima layers of an artery.…”

“…the kinematics, weak form of the boundary value problem, finite element formulation and constitutive modeling are skipped here. The reader is recommended to see [2,3,5] for more details.…”