Computational method for excluding fibers under compression in modeling soft fibrous solids

Abstract

Abstract. Soft fibrous solids often consist of a matrix reinforced by fibers that render the material anisotropic. Recently a fiber dispersion model was proposed on the basis of a weighted strain-energy function using an angular integration approach for both planar and three-dimensional fiber dispersions (G.A. Holzapfel and R.W. Ogden: Eur. J. Mech. A/Solids, 49 (2015) 561-569). This model allows the exclusion of fibers under compression. In the present study computational aspects of the model are documented. In particular, we provide expressions for the elasticity tensor and the integration boundary that admits only fibers which are extended. In addition, we give a brief description of the finite element implementation for both 2D and 3D models which make use of the von Mises distribution to describe the dispersion of the fibers.The performance and the finite element implementations of the 2D and 3D fiber dispersion models are illustrated by means of uniaxial extension in the mean fiber direction and more general directions, and simple shear with different mean fiber directions. The finite element results are in perfect agreement with the solutions computed from analytical formulas.

An exponential constitutive model excluding fibres under compression: Application to extension–inflation of a residually stressed carotid artery

“…This model incorporates a weighted strain-energy function and enables the Cauchy stress and elasticity tensors to be evaluated in a straightforward way. In addition, we have also discussed the integration boundary of the region that admits only extended fibers under any deformation state [23], implemented this model in the finite element analysis program FEAP [24] and verified it with several numerical examples. However, in that study, for purposes of illustration of the method, we demonstrated the new fiber dispersion model [17] by using a simple quadratic form of strain-energy function, namely the standard fiber-reinforcing model [25], for the fiber contribution.…”

“…However, the quadratic form of the strain-energy function is not able to capture the highly nonlinear mechanical response of some soft biological tissues such as arterial tissues, and an exponential form of the strain-energy function is more suitable for those tissues [15,26]. This can be verified by fitting the constitutive law documented in [23], which is based on the standard fiber-reinforcing model, to experimental data of of arterial tissue. It is impossible to accurately fit the highly nonlinear behavior of soft tissues, like the one in Section 3.3, by using the quadratic strain-energy function for fibers.…”

“…In Section 2 we present the continuum mechani-cal framework of the proposed constitutive model with exclusion of compressed fibers from the total strain energy in a decoupled form suitable for computational implementation, including the expressions of Cauchy stress and the elasticity tensors for 3D fiber distribution. In Section 3 the theory of Section 2 is applied to several representative examples by using the finite element based numerical integration scheme from [23]. In particular, three numerical simulations are presented with the goal of demonstrating the efficacy of the proposed constitutive model and its computational implementation.…”

On Fiber Dispersion Models: Exclusion of Compressed Fibers and Spurious Model Comparisons

“…Indeed a simple procedure for excluding fibers in compression in the GST approach forms the first part of the content of the present paper. This also complements our analysis of the exclusion procedure in the AI approach contained in [10] and its implementation described in [11]. It should also be mentioned that recently an approach to exclusion of fibers in the GST model based on the use of a Heaviside function was developed in [12].…”

“…The GST model has also been used in considering inelastic effects such as damage in, e.g., [16] and [17]. We emphasize that we have already provided a detailed analysis of the exclusion of compressed fibers for the AI approach in [10], [11]; however, it seems that the AI approach has not been implemented in commercially available finite element programs.…”