Microplane constitutive model and computational framework for blood vessel tissue

This paper presents a nonlinearly elastic anisotropic microplane formulation in 3D for computational constitutive modeling of arterial soft tissue in the passive regime. The constitutive modeling of arterial (and other biological) soft tissue is crucial for accurate finite element calculations, which in turn are essential for design of implants, surgical procedures, bioartificial tissue, as well as determination of effect of progressive diseases on tissues and implants. The model presented is defined at a lower scale (mesoscale) than the conventional macroscale and it incorporates the effect of all the (collagen) fibers which are anisotropic structural components distributed in all directions within the tissue material in addition to that of isotropic bulk tissue. It is shown that the proposed model not only reproduces Holzapfel's recent model but also improves on it by accounting for the actual three-dimensional distribution of fiber orientation in the arterial wall, which endows the model with advanced capabilities in simulation of remodeling of soft tissue. The formulation is flexible so that its parameters could be adjusted to represent the arterial wall either as a single material or a material composed of several layers in finite element analyses of arteries. Explicit algorithms for both the material subroutine and the explicit integration with dynamic relaxation of equations of motion using finite element method are given. To circumvent the slow convergence of the standard dynamic relaxation and small time steps dictated by the stability of the explicit integrator, an adaptive dynamic relaxation technique that ensures stability and fastest possible convergence rates is developed. Incompressibility is enforced using penalty method with an updated penalty parameter. The model is used to simulate experimental data from the literature demonstrating that the model response is in excellent agreement with the data. An experimental procedure to determine the distribution of fiber directions in 3D for biological soft tissue is suggested in accordance with the microplane concept. It is also argued that this microplane formulation could be modified or extended to model many other phenomena of interest in biomechanics.