Title: Computational mechanics of hyperelastic soft tissues: numerical solver and modeling challenges
Abstract:
An important aspect of employing computational mechanics for biomechanical systems is the
constitutive modeling of soft tissues. Even after decades-long investigations into the constitutive
modeling using ex-vivo, in-vivo, and in-silico models, several challenges remain. In this talk, I will discuss
two of these challenges: 1) numerical solvers based on linearization are difficult to converge and 2)
deterministic models do not capture the uncertainty and variability in soft tissues’ mechanical response.
I will present some of the solutions we have proposed to address these challenges.
For the numerical solvers, I will present modified formulations for both forward and inverse models that
lead to improved convergence. One approach in these formulations is specific to the exponential
nonlinearity normally seen in soft tissues [1-4], while the second approach is more general, applicable to
any nonlinearity, and builds upon the Newton and Gauss-Newton methods [5].
To capture the uncertainty and variations in soft tissue mechanics, I will first present a Bayesian
approach for selecting the most probable constitutive model [6]. Lastly, I will present a new
Gaussian-process based constitutive modeling framework that provides excellent fit to the ex-vivo
data of soft tissues while facilitating a stochastic finite element solution to capture the uncertainty [7].
References:
[1] Aggarwal, Ankush, and Michael S. Sacks. “An inverse modeling approach for semilunar heart valve
leaflet mechanics: exploitation of tissue structure.” Biomechanics and modeling in mechanobiology 15
(2016): 909-932.
[2] Aggarwal, Ankush. “An improved parameter estimation and comparison for soft tissue constitutive
models containing an exponential function.” Biomechanics and modeling in mechanobiology 16.4
(2017): 1309-1327.
[3] Mei, Yue, et al. “On improving the numerical convergence of highly nonlinear elasticity problems.”
Computer Methods in Applied Mechanics and Engineering 337 (2018): 110-127.
[4] Aggarwal, Ankush. “Effect of residual and transformation choice on computational aspects of
biomechanical parameter estimation of soft tissues.” Bioengineering 6.4 (2019): 100.
[5] Aggarwal, Ankush, and Sanjay Pant. “Beyond Newton: A new root-finding fixed-point iteration for
nonlinear equations.” Algorithms 13.4 (2020): 78.
[6] Aggarwal, Ankush, et al. “A Bayesian constitutive model selection framework for biaxial mechanical
testing of planar soft tissues: Application to porcine aortic valves.” journal of the mechanical behavior of
biomedical materials 138 (2023): 105657.
[7] Aggarwal, Ankush, et al. “Strain energy density as a Gaussian process and its utilization in stochastic
finite element analysis: Application to planar soft tissues.” Computer Methods in Applied Mechanics and
Engineering 404 (2023): 115812.
