A finite element method for non-linear hyperelasticity applied for the simulation of octopus ARM motions

An implicit non-linear finite element (FE) numerical procedure for the simulation of biological muscular tissues is presented. The method has been developed for studying the motion of muscular hydrostats, such as squid and octopus arms and its general framework is applicable to other muscular tissues. The FE framework considered is suitable for the dynamic numerical simulations of three-dimensional non-linear nearly incompressible hyperelastic materials that undergo large displacements and deformations. Human and animal muscles, consisting of fibers and connective tissues, belong to this class of materials. The stress distribution inside the muscular FE model is considered as the superposition of stresses along the muscular fibers and the connective tissues. The stresses along the fibers are modeled as the sum of active and passive stresses, according to the muscular model of Van Leeuwen and Kier (1997) Philos. Trans. R. Soc. London, 352: 551-571. Passive stress distribution is an experimentally-defined function of fibers’ deformation; while active stress distribution is the product of an activation level time function, a force-stretch function and a force-stretch ratio function. The mechanical behavior of the surrounding tissues is determined adopting a Mooney-Rivlin constitutive model. The incompressibility criterion is met by enforcing large bulk modulus and by introducing modified deformation measures. Due to the non-linear nature of the problem, approximate determination of the Jacobian matrix is performed, in order to utilize the full Newton-Raphson iterative procedure within each time-step. In addition, time discretization is performed via the implicit Newmark method. We developed an open-source finite element code that is capable of simulating large deflection maneuvers of muscular hydrostats. The proposed methodology is validated by comparing the numerical results with existing measurements for the squid arm extension. The efficiency and robustness of the proposed numerical method is demonstrated through a series of octopus arm maneuvers, such as extension, compression and bending

Computational investigation of octopus arm hydrodynamics

Existed studies of bio-inspired robotic systems navigating in fluid environments have oversimplified the effects of flow in their dynamic models, and hence the generated hydrodynamic forces. Utilizing computational fluid dynamic techniques, we investigate the hydrodynamics of the octopus arm. Large size hybrid-type meshes were constructed to accurately describe the complex geometry details and for capturing complex flow features. The results obtained will be used for assisting the design of robotic octopus prototypes and of corresponding control strategies

Propagating Dam Breach Parametric Uncertainty in a River Reach Using the HEC-RAS Software

Dam break studies consist of two submodels: (a) the dam breach submodel which derives the flood hydrograph and (b) the hydrodynamic submodel which, using the flood hydrograph, derives the flood peaks and maximum water depths in the downstream reaches of the river. In this paper, a thorough investigation of the uncertainty observed in the output of the hydrodynamic model, due to the seven dam breach parameters, is performed in a real-world case study (Papadiana Dam, located at Tavronitis River in Crete, Greece). Three levels of uncertainty are examined (flow peak of the flood hydrograph at the dam location, flow peaks and maximum water depths downstream along the river) with two methods: (a) a Morris-based sensitivity analysis for investigating the influence of each parameter on the final results; (b) a Monte Carlo-based forward uncertainty analysis for defining the distribution of uncertainty band and its statistical characteristics. Among others, it is found that uncertainty of the flow peaks is greater than the uncertainty of the maximum water depths, whereas there is a decreasing trend of uncertainty as we move downstream along the river.</jats:p

Propagating Dam Breach Parametric Uncertainty in a River Reach Using the HEC-RAS Software

Dam break studies consist of two submodels: (a) the dam breach submodel which derives the flood hydrograph and (b) the hydrodynamic submodel which, using the flood hydrograph, derives the flood peaks and maximum water depths in the downstream reaches of the river. In this paper, a thorough investigation of the uncertainty observed in the output of the hydrodynamic model, due to the seven dam breach parameters, is performed in a real-world case study (Papadiana Dam, located at Tavronitis River in Crete, Greece). Three levels of uncertainty are examined (flow peak of the flood hydrograph at the dam location, flow peaks and maximum water depths downstream along the river) with two methods: (a) a Morris-based sensitivity analysis for investigating the influence of each parameter on the final results; (b) a Monte Carlo-based forward uncertainty analysis for defining the distribution of uncertainty band and its statistical characteristics. Among others, it is found that uncertainty of the flow peaks is greater than the uncertainty of the maximum water depths, whereas there is a decreasing trend of uncertainty as we move downstream along the river

A Non-linear Dynamic Finite Element Approach for Simulating Muscular Hydrostats

An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching