Towards Real-Time Simulation Of Hyperelastic Materials

We propose a new method for physics-based simulation supporting many different types of hyperelastic materials from mass-spring systems to three-dimensional finite element models, pushing the performance of the simulation towards real-time. Fast simulation methods such as Position Based Dynamics exist, but support only limited selection of materials; even classical materials such as corotated linear elasticity and Neo-Hookean elasticity are not supported. Simulation of these types of materials currently relies on Newton\u27s method, which is slow, even with only one iteration per timestep. In this work, we start from simple material models such as mass-spring systems or as-rigid-as-possible materials. We express the widely used implicit Euler time integration as an energy minimization problem and introduce auxiliary projection variables as extra unknowns. After our reformulation, the minimization problem becomes linear in the node positions, while all the non-linear terms are isolated in individual elements. We then extend this idea to efficiently simulate a more general spatial discretization using finite element method. We show that our reformulation can be interpreted as a quasi-Newton method. This insight enables very efficient simulation of a large class of hyperelastic materials. The quasi-Newton interpretation also allows us to leverage ideas from numerical optimization. In particular, we show that our solver can be further accelerated using L-BFGS updates (Limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm). Our final method is typically more than ten times faster than one iteration of Newton\u27s method without compromising quality. In fact, our result is often more accurate than the result obtained with one iteration of Newton\u27s method. Our method is also easier to implement, implying reduced software development costs

Bridging the computational gap between mesoscopic and continuum modeling of red blood cells for fully resolved blood flow

We present a computational framework for the simulation of blood flow with fully resolved red blood cells (RBCs) using a modular approach that consists of a lattice Boltzmann solver for the blood plasma, a novel finite element based solver for the deformable bodies and an immersed boundary method for the fluid-solid interaction. For the RBCs, we propose a nodal projective FEM (npFEM) solver which has theoretical advantages over the more commonly used mass-spring systems (mesoscopic modeling), such as an unconditional stability, versatile material expressivity, and one set of parameters to fully describe the behavior of the body at any mesh resolution. At the same time, the method is substantially faster than other FEM solvers proposed in this field, and has an efficiency that is comparable to the one of mesoscopic models. At its core, the solver uses specially defined potential energies, and builds upon them a fast iterative procedure based on quasi-Newton techniques. For a known material, our solver has only one free parameter that demands tuning, related to the body viscoelasticity. In contrast, state-of-the-art solvers for deformable bodies have more free parameters, and the calibration of the models demands special assumptions regarding the mesh topology, which restrict their generality and mesh independence. We propose as well a modification to the potential energy proposed by Skalak et al. 1973 for the red blood cell membrane, which enhances the strain hardening behavior at higher deformations. Our viscoelastic model for the red blood cell, while simple enough and applicable to any kind of solver as a post-convergence step, can capture accurately the characteristic recovery time and tank-treading frequencies. The framework is validated using experimental data, and it proves to be scalable for multiple deformable bodies

A novel approach to modelling and simulating the contact behaviour between a human hand model and a deformable object

A deeper understanding of biomechanical behaviour of human hands becomes fundamental for any human hand-operated Q2 activities. The integration of biomechanical knowledge of human hands into product design process starts to play an increasingly important role in developing an ergonomic product-to-user interface for products and systems requiring high level of comfortable and responsive interactions. Generation of such precise and dynamic models can provide scientific evaluation tools to support product and system development through simulation. This type of support is urgently required in many applications such as hand skill training for surgical operations, ergonomic study of a product or system developed and so forth. The aim of this work is to study the contact behaviour between the operators’ hand and a hand-held tool or other similar contacts, by developing a novel and precise nonlinear 3D finite element model of the hand and by investigating the contact behaviour through simulation. The contact behaviour is externalised by solving the problem using the bi-potential method. The human body’s biomechanical characteristics, such as hand deformity and structural behaviour, have been fully modelled by implementing anisotropic hyperelastic laws. A case study is given to illustrate the effectiveness of the approac

A consistent interface element formulation for geometrical and material nonlinearities

Decohesion undergoing large displacements takes place in a wide range of applications. In these problems, interface element formulations for large displacements should be used to accurately deal with coupled material and geometrical nonlinearities. The present work proposes a consistent derivation of a new interface element for large deformation analyses. The resulting compact derivation leads to a operational formulation that enables the accommodation of any order of kinematic interpolation and constitutive behavior of the interface. The derived interface element has been implemented into the finite element codes FEAP and ABAQUS by means of user-defined routines. The interplay between geometrical and material nonlinearities is investigated by considering two different constitutive models for the interface (tension cut-off and polynomial cohesive zone models) and small or finite deformation for the continuum. Numerical examples are proposed to assess the mesh independency of the new interface element and to demonstrate the robustness of the formulation. A comparison with experimental results for peeling confirms the predictive capabilities of the formulation.Comment: 14 pages, 11 figure

Effects of finite strains in fully coupled 3D geomechanical simulations

Numerical modeling of geomechanical phenomena and geo-engineering problems often involves complex issues related to several variables and corresponding coupling effects. Under certain circumstances, both soil and rock may experience a nonlinear material response caused by, for example, plastic, viscous, or damage behavior or even a nonlinear geometric response due to large deformations or displacements of the solid. Furthermore, the presence of one or more fluids (water, oil, gas, etc.) within the skeleton must be taken into account when evaluating the interaction between the different phases of the continuum body. A multiphase three-dimensional (3D) coupled model of finite strains, suitable for dealing with solid-displacement and fluid-diffusion problems, is described for assumed elastoplastic behavior of the solid phase. Particularly, a 3D mixed finite element was implemented to fulfill stability requirements of the adopted formulation, and a permeability tensor dependent on deformation is introduced. A consolidation scenario induced by silo filling was investigated, and the effects of the adoption of finite strains are discusse