Finite strain poro-hyperelasticity: an asymptotic multi-scale ALE-FSI approach supported by ANNs

in Computational Mechanics (2023)

This contribution introduces and discusses a formulation of poro-hyperelasticity at finite strains. The prediction of the time-dependent response of such media requires consideration of their ... [more ▼]

This contribution introduces and discusses a formulation of poro-hyperelasticity at finite strains. The prediction of the time-dependent response of such media requires consideration of their characteristic multi-scale and multi-physics parameters. In the present work this is achieved by formulating a non-dimensionalised fluid–solid interaction problem (FSI) at the pore level using an arbitrary Lagrange–Euler description (ALE). The resulting coupled systems of PDEs on the reference configuration are expanded and analysed using the asymptotic homogenisation technique. This approach yields three partially novel systems of PDEs: the macroscopic/effective problem and two supplementary microscale problems (fluid and solid). The latter two provide the microscopic response fields whose average value is required in real-time/online form to determine the macroscale response (a concurrent multi-scale approach). In order to overcome the computational challenges related to the above multi-scale closure, this work introduces a surrogate approach for replacing the direct numerical simulation with an artificial neural network. This methodology allows for solving finite strain (multi-scale) porohyperelastic problems accurately using direct automated differentiation through the strain energy. Optimal and reliable training data sets are produced from direct numerical simulations of the fully-resolved problem by including a simple real-time output density check for adaptive sampling step refinement. The data-driven approach is complemented by a sensitivity analysis of the RVE response. The significance of the presented approach for finite strain poro-elasticity/poro-hyperelasticity is shown in the numerical benchmark of a multi-scale confined consolidation problem. Finally, to show the robustness of the method, the system response is dimensionalised using characteristic values of soil and brain mechanics scenarios. [less ▲]

A Reissner-Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations

E-print/Working paper (2023)

In this work we develop new finite element discretisations of the shear-deformable Reissner--Mindlin plate problem based on the Hellinger-Reissner principle of symmetric stresses. Specifically, we use ... [more ▼]

In this work we develop new finite element discretisations of the shear-deformable Reissner--Mindlin plate problem based on the Hellinger-Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to discretise the bending moments in the space of symmetric square integrable fields with a square integrable divergence. The latter results in highly accurate approximations of the bending moments M and in the rotation field being in the discontinuous Lebesgue space , such that the Kirchhoff-Love constraint can be satisfied for t tending to zero. In order to preserve optimal convergence rates across all variables for the case t tending to zero, we present an extension of the formulation using Raviart-Thomas elements for the shear stress. We prove existence and uniqueness in the continuous setting and rely on exact complexes for inheritance of well-posedness in the discrete setting. This work introduces an efficient construction of the Hu-Zhang base functions on the reference element via the polytopal template methodology and Legendre polynomials, making it applicable to hp-FEM. The base functions on the reference element are then mapped to the physical element using novel polytopal transformations, which are suitable also for curved geometries. The robustness of the formulations and the construction of the Hu-Zhang element are tested for shear-locking, curved geometries and an L-shaped domain with a singularity in the bending moments. Further, we compare the performance of the novel formulations with the primal-, MITC- and recently introduced TDNNS methods. [less ▲]

Nonlinear analysis of thin-walled structures based on tangential differential calculus with FEniCSx

Scientific Conference (2022, August)

We present an approach to implement the Tangential Differential Calculus (TDC) for a variety of thin-walled structures (beams, membranes, shells) in the framework of nonlinear kinematics and/or material ... [more ▼]

We present an approach to implement the Tangential Differential Calculus (TDC) for a variety of thin-walled structures (beams, membranes, shells) in the framework of nonlinear kinematics and/or material behaviour. In contrast to classical formulations the TDC describes kinematics, equilibrium and constitutive relation of the thin structure (as two-dimensional manifold) on the basis of a full three-dimensional deformation state. This allows to introduce the undeformed configuration of e.g. a shell directly in terms of a mesh of topological dimension 2 and geometrical dimension 3. Of particular interest is the use of finite elements of higher-order geometrical order to capture the (interpolated) curvature of the manifold with high accuracy. Numerical examples and reference implementations of this work to support nonlinear stress and post-buckling analyses (using a realisation of the classical arc-length method in FEniCSx) will be provided as a part of the package dolfiny (https://github.com/michalhabera/dolfiny). [less ▲]

Data-driven constitutive laws for hyperelasticity in principal space: numerical challenges and remedies

Presentation (2022, April 04)

This contribution discusses a formalism for data-driven modelling of advanced materials with a special interest in the large deformation response of three-dimensional specimens. The underlying ... [more ▼]

This contribution discusses a formalism for data-driven modelling of advanced materials with a special interest in the large deformation response of three-dimensional specimens. The underlying hyperelastic deformation problem is formulated in the principal space using principal stretches and principal stresses. The associated constitutive relation is consequently using principal quantities and captured by the parameter-free representation using a deep neural network. The presentation investigates certain physics-motivated requirements imposed on the architecture of the artificial neural network such as symmetry and objectivity criteria. The training phase of the constitutive ANN operator employs a loss function which ensures the identified consistency conditions. The prediction phase exploits a constitutive blending approach to stabilise the numerical solution procedure in the presence of typically local stretch/stress extrema. The presented approach is implemented using FEniCS and builds on symbolic representation of the ANN operator based on the Unified Form Language (UFL). The neural network is constructed, trained, and tested using PyTorch. Numerical benchmarks demonstrate the ability of the presented formalism to describe non-trivial load-deformation trajectories of 3D test specimens. [less ▲]

AI-supported Modelling of Brain tissue as Soft Multiscale Multiphysics (Poroelastic) medium

Presentation (2022, January)

Modeling and simulation of thin-walled piezoelectric energy harvesters immersed in flow using monolithic fluid–structure interaction

in Finite Elements in Analysis and Design (2022), 206

Simulation of gas-dynamic, pressure surges and adiabatic compression phenomena in geometrically complex respirator oxygen valves

in Thermal Science and Engineering Progress (2021), 24

Gas-dynamic pressure surges and adiabatic compression phenomena are generally hard to predict numerically. In this contribution, we study the effect of the pressure reserve capacity on the compressible ... [more ▼]

Gas-dynamic pressure surges and adiabatic compression phenomena are generally hard to predict numerically. In this contribution, we study the effect of the pressure reserve capacity on the compressible gas-dynamics pressure surge and adiabatic compression in a fitted respirator oxygen valve geometry. A three-dimensional remeshed smoothed particle hydrodynamics method for the simulation of isotropic turbulence is used, the method is coupled with Brinkman penalisation technique for flow simulation inside the complex valve geometry. Simulations are carried out for three different pressure reserve quantities, to replicate the opening of the valve, two time-based pressure inlet boundary condition functions were simulated along with an impulsively started scenario. A geometrical sensitivity analysis is provided, where the simulation is performed on a modified valve design which exhibits a damping effect on the gas dynamics and flow characteristics, which has a favourable effect on the valve functionality and safety. It is found that the capacity of the pressure reserve has a considerable effect on the simulated flow fields (velocity, temperature), as the temperature could rise 6.0X the reference temperature, and up to 2.7X the reference velocity. The numerical results are compared with a previous study carried out by Rotarex S.A., demonstrating that the remeshed particle-mesh method coupled with Brinkman penalisation provides a good quality simulation and the results are in agreement with the reference solution. [less ▲]

Multiphysics Modelling of Flow-Driven Piezoelectric Energy Harvesters

Poster (2021, May 21)

ANN-aided incremental multiscale-remodelling-based finite strain poroelasticity

in Computational Mechanics (2021)

Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical ... [more ▼]

Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only straightforward assuming infinitesimal strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental numerical approach that considers rearrangement of the cell properties based on its current deformation, which leads to the remodelling of the macroscopic model after each time increment. This computational framework is valid for finite strain and large deformation problems while it ensures infinitesimal strain increments within time steps. The full effects of the interdependency between the properties and response of macro and micro scales are considered for the first time providing a more accurate predictive analysis of fluid-saturated porous media which is studied via a numerical consolidation example. Furthermore, the (nonlinear) deviation from Darcy’s law is captured in fluid filtration numerical analyses. Finally, the brain tissue mechanical response under the uniaxial cyclic test is simulated and studied. [less ▲]

Frictional interactions for non-localised beam-to-beam and beam-inside-beam contact

in International Journal for Numerical Methods in Engineering (2021), 122(7), 1706-1731

This contribution presents the extensions of beam-to-beam and beam-inside-beam contact schemes of the same authors towards frictional interactions. Since the schemes are based on the beams’ true surfaces ... [more ▼]

This contribution presents the extensions of beam-to-beam and beam-inside-beam contact schemes of the same authors towards frictional interactions. Since the schemes are based on the beams’ true surfaces (instead of surfaces implicitly deduced from the beams’ centroid lines), the presented enhancements are not only able to account for frictional sliding in the beams’ axial directions, but also in the circumferential directions. Both the frictional beam-to-beam approach as well as the frictional beam-inside-beam approach are applicable to shear-deformable and shear-undeformable beams, as well as to beams with both circular and elliptical cross-sections (although the cross-sections must be rigid). A penalty formulation is used to treat unilateral and frictional contact constraints. FE implementation details are discussed, where automatic differentiation techniques are used to derive the implementations. Simulations involving large sliding displacements and large deformations are presented for both beam-to-beam and beam-inside-beam schemes. All simulation results are compared to those of the frictionless schemes. [less ▲]