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 ▲]

Nonlinear local solver

Scientific Conference (2022, August)

Many engineering applications require solution of a global finite element problem coupled with nonlinear equations of local nature. Local in the sense, that for a known global state the local solution ... [more ▼]

Many engineering applications require solution of a global finite element problem coupled with nonlinear equations of local nature. Local in the sense, that for a known global state the local solution could be found on cell-by-cell basis. Examples include plastic deformation problems, static condensation (hybridization) of displacement-stress formulation or just a simple nonlinear constitutive laws to be satisfied at each quadrature point. These types of problems either required special libraries and extensions in order to be solved with FEniCS (and FEniCS-X) tools, or lead to very slow implementations due to hacks and tricks needed to achieve the solution (e.g. monolithic schemes which increase the matrix problem size). In this talk a unified approach tailored for the current state of FEniCS-X interfaces is presented. The approach computes consistent global tangent operator for nonlinear problems. In addition, local equations are formulated symbolically in UFL, and their derivatives are therefore computed automatically. Several low-level examples (incl. plasticity with symbolic yield surface, nonlinear static condensation and materials with implicit constitutive laws) that demonstrate the main concepts are presented. Finally, high-level wrappers for this functionality are presented. These come as a part of package `dolfiny` (https://github.com/michalhabera/dolfiny). [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

AI-aided, incremental numerical approach for fi nite strain poroelasticity: On the brain tissue deformation

Scientific Conference (2021, May 21)

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 ▲]

Thermo-mechanical coupling and part-level analysis for additive manufacturing processes

Scientific Conference (2021, January 13)

[1] Hussein, A. and Hao, L. and Yan, C. and Everson, R. Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Materials & Design ... [more ▼]

[1] Hussein, A. and Hao, L. and Yan, C. and Everson, R. Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Materials & Design (1980-2015), (2013), 52:638–647. [2] Bangerth, W. and Hartmann, R. and Kanschat, G. deal.II – a General Purpose Object Oriented Finite Element Library. ACM Trans. Math. Softw.(2007), Vol. 33., 4:24/1–24/27. [less ▲]

A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs

E-print/Working paper (2020)

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems ... [more ▼]

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs via ANNs (Artificial Neural Networks). This presented approach allows the selection of a number of locations of interest at which the state variables are expected to fulfil the governing equations associated with a physical problem. Unlike classical PDE approximation methods such as finite differences or the finite element method, there is no need to establish and reconstruct the physical field quantity throughout the computational domain in order to predict the mechanical response at specific locations of interest. The basic idea of MGA-MSGD is the manipulation of the learnable parameters’ components responsible for the error explosion so that we can train the network with relatively larger learning rates which avoids trapping in local minima. The proposed training approach is less sensitive to the learning rate value, training points density and distribution, and the random initial parameters. The distance function to minimise is where we introduce the PDEs including any physical laws and conditions (so-called, Physics Informed ANN). The Genetic algorithm is modified to be suitable for this type of ANN in which a Coarse-level Stochastic Gradient Descent (CSGD) is exploited to make the decision of the offspring qualification. Employing the presented approach, a considerable improvement in both accuracy and efficiency, compared with standard training algorithms such classical SGD and Adam optimiser, is observed. The local displacement accuracy is studied and ensured by introducing the results of Finite Element Method (FEM) at sufficiently fine mesh as the reference displacements. A slightly more complex problem is solved ensuring the feasibility of the methodology [less ▲]

Contact between shear-deformable beams with elliptical cross-sections

in Acta Mechanica (2020), 231

Slender constituents are present in many structures and materials. In associated mechanical models, each slender constituent is often described with a beam. Contact between beams is essential to ... [more ▼]

Slender constituents are present in many structures and materials. In associated mechanical models, each slender constituent is often described with a beam. Contact between beams is essential to incorporate in mechanical models, but associated contact frameworks are only demonstrated to work for beams with circular cross-sections. Only two studies have shown the ability to treat contact between beams with elliptical cross-sections, but those frameworks are limited to point-wise contact, which narrows their applicability. This contribution presents initial results of a framework for shear-deformable beams with elliptical cross-sections if contact occurs along a line or at an area (instead of at a point). This is achieved by integrating a penalty potential over one of the beams’ surfaces. Simo-Reissner Geometrically Exact Beam (GEB) elements are employed to discretise each beam. As the surface of an assembly of such beam elements is discontinuous, a smoothed surface is introduced to formulate the contact kinematics. This enables the treatment of contact for large sliding displacements and substantial deformations. [less ▲]

Non-localised contact between beams with circular and elliptical cross-sections

in Computational Mechanics (2020), 65

The key novelty of this contribution is a dedicated technique to e fficiently determine the distance (gap) function between parallel or almost parallel beams with circular and elliptical cross-sections ... [more ▼]

The key novelty of this contribution is a dedicated technique to e fficiently determine the distance (gap) function between parallel or almost parallel beams with circular and elliptical cross-sections. The technique consists of parametrizing the surfaces of the two beams in contact, fixing a point on the centroid line of one of the beams and searching for a constrained minimum distance between the surfaces (two variants are investigated). The resulting unilateral (frictionless) contact condition is then enforced with the Penalty method, which introduces compliance to the, otherwise rigid, beams' cross-sections. Two contact integration schemes are considered: the conventional slave-master approach (which is biased as the contact virtual work is only integrated over the slave surface) and the so-called two-half-pass approach (which is unbiased as the contact virtual work is integrated over the two contacting surfaces). Details of the finite element formulation which is suitably implemented using Automatic Di fferentiation techniques are presented. A set of numerical experiments shows the overall performance of the framework and allows a quantitative comparison of the investigated variants. [less ▲]