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We develop a novel methodology for data-driven simulation of coupled multi-physics systems. The result of the method is a learned numerical integrator of the coupled system dynamics. In order to preserve the fundamental physics of the coupled systems, and thus preserve the geometrical properties of the governing equations—even if they may be completely unknown—we impose a port-metriplectic structure on the system evolution, i.e., a combination of a symplectic evolution for the system energy with a gradient flow for the entropy of each system, which can be exchanged through predefined ports. The resulting method guarantees by construction the satisfaction of the laws of thermodynamics for open systems, leading to accurate predictions of the future states of their dynamics. Examples are given for systems of varying complexity, based on synthetic as well as experimental data. [ABSTRACT FROM AUTHOR]

The immiscible multiphase fluid flow in intact and fractured porous media is relevant to numerous engineering sectors, including industrial processes, geo‐engineering, and civil engineering. These encompass crucial applications that pose significant challenges in modeling, such as carbon dioxide (CO2${\rm CO}_2$) storage in underground reservoirs, contaminant transport, and desiccation‐induced hydraulic fracturing in unsaturated soils. In this work, a macroscopic framework is developed to describe the transport of immiscible and multiphase fluids in intact and fractured porous materials. The modeling approach utilizes the embedding of two phase‐field models within the continuum Theory of Porous Media (TPM). The case of negligible capillary pressure in the macroscopic scale is associated with many numerical challenges in solving this nonlinear DAEs system, which forms the major subject of the current work. Hence, the problem of the neglected capillary pressure is defined as a target problem. To deal with this, a thermodynamically consistent modified problem is defined, which incorporates an additional artificial macroscopic capillary pressure based on the Cahn–Hilliard phase‐field approach. To increase the robustness and stability of the numerical solution, the Newton–Raphson method is replaced by a homotopy method that allows a gradual transformation of a simpler, solvable problem into the original target problem that usually converges poorly. The sharp crack topology in the fracture regions is approximated by another phase‐field method, which forms a diffusive transition zone across the crack edges of the deformable porous material. For the solid matrix, we consider a small strain assumption with a heterogeneous distribution of the permeability parameter. The inclusion of heterogeneity allows for a more realistic modeling of crack propagation and fluid‐fluid interaction. For the numerical framework, the coupled DAE system is approximated by the finite element method (FEM), implemented in the open‐source project FEniCSx. Appropriate stabilization techniques are also discussed. [ABSTRACT FROM AUTHOR]

A number of initial boundary-value problems of classical mathematical physics is generally represented in the linear operator equation and its well-posedness and causality in a Hilbert space setting was established. If a problem has a unique solution and the solution continuously depends on given data, then the problem is called well-posed. The independence of the future behavior of a solution until a certain time indicates the causality of the solution. In this article, we established the well-posedness and causality of the solution of the evolutionary problems with a perturbation, which is defined by a quadratic form. As an example, we considered the coupled system of the heat and Maxwell’s equations (the microwave heating problem).

Abstract The human brain’s distinctive folding pattern has attracted the attention of researchers from different fields. Neuroscientists have provided insights into the role of four fundamental cell types crucial during embryonic development: radial glial cells, intermediate progenitor cells, outer radial glial cells, and neurons. Understanding the mechanisms by which these cell types influence the number of cortical neurons and the emerging cortical folding pattern necessitates accounting for the mechanical forces that drive the cortical folding process. Our research aims to explore the correlation between biological processes and mechanical forces through computational modeling. We introduce cell-density fields, characterized by a system of advection-diffusion equations, designed to replicate the characteristic behaviors of various cell types in the developing brain. Concurrently, we adopt the theory of finite growth to describe cortex expansion driven by increasing cell density. Our model serves as an adjustable tool for understanding how the behavior of individual cell types reflects normal and abnormal folding patterns. Through comparison with magnetic resonance images of the fetal brain, we explore the correlation between morphological changes and underlying cellular mechanisms. Moreover, our model sheds light on the spatiotemporal relationships among different cell types in the human brain and enables cellular deconvolution of histological sections.

The human brain's distinctive folding pattern has attracted the attention of researchers from different fields. Neuroscientists have provided insights into the role of four fundamental cell types crucial during embryonic development: radial glial cells, intermediate progenitor cells, outer radial glial cells, and neurons. Understanding the mechanisms by which these cell types influence the number of cortical neurons and the emerging cortical folding pattern necessitates accounting for the mechanical forces that drive the cortical folding process. Our research aims to explore the correlation between biological processes and mechanical forces through computational modeling. We introduce cell-density fields, characterized by a system of advection-diffusion equations, designed to replicate the characteristic behaviors of various cell types in the developing brain. Concurrently, we adopt the theory of finite growth to describe cortex expansion driven by increasing cell density. Our model serves as an adjustable tool for understanding how the behavior of individual cell types reflects normal and abnormal folding patterns. Through comparison with magnetic resonance images of the fetal brain, we explore the correlation between morphological changes and underlying cellular mechanisms. Moreover, our model sheds light on the spatiotemporal relationships among different cell types in the human brain and enables cellular deconvolution of histological sections. [ABSTRACT FROM AUTHOR]

The aim of this work is the derivation and examination of a material model, accounting for large elastic deformations, coupled with species diffusion and thermal effects. This chemo-thermo-mechanical material model shows three key aspects regarding its numerical formulation. Firstly, a multiplicative split of the deformation gradient into a mechanical, a swelling and a thermal part. Secondly, temperature-scaled gradients for a numerical design comprising symmetric tangents and, thirdly, dissipation potentials for the modelling of dissipative effects. Additionally, the derived general material model is specialised to thermoresponsive hydrogels to study its predictive capabilities for a relevant example material class. An appropriate finite element formulation is established and its implementation discussed. Numerical examples are investigated, including phase transition and stability phenomena, to verify the ability of the derived chemo-thermo-mechanical material model to predict relevant physical effects properly. We compare our results to established models in the literature and discuss emerging deviations. [ABSTRACT FROM AUTHOR]

The material point method (MPM) has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation. In this paper, we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials. The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations. The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems, which will provide some direct reference for both practitioners and researchers.

We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on aggregation-based algebraic multigrid methods with custom smoothers that preserve the coupling information on each coarse level. We prove that, with the proper choice of subspace splitting, we obtain uniform convergence in discretization and physical parameters in the two-level setting. Additionally, we show parameter robustness and scalability with regard to the number of the degrees of freedom of the system on several numerical examples related to the biophysical processes in the brain, namely, the electric signaling in excitable tissue modeled by bidomain, the extracellular-membrane-intracellular (EMI) model, and reduced EMI equations. [ABSTRACT FROM AUTHOR]

In literature, the cost of a partitioned fluid‐structure interaction scheme is typically assessed by the number of coupling iterations required per time step, while ignoring the internal iterations within the nonlinear subproblems. In this work, we demonstrate that these internal iterations have a significant influence on the computational cost of the coupled simulation. Particular attention is paid to how limiting the number of iterations within each solver call can shorten the overall run time, as it avoids polishing the subproblem solution using unconverged coupling data. Based on systematic parameter studies, we investigate the optimal number of subproblem iterations per coupling step. In addition, this work proposes a new convergence criterion for partitioned algorithms that is based solely on the number of subproblem iterations required to reach the subproblem residual tolerances and therefore does not require any additional convergence tolerance for the coupling loop. [ABSTRACT FROM AUTHOR]

This paper presents application and tuning of the equilibrated residual method (ERM) of a posteriori error estimation for coupled electromechanical problems of direct, inverse and general piezoelectricity. In these three cases, either electric potential is induced by strains or strains appear due to the applied electric potential or both phenomena occur simultaneously. The mentioned ERM is assigned for the assessment of modeling and approximation errors of the numerical finite element solution. Such error values usually serve as indication for adaptive hierarchical modeling and adaptive mesh changes within thin and/or solid piezoelectric members so as to obtain the solution of assumed accuracy. [ABSTRACT FROM AUTHOR]

We present a particular derivation of the face-centred finite volume (FCFV) method and study its performance in non-linear, coupled transport problems commonly encountered in geoscientific and geotechnical applications. The FCFV method is derived from the hybridisable discontinuous Galerkin formulation, using a constant degree of approximation for the discretization of the unknowns defined on the mesh faces (edges in two dimensions). The piecewise constant degrees of freedom are determined in a global problem over the mesh skeleton. Then, the solution and its gradient are recovered at the cells centroid in a set of element-by-element independent postprocesses, both exhibiting linear convergence. The formulation of the transient advection-diffusion-reaction equation is presented in detail and the numerical analysis under challenging advective/diffusive regimes is studied. Finally, we use several numerical examples to illustrate the advantages and limitations of the FCFV method to solve problems of geoscientific and geotechnical relevance governed by the non-linear coupling between advection-diffusion-reactive transport and Stokes flow. Our results show that the FCFV method is an attractive and highly competitive alternative to other commonly used methods. • FCFV approach for solving ADR problems coupled with Stokes flow. • Linear convergence of the primal variable's gradient without flux reconstruction. • Accurate in advection-dominated scenarios with both uniform and distorted meshes. • All unknowns defined on the same nodes, favourable for non-linear coupled problems. • Performance is validated with multiple challenging cases of geoscientific relevance. [ABSTRACT FROM AUTHOR]

In this work, a cost-efficient space-time adaptive algorithm based on the Dual Weighted Residual (DWR) method is developed and studied for a coupled model problem of flow and convection-dominated transport. Key ingredients are a multirate approach adapted to varying dynamics in time of the subproblems, weighted and non-weighted error indicators for the transport and flow problem, respectively, and the concept of space-time slabs based on tensor product spaces for the data structure. In numerical examples, the performance of the underlying algorithm is studied for benchmark problems and applications of practical interest. Moreover, the interaction of stabilization and goal-oriented adaptivity is investigated for strongly convection-dominated transport. [ABSTRACT FROM AUTHOR]

Abstract Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We present a Bayesian calibration approach for surface coupled problems in computational mechanics based on measured deformation of an interface when no displacement data of material points is available. The interpretation of such a calibration problem as a statistical inference problem, in contrast to deterministic model calibration, is computationally more robust and allows the analyst to find a posterior distribution over possible solutions rather than a single point estimate. The proposed framework also enables the consideration of unavoidable uncertainties that are present in every experiment and are expected to play an important role in the model calibration process. To mitigate the computational costs of expensive forward model evaluations, we propose to learn the log-likelihood function from a controllable amount of parallel simulation runs using Gaussian process regression. We introduce and specifically study the effect of three different discrepancy measures for deformed interfaces between reference data and simulation. We show that a statistically based discrepancy measure results in the most expressive posterior distribution. We further apply the approach to numerical examples in higher model parameter dimensions and interpret the resulting posterior under uncertainty. In the examples, we investigate coupled multi-physics models of fluid–structure interaction effects in biofilms and find that the model parameters affect the results in a coupled manner.

Understanding of desiccation-induced cracking in soil has improved over the last 20–30 years through experimental studies, but progress in predictive modelling of desiccation cracking has been limited. The heterogeneous structure of soils and the multi-physics nature of the phenomenon, involving emergence and propagation of discontinuities, make the mathematical description and analysis a challenging task. The authors present a non-local hydro-mechanical model for soil desiccation cracking capable of predicting crack initiation and growth. The model is based on peridynamics (PD) theory. Attempts to model soil desiccation cracking by PD are limited to a purely mechanical description of the process that involves calibration of the parameters. In contrast, the model presented in this paper describes soil desiccation cracking as a hydro-mechanical problem, where moisture flow and deformation are coupled. This allows for investigating and explaining the mechanisms controlling the initiation and propagation of discontinuities. The model is applied and tested against two sets of experimental data to explain the typical features of drying-induced cracking of clays. The validations use experimental parameters (Young's modulus, water retention characteristics) and avoid calibrations to test the accuracy of the model. The correlations between the shrinkage of soil clay, changes in displacement fields and crack growth are demonstrated. Crack initiation, propagation and ultimate crack patterns simulated by the model are found to be in very good agreement with experimental observations. The results show that the model can capture realistically key hydraulic, mechanical and geometry effects on clay desiccation cracking. [ABSTRACT FROM AUTHOR]

One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to different numerical schemes or domain discretizations employed. Moreover, very often complex submodels depend on (e.g., physical or geometrical) parameters, thus making the repeated solutions of the coupled problem through high-fidelity, full-order models extremely expensive, if not unaffordable. In this paper, we propose a reduced order modeling (ROM) strategy to tackle parametrized one-way coupled problems made by a first, master model and a second, slave model; this latter depends on the former through Dirichlet interface conditions. We combine a reduced basis method, applied to each subproblem, with the discrete empirical interpolation method to efficiently interpolate or project Dirichlet data across either conforming or non-conforming meshes at the domains interface, building a low-dimensional representation of the overall coupled problem. The proposed technique is numerically verified by considering a series of test cases involving both steady and unsteady problems, after deriving a posteriori error estimates on the solution of the coupled problem in both cases. This work arises from the need to solve staggered cardiac electrophysiological models and represents the first step towards the setting of ROM techniques for the more general two-way Dirichlet-Neumann coupled problems solved with domain decomposition sub-structuring methods, when interface non-conformity is involved. [ABSTRACT FROM AUTHOR]

This paper presents a methodology to program the weak coupling between magnetic and structural vector fields in an electromagnetic device modeled in two dimensions. The magneto-mechanical coupling phenomenon is present in electromagnetic devices where magnetic forces cause displacements in metallic materials. This work proposes a numerical solution to this problem by applying the 2D finite element method to the governing equations of this coupled multiphysics phenomenon. The well-known formulation yields accurate results; however, it is often not properly integrated into a computer program. This manuscript proposes a flexible and intuitive methodology for the implementation of the complex mathematics involved in this phenomenon into a computer program. The computer code receives the input parameters, discretizes the geometry by generating a 2D finite mesh, solves the resulting equations using the finite element method, and finally exports the results of the magnetic ang mechanical fields. The modeling is performed using an open-source platform for programming the finite element method in the programming language Python, and afterwards, the results are compared against a commercial software as validation of the proposed numerical approach. The novel magneto-mechanical coupling methodology is used to solve an engineering application, namely an electromagnetic actuator. [ABSTRACT FROM AUTHOR]

A model of thermoelastic-visco-plastic deformation of a composite material cross reinforced with continuous fibers in arbitrary directions has been developed. The materials of the components of the composition are isotropic; their plastic deformation is described by the flow theory with isotropic hardening. The dependences of the loading functions on temperature and strain rate of these materials are taken into account. A mathematical model of thermoelastic-visco-plastic bending behavior of reinforced plates has been constructed. The weak resistance to transverse shears of such thin-walled structures is taken into account in the framework of Ambarcumian's theory. Geometric nonlinearity is taken into account in the Karman approximation. The relation of the mechanical and thermophysical components of the problem of dynamic inelastic deformation of composite plates is taken into account. The temperature over the thickness of the constructions is approximated by polynomials of various orders. An explicit numerical scheme is used to solve the formulated two-dimensional problem. The thermoelastic-visco-plastic behavior of two-dimensionally and spatially reinforced fiberglass and metal-composite plates, dynamically bent under the action of an air blast wave, has been investigated. It is shown that in order to adequately determine the temperature in such structures, it must be approximated by polynomials of the 6th or 7th order over the thickness of the plates. It has been demonstrated that relatively thin composite plates heat up by 15...30°C, and relatively thick ones by 1.5...2.5°C. Due to such a low level of heating of reinforced constructions, their dynamic calculation under the action of loads such as an air blast wave can be carried out without taking into account the thermal effect if there are no additional heat sources of non-mechanical origin. In this case, it is necessary to take into account the sensitivity of the plastic properties of the components of the composition to the rate of their deformation. [ABSTRACT FROM AUTHOR]

We consider Waveform Relaxation (WR) methods for parallel and partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on independent and adaptive time-grids, while maintaining high time-integration orders. Classical WR methods such as Jacobi or Gauss-Seidel WR are typically either parallel or converge quickly. We present a novel parallel WR method utilizing asynchronous communication techniques to get both properties. Classical WR methods exchange discrete functions after time-integration of a subproblem. We instead asynchronously exchange time-point solutions during time-integration and directly incorporate all new information in the interpolants. We show both continuous and time-discrete convergence in a framework that generalizes existing linear WR convergence theory. An algorithm for choosing optimal relaxation in our new WR method is presented. Convergence is demonstrated in two conjugate heat transfer examples. Our new method shows an improved performance over classical WR methods. In one example, we show a partitioned coupling of the compressible Euler equations with a nonlinear heat equation, with subproblems implemented using the open source libraries DUNE and FEniCS. [ABSTRACT FROM AUTHOR]

This paper presents a multirate in time approach for coupled flow and transport problems combined with goal-oriented error control based on the Dual Weighted Residual (DWR) method. The focus is on the implementation of the multirate concept regarding different time scales for the underlying subproblems. Key ingredients are an arbitrary degree discontinuous Galerkin time discretization, an a posteriori error representation for the transport problem coupled with flow and the concept of space-time slabs based on tensor-product spaces. From the latter, a space-time mesh adaptation with highly economical grids is developed. The performance of the approach is studied carefully by numerical convergence examples as well as an example of physical interest for convection-dominated transport. [ABSTRACT FROM AUTHOR]

In this article, we present a novel explicit time‐integration algorithm for the coupled hydromechanical soil mechanics problems in a pseudo‐static regime. After introducing the finite element discretization, the semidiscrete ordinary system of equations is integrated explicitly in time with the Runge–Kutta method. It is noted that this formulation is conditionally stable in time. By introducing a stabilization technique, the Polynomial Pressure Projection, and selecting appropriately the stabilization parameter, the formulation becomes unconditionally stable. To illustrate the performance of the method several numerical analysis are reported, considering both elastic and elasto‐plastic soil behavior. [ABSTRACT FROM AUTHOR]

In this article, we evaluate the modeling of a real operation of a real system using the corresponding adequate theory. We show that the smart theories often used do not directly correspond to reality because these theories have been established in idealized frameworks. The need to adapt such frames to real landscape situations necessitates modifying the models used. This can be achieved by taking into account the different existing physical phenomena, which are normally overlooked in smart idealized models, in a revised coupled model. This contribution aims to analyze and illustrate the relationship between smart theories and coupled realistic models through a literature review. The strategy for constructing such models is discussed and highlighted. The understanding of this approach is illustrated by an application to the case of electromagnetic and energy conversion systems. In these systems, intelligent energy management, conversion and control involve the use of an accurate realistic coupled model in system design, optimization and control. It is a question of coupling and solving equations representing these systems by taking into account the real phenomena involved, which are electrical, magnetic, mechanical, thermal and material. The obvious advantage of using such realistic models in computer-aided design and optimization tools is illustrated. Moreover, the interest of using such models in the supervision of systems is assessed. These demonstrations are supported by a review of examples of work carried out in the field. [ABSTRACT FROM AUTHOR]

This work presents a self-contained continuum formulation for coupled chemical, mechanical, and thermal contact interactions. The formulation is very general and, hence, admits arbitrary geometry, deformation, and material behavior. All model equations are derived rigorously from the balance laws of mass, momentum, energy, and entropy in the framework of irreversible thermodynamics, thus exposing all the coupling present in the field equations and constitutive relations. In the process, the conjugated kinematic and kinetic variables for mechanical, thermal, and chemical contact are identified, and the analogies between mechanical, thermal, and chemical contact are highlighted. Particular focus is placed on the thermodynamics of chemical bonding distinguishing between exothermic and endothermic contact reactions. Distinction is also made between long-range, non-touching surface interactions and short-range, touching contact. For all constitutive relations, examples are proposed and discussed comprehensively with particular focus on their coupling. Finally, three analytical test cases are presented that illustrate the thermo-chemo-mechanical contact coupling and are useful for verifying computational models. Although the main novelty is the extension of existing contact formulations to chemical contact, the presented formulation also sheds new light on thermo-mechanical contact, because it is consistently derived from basic principles using only a few assumptions. [ABSTRACT FROM AUTHOR]

Abstract We propose a hybrid interface preconditioner for the monolithic solution of surface-coupled problems. Powerful preconditioning techniques are crucial when it comes to solving large monolithic systems of linear equations efficiently, especially when arising from coupled multi-physics problems like in fluid–structure interaction. Existing physics-based block preconditioners have proven to be efficient, but their error assessment reveals an accumulation of the error at the coupling surface. We address this issue by combining them with an additional additive Schwarz preconditioner, whose subdomains span across the interface on purpose. By performing cheap but accurate subdomain solves that do not depend on the separation of physical fields, this error accumulation can be reduced effectively. Numerical experiments compare the performance of the hybrid preconditioner to existing approaches, demonstrate the increased efficiency, and study its parallel performance.

Modeling of cancellous bone has important applications in the detection and treatment of fatigue fractures and diseases like osteoporosis. In this paper, we present a fully coupled multiscale approach considering mechanical, electric and magnetic effects by using the multiscale finite element method and a two-phase material model on the microscale. We show numerical results for both scales, including calculations for a femur bone, comparing a healthy bone to ones affected by different stages of osteoporosis. Here, the magnetic field strength resulting from a small mechanical impact decreases drastically for later stages of the disease, confirming experimental research. [ABSTRACT FROM AUTHOR]

The new software FEniCS–preCICE is a middle software layer, sitting in between the existing finite-element library FEniCS and the coupling library preCICE. The middle layer simplifies coupling (existing) FEniCS application codes to other simulation software via preCICE. To this end, FEniCS–preCICE converts between FEniCS and preCICE mesh and data structures, provides easy-to-use coupling conditions, and manages data checkpointing for implicit coupling. The new software is a library itself and follows a FEniCS-native style. Only a few lines of additional code are necessary to prepare a FEniCS application code for coupling. We illustrate the functionality of FEniCS–preCICE by two examples: a FEniCS heat conduction code coupled to OpenFOAM and a FEniCS linear elasticity code coupled to SU2. The results of both scenarios are compared with other simulation software showing good agreement.

In this two-part paper, a stable and efficient nodally-integrated reproducing kernel particle method (RKPM) approach for solving the governing equations of generalized thermomechanical theories is developed. Part I investigated quadrature in the weak form using classical thermoelasticity as a model problem, and a stabilized and corrected nodal integration was proposed. In this sequel, these methods are developed for generalized thermoelasticity and generalized finite-strain plasticity theories of the hyperbolic type, which are more amenable to explicit time integration than the classical theories. Generalized thermomechanical models yield finite propagation of temperature, with a so-called second sound speed. Since this speed is not well characterized for common engineering materials and environments, equating the elastic wave speed with the second sound speed is investigated to obtain results close to classical thermoelasticity, which also yields a uniform critical time step. Implementation of the proposed nodally integrated RKPM for explicit analysis of finite-strain thermoplasticity is also described in detail. Several benchmark problems are solved to demonstrate the effectiveness of the proposed approach for thermomechanical analysis. [ABSTRACT FROM AUTHOR]

In this two-part paper, a stable and efficient nodally-integrated reproducing kernel particle method (RKPM) is introduced for solving the governing equations of generalized thermomechanical theories. Part I investigates quadrature in the weak form using coupled and uncoupled classical thermoelasticity as model problems. It is first shown that nodal integration of these equations results in spurious oscillations in the solution many orders of magnitude greater than pure elasticity. A naturally stabilized nodal integration is then proposed for the coupled equations. The variational consistency conditions for nth order exactness and convergence in the two-field problem are then derived, and a uniform correction on the test function approximations is proposed to achieve these conditions. Several benchmark problems are solved to demonstrate the effectiveness of the proposed method. In the sequel, these methods are developed for generalized thermoelasticity and generalized finite-strain thermoplasticity theories of the hyperbolic type that are amenable to efficient explicit time integration. [ABSTRACT FROM AUTHOR]

The work is devoted to the investigation of a caprock integrity during oil production by steam-assisted gravity drainage method. An originally proposed thermo-hydro-mechanical model was used for the evaluation of mechanical loading acting on the over-burden. The model includes mass conservation laws, the energy conservation law and the linear momentum balance. Filtration of each phase of the three-phase flow (steam, oil and water) is described by Darcy�s law. Effective stress concept is used to take into account the effect of pore pressure on the stress-strain state. Inelastic deformations are described by the phenomenological viscoplastic model based on Drucker-Prager yield criterion. Two qualitatively and quantitatively different scenarios of porosity evolution are considered. The first scenario corresponds to the case of the pore compression while the second one describes increase in porosity induced by the volumetric strains. The obtained stress-strain state in the reservoir was used for the assessment of the caprock integrity for both cases of porosity evolution. In addition, the effect of the porosity evolution on the oil production rate is studied. It has been shown that the oil production rate strongly depends on the prevailing physical mechanism of the porosity evolution.

In this article, we propose an optimisation framework that can contribute to the prevention of premature failure or damage to building structures and can thereby strengthen their longevity. We concentrate on structures that are contaminated by chemical substances and that have strong destructive effects on the material. The aim of this contribution is a mathematical algorithm that allows the optimisation of a structure exposed to chemical influences and thus the assurance of the static load capacity. To achieve this, we present a coupled mechanical-diffusion-degradation approach embedded in a finite element (FE) framework. Furthermore, we integrate an optimisation algorithm to reduce material degradation. In this paper, we establish shape optimisation of a structure with a gradient based optimisation algorithm. [ABSTRACT FROM AUTHOR]

In this work, aspects considering material modeling of electro‐mechanical coupling in fiber reinforced electro‐active polymers (EAP) and the corresponding finite element implementation are considered. We propose a constitutive model that takes into account the electro‐viscoelastic behavior of the isotropic matrix and the influence of unidirectional fibers on both the hyperelastic response and the viscous behavior of the whole composite. Two distinct existing models that describe the electro‐mechanical coupling, are demonstrated and implemented, moreover, a numerical link between both models for three‐dimensional continua in terms of tensor calculus, is identified. We propose the extended‐tube model for the elastic response with some of its parameters evolving in response to the electric field, in order to fit electro‐viscoelastic experiments. Regarding the finite element implementation, in addition to the deformation field and the electric potential, two pairs of field variables are introduced on the element level, to enforce quasi‐incompressibility and quasi‐inextensibility. It is shown that using the mixed finite element improves the convergence behavior for the simulation of soft EAP with relatively stiff fibers. Moreover, the choice of the model that expresses the nature of the underlying coupling is shown to noticeably affect the degree of simulated actuation in fiber reinforced actuators. [ABSTRACT FROM AUTHOR]

This paper describes a numerical simulation of vibrations of an elastic rod whose height is significantly greater than its transverse dimension and which is placed perpendicularly to the external flow and rigidly mounted on a substrate. Simulation is carried out in the ANSYS software package using bidirectional coupling technology. The natural frequencies and vibration modes of the rod are calculated. The airflow structure is analyzed and its features in the vicinity of the model are described. The process of exciting the vibrations of an elastic rod under the action of an external flow is investigated and its stress-strain state is determined. Vibration modes in the direction of an incident flow and in the transverse direction are determined. It is shown that, if the first natural frequency and the vortex shedding frequency reach close values, the amplitude of the rod vibrations in the transverse direction sharply increases to a value approximately equal to 0.06 of the rod height, which is followed by natural vibrations with a constant amplitude in the transverse direction and variable amplitude in the direction of the incident flow. [ABSTRACT FROM AUTHOR]

In this article, we evaluate the modeling of a real operation of a real system using the corresponding adequate theory. We show that the smart theories often used do not directly correspond to reality because these theories have been established in idealized frameworks. The need to adapt such frames to real landscape situations necessitates modifying the models used. This can be achieved by taking into account the different existing physical phenomena, which are normally overlooked in smart idealized models, in a revised coupled model. This contribution aims to analyze and illustrate the relationship between smart theories and coupled realistic models through a literature review. The strategy for constructing such models is discussed and highlighted. The understanding of this approach is illustrated by an application to the case of electromagnetic and energy conversion systems. In these systems, intelligent energy management, conversion and control involve the use of an accurate realistic coupled model in system design, optimization and control. It is a question of coupling and solving equations representing these systems by taking into account the real phenomena involved, which are electrical, magnetic, mechanical, thermal and material. The obvious advantage of using such realistic models in computer-aided design and optimization tools is illustrated. Moreover, the interest of using such models in the supervision of systems is assessed. These demonstrations are supported by a review of examples of work carried out in the field.

We present version 3 of the open-source simulator for flow and transport processes in porous media DuMux. DuMux is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMux, version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility. [ABSTRACT FROM AUTHOR]

We propose a hybrid interface preconditioner for the monolithic solution of surface-coupled problems. Powerful preconditioning techniques are crucial when it comes to solving large monolithic systems of linear equations efficiently, especially when arising from coupled multi-physics problems like in fluid–structure interaction. Existing physics-based block preconditioners have proven to be efficient, but their error assessment reveals an accumulation of the error at the coupling surface. We address this issue by combining them with an additional additive Schwarz preconditioner, whose subdomains span across the interface on purpose. By performing cheap but accurate subdomain solves that do not depend on the separation of physical fields, this error accumulation can be reduced effectively. Numerical experiments compare the performance of the hybrid preconditioner to existing approaches, demonstrate the increased efficiency, and study its parallel performance. [ABSTRACT FROM AUTHOR]