Boundary Value Problems In Mechanics Research Articles

Numerical implementation of boundary element method for determining aerodynamic characteristics around airfoil system by viscous media

In this paper, the boundary element method is applied to determine the characteristics of distributed flow around the airfoil group. Because the boundary integral equation can describe various initial boundary value problems in mechanics and has many advantages such as good convergence, it can be used as a tool to establish appropriate mathematical models and numerical realization methods, so as to comprehensively study the distribution kinematics and dynamics of the airfoil group motion system in the viscous fluid flow co-flow process. In this paper, some numerical results are presented to determine the aerodynamic distribution characteristics of the viscous flow field around the airfoil group in the control area.

A meshless multiscale approach to modeling severe plastic deformation of metals: Application to ECAE of pure copper

Severe plastic deformation (SPD), occurring ubiquitously across metal forming processes, has been utilized to significantly improve bulk material properties such as the strength of metals. The latter is achieved by ultra-fine grain refinement at the polycrystalline mesoscale via the application of large plastic strains on the macroscale. We here present a multiscale framework that aims at efficiently modeling SPD processes while effectively capturing the underlying physics across all relevant scales. At the level of the macroscale boundary value problem, an enhanced maximum-entropy (max-ent) meshless method is employed. Compared to finite elements and other meshless techniques, this method offers a stabilized finite-strain updated-Lagrangian setting for improved robustness with respect to mesh distortion arising from large plastic strains. At each material point on the macroscale, we describe the polycrystalline material response via a Taylor model at the mesoscale , which captures discontinuous dynamic recrystallization through the nucleation and growth/shrinkage of grains. Each grain, in turn, is modeled by a finite-strain crystal plasticity model at the microscale . We focus on equal-channel angular extrusion (ECAE) of polycrystalline pure copper as an application, in which severe strains are generated by extruding the specimen around a 90 ° -corner. Our framework describes not only the evolution of strain and stress distributions during the process but also grain refinement and texture evolution, while offering a computationally feasible treatment of the macroscale mechanical boundary value problem. Though we here focus on ECAE of copper, the numerical setup is sufficiently general for other applications including SPD and thermo-mechanical processes (e.g., rolling, high-pressure torsion, etc.) as well as other materials systems.

Atomistic-continuum coupling of random alloys

Random alloys are multicomponent systems where the atomic type on each lattice site is independent of the atom types on any other lattice site. The fluctuations in local atomic configurations inherent to the random alloy prevents the accurate application of standard force-based atomistic/continuum (a/c) coupling. Errors arise because the two transitions, from atomistic to continuum and from random-to-homogeneous, occur at the same location. Here, two methods for a/c coupling that mitigate errors arising in the standard method are proposed, studied, and validated. In one method, the desired atomistic domain and its nearby surroundings are fully relaxed to an equilibrium structure and then inserted into the coupled problem as the reference configuration. This reduces the effects of the random-to-homogeneous transition, and guarantees no spurious stress at zero load. In the second method, the random-to-homogeneous transition is spatially separated from the atomistic-continuum transition by introducing a small buffer zone of well-defined ‘average atoms’. The random-to-homogeneous transition is then accomplished fully atomistically while the atomistic to continuum transition is accomplished in a homogeneous material. The two methods are validated through comparisons of the stresses in the coupled method versus the true atomistic system for three different solid solution alloys (Al-5%Mg, Ni-15%Al, and medium entropy FeNiCr) as described by EAM interatomic potentials. Spurious stresses for both methods and across all three materials are negligible (≈5 MPa) relative to stresses arising in realistic mechanical problems of interest. These new methods thus enable the accurate study of mechanics boundary value problems in random alloys for problems where it is essential to capture atomistic phenomena in some localized region of the random alloy.

On the Application of Modified Finite Sine Transform to Structural Mechanics

The method of modified finite sine transform (MFST) was introduced to solve fourth-order boundary value problems in structural mechanics. The analytical features and computational aspects of MFST were presented, including integral transforms of the derivatives of functions and the term-by-term differentiation of inverse MFST. For the simplicity of demonstrating the solution process, the cantilever beam was used in the discussion. Numerical results for transverse vibration based on the present method were compared and validated with existing results for natural frequencies. Although the present method is not superior to conventional finite sine transform method in one-dimensional structures, it could be significantly efficient for two-dimensional structures with asymmetric boundary conditions, especially including cantilever plates and other plates with only one free edge or two adjacent free edges.

Structural Optimisation Using Parametrised Level Set Methods and Extended Finite Element Method

AbstractIn the framework of level‐set‐based optimisation, several approaches to solve bi‐material and topological problems have been developed. In this study a combined concept of different approaches is introduced, joining together a parametrised geometry description with superellipses or b‐splines and a modified approach for the extended finite element method within an optimisation setup of topological and shape iterations introduced by Allaire [1]. The parametrisation with geometric figures or splines allows us to reduce the number of design variables to a minimum whereas we hold up a sufficient precision in the geometry description. Moreover it simplifies the shape derivatives as we gain an implicit description for the moving interfaces. In order to solve the boundary value problem of structural mechanics, we introduce a modified extended finite element approach which uses a sub‐meshing technique that enables us to keep existing strategies from homogeneous structures and transform them onto a discontinuous material using enriched shape functions provided by the standard extended finite element method. Shape sensitivities are evaluated on the sub‐elements and extrapolated to the element nodes. The topological derivative as developed by Novotny [4] is evaluated and prescribes the initiation of new discontinuities as inclusions or holes.

Enhanced local maximum-entropy approximation for stable meshfree simulations

We introduce an improved meshfree approximation scheme which is based on the local maximum-entropy strategy as a compromise between shape function locality and entropy in an information-theoretical sense. The improved version is specifically designed for severe, finite deformation and offers significantly enhanced stability as opposed to the original formulation. This is achieved by (i) formulating the quasistatic mechanical boundary value problem in a suitable updated-Lagrangian setting, (ii) introducing anisotropy in the shape function support to accommodate directional variations in nodal spacing with increasing deformation and eliminate tensile instability, (iii) spatially bounding and evolving shape function support to restrict the domain of influence and increase efficiency, (iv) truncating shape functions at interfaces in order to stably represent multi-component systems like composites or polycrystals. The new scheme is applied to benchmark problems of severe elastic and elastoplastic deformation that demonstrate its performance both in terms of accuracy (as compared to exact solutions and, where applicable, finite element simulations) and efficiency. Importantly, the presented formulation overcomes the classical tensile instability found in most meshfree interpolation schemes, as shown for stable simulations of, e.g., the inhomogeneous extension of a hyperelastic block up to 100% or the torsion of a hyperelastic cube by 200° — both in an updated Lagrangian setting and without the need for remeshing.

Three-dimensional lower bound finite element limit analysis of Hoek-Brown material using semidefinite programming

A reliable and accurate stability analysis in Hoek-Brown rock masses under fully three-dimensional geometries requires an efficient and powerful computational method. This paper presents a computational implementation of a three-dimensional lower bound finite element limit analysis using semidefinite programming for Hoek-Brown rock masses. Its computational performance is investigated extensively through a variety of boundary value problems in rock mechanics, namely triaxial compression, bearing capacity and cavity contraction. New lower bound solutions are numerically derived, including bearing capacity of square footings, uniaxial compression of cube and cylindrical rock specimens with fully rough platens and tension test on double notched rock specimens.

Solution of Quantum Mechanical Problems Using Finite Element Method and Parametric Basis Functions

New computational schemes, symbolic-numerical algorithms and programs implementing the high-accuracy finite element method (FEM) for the solution of quantum mechanical boundary-value problems (BVPs) are reviewed. The elliptic BVPs in 2D and 3D domains are solved using the multivariable FEM and Kantorovich method using parametric basis functions. We demonstrate and compare the efficiency of the proposed calculation schemes, algorithms, and software by solving the benchmark BVPs that describe the scattering on a barrier and a well, the bound states of a helium atom, and the quadrupole vibration in a collective nuclear model.

Algorithms for Solving Boundary Value Problems of Deformable Solid Mechanics in View of Creep Strain

Further development of power and, primarily, engine engineering is associated with significantly increasing specific indicators. For example, the main trend in development of gas turbine engines is to increase gas parameters before the turbine. At the same time, there is an intensive growth of thermal and mechanical tension, and first of all this applies to the parts and components of the flow range. The destruction of these structural elements may have grave consequences. Increasing reliability and durability of responsible components of engines under operating conditions of complex cyclic thermo-mechanical loading is one of the priority tasks of modern engine engineering.One of the factors to determine a design performance is high-temperature creep. When solving the problems of deformable solid mechanics (DSM) in terms of creep, various options of the theory of hereditary creep and three main technical theories of aging, flow and hardening are widely used. There are also theories known that use an apparatus of the structural models and mechanical analogues to describe the creep. Most theories satisfactorily describe the creep strain under constant or slowly changing loads. Analysis of stress-strain states under variable loads is better described by the theories of flow and hardening, and the theory of hardening has some advantages over the theories of flow, as it gives more exact approximation for experiment results. From the point of view of the computing cycle arrangement, the technical theories have well-known advantages over the hereditary ones.When using the finite element method (FEM) to solve the boundary value problems of DSM considering the creep strain, an explicit or implicit Euler scheme is very often used. Depending on the features of the problem under consideration, a solution algorithm is constructed either in accordance with the method of initial stress, or by the method of initial strains. The method of initial strains when solving the problems in terms of creep is used more often, because the application of an initial stress method for this class of problems is technically much more complicated. The paper examines the explicit and implicit Euler schemes in combination with FEM. Both schemes are formulated in accordance with the method of initial strains. A constitutive relation was chosen in the form of the theory of flows.

Symmetry reduction and numerical solution of a nonlinear boundary value problem in fluid mechanics

PurposeThe purpose of this paper is to study the applications of Lie symmetry method on the boundary value problem (BVP) for nonlinear partial differential equations (PDEs) in fluid mechanics.Design/methodology/approachThe authors solved a BVP for nonlinear PDEs in fluid mechanics based on the effective combination of the symmetry, homotopy perturbation and Runge–Kutta methods.FindingsFirst, the multi-parameter symmetry of the given BVP for nonlinear PDEs is determined based on differential characteristic set algorithm. Second, BVP for nonlinear PDEs is reduced to an initial value problem of the original differential equation by using the symmetry method. Finally, the approximate and numerical solutions of the initial value problem of the original differential equations are obtained using the homotopy perturbation and Runge–Kutta methods, respectively. By comparing the numerical solutions with the approximate solutions, the study verified that the approximate solutions converge to the numerical solutions.Originality/valueThe application of the Lie symmetry method in the BVP for nonlinear PDEs in fluid mechanics is an excellent and new topic for further research. In this paper, the authors solved BVP for nonlinear PDEs by using the Lie symmetry method. The study considered that the boundary conditions are the arbitrary functions Bi(x)(i = 1,2,3,4), which are determined according to the invariance of the boundary conditions under a multi-parameter Lie group of transformations. It is different from others’ research. In addition, this investigation will also effectively popularize the range of application and advance the efficiency of the Lie symmetry method.

A mixed finite element formulation for slightly compressible finite elasticity with stiff fibre reinforcement. Two fibre families. Uniaxial tension formulation

We propose a novel finite element based formulation for the solution of the static mechanical mixed boundary value problem of a finite elastic solid reinforced by two distinct, stiff fibre families. The fibre tensions, are assumed decoupled and uniaxial, at out-set. The associated energy conjugate fibre stretch rates are shown to be uniaxial by duality. The natively displacement dependent fibre tension–fibre stretch pairs are replaced by auxiliary independent variables. The complementary, displacement based, stresses and energy conjugate strain rates become tensionless and stretch-rate-less in the two fibre directions, respectively, by construction. An additively decoupled hyperelastic strain energy ansatz in terms of the fibre stretches and a novel apparently doubly stretchless Cauchy–Green tensor is used. The displacement based part of the formulation is set in an apparently inextensible fibre metric space. The proposed uniaxial fibre tension description is statically exact for the fully constrained problem, and the novel doubly stretchless Cauchy–Green tensor is conditionally kinematically admissible in its vicinity. The formulation is realised as a five-field mixed finite element method admitting separate higher order approximations in H1, for the displacement, and in L2, for the energy conjugate fibre tensions and stretches, respectively. The convergence and correctness of the implementation is verified by numerical and analytical examples.

On the rate dependent behaviour of epoxy adhesive joints: Experimental characterisation and modelling of mode I failure

The increasing use of adhesive joints in dynamic applications require reliable measurements of the rate-dependent stress-displacement behaviour. The direct measurement of the stress-displacement curve is necessary when using cohesive models in discretised solutions of boundary value problems in solid mechanics. This paper aims to investigate the rate-dependent tensile failure of adhesive joints by using a new experimental methodology – it relies upon the combination of the stress wave propagation theory and digital image correlation methods on high speed footage to quantify the tensile stress and the dissipated energy respectively. For this purpose, the Split Hopkinson Bar methodology was employed – the experimental configuration was optimised using numerical modelling. To prove the sensitivity of our framework, two different adhesives are characterised at different loading rates: the adhesive failure strength was found to increase considerably with the strain rate, while the plastic deformation of these adhesives was reduced. The film adhesive showed superior performance over the particle toughened one. In the final part, a rate-dependent cohesive zone model is proposed, one which captures the measured behaviour and which has the potential to be used in industrial applications.

Finit element solution of Poisson Equation over Polygonal Domains using a novel auto mesh generation technique and an explicit integration scheme for linear convex quadrilaterals of cubic order Serendipity and Lagrange families

This paper presents an explicit integration scheme to compute the stiffness matrix of twelve node and sixteen node linear convex quadrilateral finite elements of Serendipity and Lagrange families using an explicit integration scheme and discretisation of polygonal domain by such finite elements using a novel auto mesh generation technique, In finite element analysis, the boundary value problems governed by second order linear partial differential equations, the element stiffness matrices are expressed as integrals of the product of global derivatives over the linear convex quadrilateral region. These matrices can be shown to depend on the material properties matrices and the matrix of integrals with integrands as rational functions with polynomial numerator and the linear denominator (4+) in the bivariates over a 2-square (-1 ) with the nodes on the boundary and in the interior of this simple domain. The finite elements up to cubic order have nodes only on the boundary for Serendipity family and the finite elements with boundary as well as some interior nodes belong to the Lagrange family. The first order element is the bilinear convex quadrilateral finite element which is an exception and it belongs to both the families. We have for the present ,the cubic order finite elements which havee 12 boundary nodes at the nodal coordinates {(-1,-1),(1,-1),(1,1),(-1,1),(-1/3,-1), (1/3,-1),(1,-1/3),(1,1/3),(1/3,1),(-1/3,1),(-1,1/3),(-1,-1/3)} and the four interoior nodal coordinates at the points (-1/3,-1/3),(1/3,-1/3),(1/3,1/3),(-1/3,1/3)} in the local parametric space ( In this paper, we have computed the integrals of local derivative products with linear denominator (4+) in exact forms using the symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme can be then applied to solve boundary value problems in continuum mechanics over convex polygonal domains. We have also developed a novel auto mesh generation technique of all 12-node and 16-node linear(straight edge) convex quadrilaterals for a polygonal domain which provides the nodal coordinates and the element connectivity. We have used the explicit integration scheme and this novel auto mesh generation technique to solve the Poisson equation u ,where u is an unknown physical variable and in with Dirichlet boundary conditions over the convex polygonal domain.

To the problem of decomposition of the initial boundary value problems in mechanics

We consider the questions on the decomposition of the initial boundary value problems of elasticity theory and thin bodies for some anisotropic media. In particular, the initial boundary problems of the micropolar (and classical) theory of elasticity are presented, i.e. to introduce tensor-block matrix operators (tensor-operators). In the case of an isotropic micropolar elastic medium (isotropic and transversally isotropic classical media) tensor-block matrix operators (tensor-operators) of cofactors corresponding to the tensor-block matrix operators (tensor-operators) of of the initial boundary value problems are obtained, which are splitting the initial boundary value problems. From three-dimensional decomposed initial boundary value problems the corresponding decomposed initial boundary value problems for the theory of thin bodies are obtained.

Finite element solution of Poisson Equation over Polygonal Domains using a novel auto mesh generation technique and an explicit integration scheme for nine node linear convex quadrilateral of Lagrange family

This paper presents an explicit integration scheme to compute the stiffness matrix of a nine node linear convex quadrilateral element of Lagrange family using symbolic mathematics and discretisation of polygonal domain by such finite elements using a novel auto mesh generation technique , In finite element analysis, the boundary value problems governed by second order linear partial differential equations, the element stiffness matrices are expressed as integrals of the product of global derivatives over the linear convex quadrilateral region. These matrices can be shown to depend on the material properties and the matrix of integrals with integrands as rational functions with polynomial numerator and the linear denominator (4+ ) in the bivariates over a nine node 2-square (-1 ) with nodes at the points {(-1,-1),(1,-1),(1,1),(-1,1),(0,-1),(1,0).(0,1),(- 1,0),(0,0)} in local parametric space. In this paper, we have computed these integrals in exact forms using the symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme can be applied to solve boundary value problems in continuum mechanics over convex polygonal domains. We have also developed a novel auto mesh generation technique of all nine node linear convex quadrilaterals for a polygonal domain which provides the nodal coordinates and element connectivity. We have used the explicit integration scheme and this novel auto mesh generation technique to solve the Poisson equation u ,where u is unknown physical variable and in with given Dirichlet boundary conditions over the given convex polygonal domain.

Modeling the Effect of Mechanics on Ion Transport and Reaction Kinetics in Solid Electrolytes

Solid state batteries are gaining increasing attention due to their potential for high energy densities and their enhanced safety properties when using a solid electrolyte separator with a metal anode such as Lithium or Sodium. The solid electrolyte can be designed as a single ion conductor or as a solid solvent with both mobile anions and cations. Especially for the description of the latter case, the influence of mechanics on ion transport and reaction kinetics cannot be neglected or treated in a simplified manner as is usually done for liquid electrolytes, see e.g. [1]. In this contribution we present a coupled electro-chemo-mechanical modeling framework for ion transport in solid electrolytes and investigate the influence of mechanics on both ion transport and reaction kinetics. Drawing on ideas from Bucci et al. [2], we formulate a fully coupled large strain theory for ionic transport in terms of electric field, mechanical deformation and anion and cation concentrations. We derive suitable constitutive relations based on the Helmholtz energy and thermodynamic restrictions for the species fluxes of the different ionic constituents as done in the context of liquid electrolytes e.g. by Dreyer et al. [3]. We propose a constitutive formulation that allows the calculation of the electrochemical transport in the deformed state and consistently predicts the coupling between species transport and gradients of stress and material properties based on the choice of the Helmholtz energy, similar to e.g. lithium diffusion in active particles [4] or the swelling of polymeric gels [5]. Using the framework of the newly derived transport theory, we investigate the effect of mechanics on the interfacial kinetics at the metal anode/solid electrolyte interface. Based on energetic considerations as presented in [6] or [7], we propose a modified Butler-Volmer relation that not only establishes a relation between the exchange current density and potential/concentration differences across the interface but also takes into account the mechanical state of both solid electrolyte and metal anode. To illustrate the features of the model and to highlight cases where the electro-chemo-mechanical coupling plays an important role for ion transport and kinetics, we show numerical examples for a Lithium symmetric solid state cell with binary solid electrolyte. [1] NEWMAN, J. S.; THOMAS-ALYEA, K. E. [2004]: Electrochemical systems. J.Wiley, Hoboken, N.J., 3rd ed Edition. [2] BUCCI, G.; CHIANG, Y.-M.; CARTER, W. C. [2016]: Formulation of the coupled electrochemical mechanical boundary value problem, with applications to transport of multiple charged species. Acta Materialia, 104:33–51. [3] DREYER, W.; GUHLKE, C.; MÜLLER, R. [2013]: Overcoming the shortcomings of the Nernst–Planck model. Physical Chemistry Chemical Physics, 15(19):7075. [4] BOHN, E.; ECKL, T.; KAMLAH, M.; MCMEEKING, R. [2013]: A model for lithium diffusion and stress generation in an intercalation storage particle with phase change. Journal of the Electrochemical Society, 160(10):A1638–A1652. [5] HONG, W.; ZHAO, X.; ZHOU, J.; SUO, Z. [2008]: A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids, 56(5):1779–1793. [6] BOCKRIS, J. O.; REDDY, A. K. N.; GAMBOA-ALDECO, M. [2000]: Modern Electrochemistry 2A: Fundamentals of Electrodics. [7] MONROE, C.; NEWMAN, J. [2004]: The effect of interfacial deformation on electrodeposition kinetics. Journal of The Electrochemical Society, 151(6):A880.

Finite Element Analysis Of Linear Elastic Torsion For Regular Polygons

This paper presents an explicit finite element integration scheme to compute the stiffness matrices for linear convex quadrilaterals. Finite element formulationals express stiffness matrices as double integrals of the products of global derivatives. These integrals can be shown to depend on triple products of the geometric properties matrix and the matrix of integrals containing the rational functions with polynomial numerators and linear denominator in bivariates as integrands over a 2-square. These integrals are computed explicitely by using symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme can be applied to solve boundary value problems in continuum mechanics over convex polygonal domains.We have also developed an automatic all quadrilateral mesh generation technique for convex polygonal domain which provides the nodal coordinates and element connectivity.We have demonstrated the proposed explicit integration scheme to solve the Poisson Boundary Value Problem for a linear elastic torsion of a non-circular bar with cross sections having profiles of equilateral triangle, a square and regular polygons (pentagon(5-gon)to icosagon(20gon)) which are inscribed in a circle of unit radius. Monotonic convergence from below is observed with known analytical solutions for the Prandtl stress function and torsional constant .We have shown the solutions in Tables which list both the FEM and exact solutions. The graphical solutions of contour level curves and the corresponding finite element meshes are also displayed.

The Singular Function Boundary Integral Method for the 2-D and 3-D Laplace Equation Problems in Mechanics, with a Boundary Singularity

In this study the Singular Function Boundary Integral Method (SFBIM) is implemented in the case of a planar elliptic boundary value problem in Mechanics, with a point boundary singularity. The method is also extended in the case of a typical problem of Solid Mechanics, concerning the Laplace equation problem in three dimensions, defined in a domain with a straight edge singularity on the surface boundary. In both the 2-D and 3-D cases, the general solution of the Laplace equation is approximated by the leading terms (which contain the singular functions) of the local asymptotic solution expansion. The singular functions are used to weight the governing equation in the Galerkin sense. For the 2-D Laplacian model problem of this study, which is defined over a domain with a re-entrant corner, the resulting discretized equations are reduced to boundary integrals by means of Green’s second identity. For the 3-D model problem of this work, the volume integrals of the discretized equations are reduced to surface integrals by implementing Gauss’ divergence theorem. The Dirichlet boundary conditions are then weakly enforced by means of Lagrange multipliers. The values of the latter are calculated together with the singular coefficients, in the 2-D case or the Edge Flux Intensity Functions (EFIFs), in the 3-D model problem, which appear in the local solution expansion. For the planar problem, the numerical results are favorably compared with the analytic solution. Especially for the extension of the method in three dimensions, the preliminary numerical results compare favorably with available post-processed finite element results.

On the nonexistence of certain solutions for damage mechanics models

The objective of this paper is to demonstrate that elastic and rigid plastic boundary value problems in damage mechanics may not have a solution. Two classes of damage mechanics models are considered. The constitutive equations of one class of models consist of a pressure-independent yield criterion, its associated flow rule, Hooke’s law and a damage evolution equation. The damage parameter enters the yield criterion. Therefore, these models are partly coupled. The constitutive equations of the other class are the constitutive equations of the classical rigid perfectly plastic model (or a rigid viscoplastic model) supplemented with an empirical ductile fracture criterion. The viscoplastic model contains a saturation stress. These models are uncoupled. In the case of partly coupled models, a simple boundary value problem is formulated and solved. It is shown that the solution breaks down for certain values of input parameters. In the case of uncoupled models, it is shown that empirical ductile fracture criteria are not compatible with solution behavior in the vicinity of maximum friction surfaces. An approach to formulate a new type of empirical ductile damage models is outlined.

Formulation of the coupled electrochemical–mechanical boundary-value problem, with applications to transport of multiple charged species

A framework is presented that treats the combined effects of nonlinear elastic deformation, lattice constraints, and electrochemical potentials. The electro-chemo-mechanical diffusion potential is derived, and the particular case where ionic species are subject to a crystal lattice constraint is also derived. By combining energy balance and local entropy production, the framework provides a consistent method to treat the evolution of charged species which also carry anelastic deformations in a crystal lattice. The framework is used to derive a finite element formulation that applies to general cases of interest for diffusion of active species in battery electrodes and in fuel cells. We demonstrate the application of the finite element formulation with two cases: ambipolar diffusion and kinetic demixing. The predicted system response demonstrates how mechanical effects cannot be disregarded, even in the presence of dominant electrostatic forces acting on ion transport. A cation rich surface layer is predicted when elastic forces, due to Vegard's stress, participate in the migration of defects in a multicomponent oxides. Simulations show how stress plays a central role in the cation segregation to interfaces, a phenomenon regarded as critical to power and durability of solid oxide fuel cells.