Strain assisted diffusion: Modeling and simulation of deformation-dependent diffusion in composite media

In this work, we develop a model for strongly-coupled, deformation-dependent diffusion in composite media at finite strains. The coupling incorporates the effects of deformation into the diffusivity tensor. A time-transient, three-dimensional variational formulation is developed and then discretized using the Finite Element Method in conjunction with an implicit staggering scheme to resolve the coupled multiphysics. Numerical examples are provided to illustrate the model.

[1]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[2]  Tarek I. Zohdi,et al.  Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids , 2004 .

[3]  E. Hairer,et al.  Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .

[4]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[5]  Clifford Ambrose Truesdell,et al.  Mechanical Basis of Diffusion , 1962 .

[6]  M. R. Sitzer,et al.  Plastic boundary layers , 1982 .

[7]  E. Aifantis,et al.  On the theory of stress-assisted diffusion, I , 1982 .

[8]  E. C. Aifantis,et al.  On the theory of stress-assisted diffusion, II , 1982 .

[9]  A. Srinivasa,et al.  Diffusion of a fluid through an elastic solid undergoing large deformation , 2004 .

[10]  J. Adkins Non-linear diffusion III. Diffusion through isotropic highly elastic solids , 1964, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[11]  F. Krogh,et al.  Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.

[12]  J. E. Adkins,et al.  A contribution to the theory of non-linear diffusion , 1965 .

[13]  Elias C. Aifantis,et al.  On the problem of diffusion in solids , 1980 .

[14]  Kumbakonam R. Rajagopal,et al.  Diffusion through polymeric solids undergoing large deformations , 2003 .

[15]  F. P. Duda,et al.  Modeling of Coupled Deformation-Diffusion-Damage in Elastic Solids , 2007 .

[16]  Z. Suo,et al.  A theory of coupled diffusion and large deformation in polymeric gels , 2008 .

[17]  J. Adkins Diffusion of fluids through aeolotropic highly elastic solids , 1964 .