Hi All,
I am simulating 3D micromechanics of fiber reinforced composites, in which fiber and matrix are introduced explicitly such as the work of Camanho et al. Llorca et al, Vaughan and McCarthy etc.
From my observation, in most micro-mechanics model, people use cohesive element method to model fiber-matrix debonding. This method is known to have a spurious compliance problem which will cause inaccurate effective properties of undamaged RVE. My question is why people does not use XFEM instead? what makes people avoid of using it? Is there any problem that I dont foresee? (convergence issue maybe?)
Currently I am using abaqus, and In abaqus, both XFEM and CZM are built-in capabilities.
Thanks for your reply.
X-FEM use expansion series (Williams) for the formulation of the discontinuities. This series doesn't exist in plasticity. If one wants to use non-linear models then X-FEM becomes less obvious to use as there will be a difference between the behavior used the representation of the enriched kinematics is not in line with the real non-linear material. With cohesive elements you have the possibility to set-up your behavior using various laws. Even if they are not physically funded, non-linear problems using X-FEM are also questionable. X-FEM is interesting when you don't have a priori informations on your crack path but it doesn't have this interest for debonding as you already know the crack path possibilities. It is quite complex to implement crack with friction while it is quite obvious with cohesive elements. In fact, it is complex to justify the use of X-FEM for heterogeneous non-linear problems
As fas ar I understand, XFEM will not help you much if the crack path is already determined (as it is if you have debonding between fibre and matrix). Cohesive elements (or cohesive contact in new versions of Abaqus) make it easier to actually enter the properties of the interface - in an XFEM analysis, you would need different materials on both sides of the interface, i.e. you would either have to ensure that the crack always runs long the nodes (not splitting an element), which is a bit contrary to the whole XFEM idea, or you would also have to use XFEM to model the different materials and their boundary.
I would imagine the reason is that in XFEM the shape of the anticipated discontinuities ( say.. cracks) are parametrized using simple discontinuous polynomials and related to the DOF's (through the total energy,possibly). In real composites, such parametrization using discontinuous shape functions is not possible let alone be accurate due to the expected "high branching nature" of cracks especially in fiber micro-composites.
X-FEM use expansion series (Williams) for the formulation of the discontinuities. This series doesn't exist in plasticity. If one wants to use non-linear models then X-FEM becomes less obvious to use as there will be a difference between the behavior used the representation of the enriched kinematics is not in line with the real non-linear material. With cohesive elements you have the possibility to set-up your behavior using various laws. Even if they are not physically funded, non-linear problems using X-FEM are also questionable. X-FEM is interesting when you don't have a priori informations on your crack path but it doesn't have this interest for debonding as you already know the crack path possibilities. It is quite complex to implement crack with friction while it is quite obvious with cohesive elements. In fact, it is complex to justify the use of X-FEM for heterogeneous non-linear problems
Thanks you very much Jean. Your answer enlighten me so much.
Dear Ditho,
XFEM is perhaps less interesting in problems such as fiber-matrix debonding where the crack path is determined a priori. However, a combination of XFEM with cohesive elements (continuous or discrete) is often used in the literature for efficiently solving this kind of problems. This combination maintains the main advantage of XFEM, i.e. the possibility to use a regular structured mesh which does not have to be adapted to the internal details (cracks or material interfaces) of a microstructure.
Dear all,
I do understand that the power of XFEM is that it can predict its own crack path and does not to follow the predefined path like delamination or fiber-matrix interface.
And of course, if XFEM can do arbitrary crack path, it should also able to follow the one with predifined crack parth such as delamination.
My question was then why people did not use it? Since the exsiting CZM will make spurious compliance problem.
But now, I just found out several paper that use XFEM for solving these kind of problems.
http://www.tandfonline.com/doi/abs/10.1080/09243046.2014.915092#.VdA7WEYuxm9
or
http://www.sciencedirect.com/science/article/pii/S0927025612001802
Thanks btw.
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