# How CosmosM deals with material nonlinearity?

**Vitaly Koissin**Feb 7, 2008 9:10 PM

Hello everybody! I am new to this forum but I hope you can
help me in my trouble :-)

DESCRIPTION

CosmosM v.2.9 is used.

I consider edgewise compression of a 270mm long sandwich beam (plane problem) having thin stiff faces (2.4mm thick, glass-fibre laminate, about 20GPa Young's modulus) and relatively thick and soft foam core (50mm thick, 85MPa Young's modulus). Local buckling analysis is needed; thus, I model only half of the structure, i.e. only one face and half of the core thickness.

The bottom edge of the core layer is fixed, i.e. no overall bending is allowed. The face is meshed using BEAM2D, and the core - using SHELL4.

At the model edges, there are small (15mm long) tabs attached to the outer surface of the face sheet (the same BEAM2D elements coupled node-to-node to the underlying face sheet elements). The compressive load (concentrated force) is applied at the edge of one of the tabs. Actually, it should be applied in between the tab midplane and the face midplane or applied by two portions in two points but for simplicity it is done as it is done. The load eccentricity causes a local bending of the face sheet. In the real sandwich beams, due to this effect, the foam core near the tabs undergoes high strains, its supporting effect decreases, the local buckling is localised, and the critical stress is much lower than the theoretical estimations. In my FE analysis, I want to catch this effect :-)

I use 3 variants of this model; 1) purely elastic, 2) nonlinear elastic response of the face sheet material and 3) nonlinear elastic response of both materials (face and core). You can take the source files here: http://iccr.sutd.ru/koissin/sandwich_vk_080208.zip

RESULTS

1) The 1st variant runs OK. The local buckling load and mode are quite realistic.

2) The 2nd variant is also OK. It is a little bit strange that I get the nonlinear solution (lower critical load, localisation of buckling) directly by R_BUCKLING, without preliminary computation of the stiffness matrix on each loading step. But probably this is OK, since only material non-linearity is considered.

3) Finally, I introduce the material non-linearity for the core layer. Here, several issues appear which are not clear for me. They are the following:

a) Cosmos rejects to start calculations without entering the elastic constants using MPROP. For variant 2 it is OK - I do not use MPROP at all for the face sheet, since the tangent modulus is automatically calculated using the material curve, and the Poisson's ratio is not needed for BEAM2D in this case. But if I add a similar material curve for the core layer, then this strangely follows that I also have to define EX for the face sheet. Otherwise, I receive error "Modulus of elasticity (EX) smaller than 1e-25 for ele1081" (the 1st BEAM2D element of the face sheet).

I do not understand this point. If compare with variant 2, nothing changes for the face sheet definition. I only re-number the material curves (MPCTYP,2,0 and MPC,2,0,1,.. instead of MPCTYP,1,0 and MPC,1,0,1,..) It looks like the material curve is ignored in the analysis...

b) For the core layer (SHELL4 elements) I also need to input EX. Why?... What I also do not understand is how Cosmos deals with the nonlinear elasticity: does it preserve isotropy or automatically introduces orthotropy?

c) For variant 3, results of analysis using R_BUCKLING coincides with these for variant 1. I do not observe any nonlinear effects which are seen in this case in variant 2. Why it is so? It looks again like the material curves are ignored in the analysis...

Final question: how to deal with this? Maybe somebody has already faced similar problems?

Thanks in advance!

DESCRIPTION

CosmosM v.2.9 is used.

I consider edgewise compression of a 270mm long sandwich beam (plane problem) having thin stiff faces (2.4mm thick, glass-fibre laminate, about 20GPa Young's modulus) and relatively thick and soft foam core (50mm thick, 85MPa Young's modulus). Local buckling analysis is needed; thus, I model only half of the structure, i.e. only one face and half of the core thickness.

The bottom edge of the core layer is fixed, i.e. no overall bending is allowed. The face is meshed using BEAM2D, and the core - using SHELL4.

At the model edges, there are small (15mm long) tabs attached to the outer surface of the face sheet (the same BEAM2D elements coupled node-to-node to the underlying face sheet elements). The compressive load (concentrated force) is applied at the edge of one of the tabs. Actually, it should be applied in between the tab midplane and the face midplane or applied by two portions in two points but for simplicity it is done as it is done. The load eccentricity causes a local bending of the face sheet. In the real sandwich beams, due to this effect, the foam core near the tabs undergoes high strains, its supporting effect decreases, the local buckling is localised, and the critical stress is much lower than the theoretical estimations. In my FE analysis, I want to catch this effect :-)

I use 3 variants of this model; 1) purely elastic, 2) nonlinear elastic response of the face sheet material and 3) nonlinear elastic response of both materials (face and core). You can take the source files here: http://iccr.sutd.ru/koissin/sandwich_vk_080208.zip

RESULTS

1) The 1st variant runs OK. The local buckling load and mode are quite realistic.

2) The 2nd variant is also OK. It is a little bit strange that I get the nonlinear solution (lower critical load, localisation of buckling) directly by R_BUCKLING, without preliminary computation of the stiffness matrix on each loading step. But probably this is OK, since only material non-linearity is considered.

3) Finally, I introduce the material non-linearity for the core layer. Here, several issues appear which are not clear for me. They are the following:

a) Cosmos rejects to start calculations without entering the elastic constants using MPROP. For variant 2 it is OK - I do not use MPROP at all for the face sheet, since the tangent modulus is automatically calculated using the material curve, and the Poisson's ratio is not needed for BEAM2D in this case. But if I add a similar material curve for the core layer, then this strangely follows that I also have to define EX for the face sheet. Otherwise, I receive error "Modulus of elasticity (EX) smaller than 1e-25 for ele1081" (the 1st BEAM2D element of the face sheet).

I do not understand this point. If compare with variant 2, nothing changes for the face sheet definition. I only re-number the material curves (MPCTYP,2,0 and MPC,2,0,1,.. instead of MPCTYP,1,0 and MPC,1,0,1,..) It looks like the material curve is ignored in the analysis...

b) For the core layer (SHELL4 elements) I also need to input EX. Why?... What I also do not understand is how Cosmos deals with the nonlinear elasticity: does it preserve isotropy or automatically introduces orthotropy?

c) For variant 3, results of analysis using R_BUCKLING coincides with these for variant 1. I do not observe any nonlinear effects which are seen in this case in variant 2. Why it is so? It looks again like the material curves are ignored in the analysis...

Final question: how to deal with this? Maybe somebody has already faced similar problems?

Thanks in advance!

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