## How to specify material parameters at integr. points

## How to specify material parameters at integr. points

(OP)

Hi there,

I come into a situation where I would like to specify different material parameters (Let's say in simple elastic case, the Young's modulus) for each integration point of the finite elements. By doing this I hope I can model materials of which the parameters are spatial variables, and therefore, cannot be treated as constants for an element. Does anyone know how to implement this in ABAQUS?

To split this question into more specific ones:

1. Does ABAQUS evaluate material properties at every integration points?

2. If yes, how to specify different properties for each integration points?

3. Is there a way to get stiffness matrices evaluated at the integration points? rather than the elemental stiffness matrix being the weighted sum of those matrices.

4. The last one is weird but actually helpful for me:

Will ABAQUS analysis proceed even if some material parameters do not make sense physically? In other words, how to let ABAQUS continue to analysis, without exiting itself due to fatal error warnings, when Young's modulus is negative?

I come into a situation where I would like to specify different material parameters (Let's say in simple elastic case, the Young's modulus) for each integration point of the finite elements. By doing this I hope I can model materials of which the parameters are spatial variables, and therefore, cannot be treated as constants for an element. Does anyone know how to implement this in ABAQUS?

To split this question into more specific ones:

1. Does ABAQUS evaluate material properties at every integration points?

2. If yes, how to specify different properties for each integration points?

3. Is there a way to get stiffness matrices evaluated at the integration points? rather than the elemental stiffness matrix being the weighted sum of those matrices.

4. The last one is weird but actually helpful for me:

Will ABAQUS analysis proceed even if some material parameters do not make sense physically? In other words, how to let ABAQUS continue to analysis, without exiting itself due to fatal error warnings, when Young's modulus is negative?

## RE: How to specify material parameters at integr. points

>1. Does ABAQUS evaluate material properties at every integration points?

Material props are not evaluated as such, but are given - and used by the constitutive model - on a element-by-element level. The integration points are used as 'sampling points' (see any numerical methods book on numerical integration methods under 'Gaussian Integration') in order to integrate the FE equations.

>2. If yes, how to specify different properties for each integration points?

See above.

>3. Is there a way to get stiffness matrices evaluated at the integration points? rather than the elemental stiffness matrix being the weighted sum of those matrices.

Integration points ARE used to obtain the stiffness of each element. The total stiffness (K) is the sum of all the elemental stiffnesses found as:

Ke = Integral [B]T [D] [B]

integrated over the domain, where D is a material constant matrix and B is a strain matrix.

>4. The last one is weird but actually helpful for me:

Will ABAQUS analysis proceed even if some material parameters do not make sense physically? In other words, how to let ABAQUS continue to analysis, without exiting itself due to fatal error warnings, when Young's modulus is negative?

I'm sure the modulus must have to be entered as positive. My thinking is that physically, a global negative modulus cannot exist, otherwise a local negative strain would produce a positive displacement and vice versa(!). It may be possible to have micro levels of negative modulus, but this isn't applicable at the global level.

Hope this helps,

-- drej --

## RE: How to specify material parameters at integr. points

Your question is interesting and Drej's reply is very wise.

Apart from the negative elasticity, I'm afraid it's not possible to define but a single value for E & v for an element.

If the material properties vary spatially, why not refine your mesh and assign adjacent elements different Es and Poisson Ratios?

Dear drej: I couldn't really understand why a negative E means that a negative strain leads to a positive displacement. It is interesting for me to know why, since negative Poisson ratio is mathematically acceptable and I have actually seen synthetic materials with a negative Poisson ratio, but negative E signifies a violation from the fundamental laws of thermodynamics.