# Assumed units of material parameters in AceFEM

I want to be sure of the values I am obtaining using AceFEM, so wanted to know that the units of elastic modulus that the AceShare assumes is it MPa or N/m^2 and for density of solid is it Kg/m^3 while using "ML: SEPSQ1DFLEQ1DHooke"

AceFEM doesn't assume any unit system. It is users responsibility to choose the units of material parameters suitable for units of geometry and units of boundary conditions (e.g. forces). If you are not sure about the correctness of your units, I suggest you that you make sure with some simple test.

For example: What is the reaction force if we have a cube of steel with edge length on 1 millimeter and we stretch it in X direction for 1/100 of millimeter? (This is 1D linear elastic case.)

Analytical solution

elasticModulus = 210*10^9; (*[N/m^2]*)
edgeLength = 0.001; (*[m]*)
stretch = 0.00001;(*[m]*)
deformation = stretch/edgeLength (*[-]*)
(* 0.01 *)

(elasticModulus*deformation)*(edgeLength*edgeLength)
(*2100.*)


AceFEM solution

<< AceFEM;

SMTInputData[];
{"E *" -> 210*10^3 (*[GPa]*), "ν *" -> 0.3}
];
"A",
{{0, 0, 0}, {1, 0, 0}, {1, 1, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {1, 1, 1}, {0, 1, 1}}
];
{"X" == 0 &, 1 -> 0}, {"Y" == 0 &, 2 -> 0}, {"Z" == 0 &, 3 -> 0}, {"X" == 1 &, 1 -> 0.01}
}];
SMTAnalysis[];


We can check what are available material parameters and their values for specified domain.

SMTDomainData["A", "DomainDataNames"]
SMTDomainData["A", "Data"]
(* {"E -elastic modulus", "ν -Poisson ratio"} *)
(* {210000., 0.3} *)


Analysis in one step and reading of the result (reaction force in X direction).

SMTNextStep["λ" -> 1.];
While[SMTConvergence[10^-8, 10], SMTNewtonIteration[];];

First@Total[SMTResidual["X" == 1 &]]
(* 2100. *)
`

Analytical and AceFEM solutions match, reaction force is 2100 N.

• I think in the AceFEM code it must be MPa. So basically it assumes everywhere the same unit which we assume, it would make sense if I use SI unit everywhere thereby I won't face problems in the units right! – Swapnil Agarwal Jun 19 '17 at 12:17
• @SwapnilAgarwal I am not sure if I have fully understood your comment, but I think it is ok if you use "mm" for geometry, "N/mm^2" for elastic modulus and "kg/mm^3" for density. – Pinti Jun 19 '17 at 12:51
• "it must be MPa" No. It must be consistent with the users choice of force and length units, whatever they are. If you use millimeter for length and Newton for force then the stress (modulus) unit is Newton / ( 10^-3 meter )^2 = 10^6 Pa or MPa. But you can use whatever base force and length units you like. You could work in the fff system if you want. en.wikipedia.org/wiki/FFF_system – george2079 Jun 19 '17 at 14:11
• @george2079 thank you for clearing my doubt. – Swapnil Agarwal Jun 20 '17 at 8:57