## Spring definition

@SPRING_DEFINITION {
@SPRING_NAME {SpringName} {
@FUNCTION_1D_TYPE {Fun1DType}
@FUNCTION_1D_NAME {Fun1DName}
@FUNCTION_1D_NAME {Fun1DNameDeriv}
@INITIAL_STRETCH {Δi}
}
}

### Introduction

A spring defines the nonlinear relationship between the force and stretch of an elastic spring. Two types of springs can be defined.

1. Rectilinear springs define the relationship between the spring elastic force, Fel, and stretch, Δ. Rectilinear springs are used with relative displacement elements or are part of a more complex elastomeric device model.
2. Torsional springs define the relationship between the spring elastic moment, Mel, and rotation, φ. Torsional springs are used with relative rotation elements or are part of a more complex elastomeric device model.

### NOTES

1. Parameter Fun1DType defines the nature of the spring. It can take either of two values.
1. Fun1DType = RECTILINEAR_SPRING defines a rectilinear spring, and
2. Fun1DType = TORSIONAL_SPRING defines a torsional spring.
2. The characteristics of the spring are defined by 1D function, Fun1DName, F = F(x), which maps to Fel = Fel(Δ) and Mel = Mel(φ) for the rectilinear and torsional springs, respectively. The 1D function can be a Chebyshev function, a harmonic function, a tabulated function, or a user function. For tabulated functions, the discrete function must approximated by its expansion in terms of Chebyshev polynomials.
3. It will also be required to compute the derivative of the spring force or moment with respect to the stretch or rotation, respectively. If the 1D function is defined as a Chebyshev, harmonic, or tabulated function, this derivative is computed analytically and a 1D function associated with this derivative will be generated automatically. If the 1D function is defined as a user function, this derivative must be provided as an independent user function, Fun1DNameDeriv. In this case, both Fun1DName and Fun1DNameDeriv must refer to user functions.
4. If an initial stretch, Δi, of the spring is defined, the elastic force in the spring is computed with the total stretch s + Δi.
5. It is possible to attach comments to the definition of the object; these comments have no effect on its definition.