9.3.1 Elasticity

9.3.1.1 Linear Stiffness

Interface elements in linear structural analysis require input of the linear stiffness.

    (syntax)

DSTIF

d11 and d22 are linear stiffness moduli D₁₁ and D₂₂ . D₁₁ sets the relation between the normal traction t_n ( D₁₁ $\geq$ 0 )and the normal relative displacement $\Delta$u_n . D₂₂ sets the relation between the shear traction t_t ( D₂₂ > 0 )and the shear relative displacement $\Delta$u_t . The dimension of the stiffness moduli is force per area per length, i.e., stress per length, for instance N/mm³ .

    (file.dat)

'MATERI'
   1  DSTIF  1.E+8  0.0001
   2  DSTIF  1.E+5  1.E+5

Material 1 is an elastic bedding without shear stiffness. Material 2 has equal normal and shear stiffness.

9.3.1.2 Ambient Influence

The normal and tangential stiffness moduli may be specified depending on ambient values for maturity. In this case the stiffness moduli must be specified with DSTIF followed by the data records in this section. Maturity dependency is the only ambient influence that can be used for interface stiffness moduli. Maturity dependent stiffness can only be combined with discrete cracking [§9.3.2.1] and bond-slip [§9.3.3].

Maturity dependent stiffness moduli    (syntax)

MATDSN

specifies maturity influence of the normal stiffness modulus. d11a ...d11z are the normal stiffness moduli D₁₁ , (z $\leq$ 30 )respectively valid for the corresponding mva ...mvz maturity variables. Equivalent age is the only maturity variable that can be used for this model.

MATDST

specifies maturity influence of the tangential stiffness modulus. d22a ...d22z are the normal stiffness moduli D₂₂ , (z $\leq$ 30 )respectively valid for the corresponding mva ...mvz maturity variables. Equivalent age is the only maturity variable that can be used for this model.

9.3.1.3 Nonlinear Elasticity

This section describes the input syntax of nonlinear elasticity for interfaces. Applications cover nonlinear elastic bedding, e.g. `no tension' bedding with a constant stiffness for compression and zero stiffness for tension.

The available nonlinear elastic model sets a multilinear relation between normal traction t_n and normal relative displacement $\Delta$u_n or between the tangential traction t_t and the tangential relative displacement (shear slip) $\Delta$u_t or both.

    (syntax)

SIGDIS

specifies a diagram for the normal direction: values tn1 ...tnn ( n $\leq$ 100 )are the normal tractions t_n , un1 ...unn are the corresponding normal relative displacements $\Delta$u_n .

TAUDIS

specifies a diagram for the tangential direction: values tt1 ...ttn ( n $\leq$ 100 )are the tangential tractions t_t , ut1 ...utn are the corresponding tangential relative displacements $\Delta$u_t .

Both diagrams must start in the compressive (negative) region and end in the tension (positive) region. The specified relative displacements must be in increasing order. For numerical reasons it is recommended to use a continuous slope at (0,0) in both diagrams which corresponds with the elastic stiffness as specified with DSTIF.

    (file.dat)

'MATERI'
   1  DSTIF   1000. 500.
      SIGDIS  -100000. -100.    0.  0.     100. 100.
      TAUDIS       -5. -100.   -5. -0.01     5.   0.01    5. 100.

This example is stiff in compression and weak in tension normal to the interface. Tangential to interface the maximum shear traction is 5.0.