This is a damage lattice material used together with latticedamage2d elements. It uses a scalar damage relationship of the form


where is a vector of tractions and is a vector of strains obtained from displacement jumps smeared over the element length. Furthermore, $ \omega$ is the damage variable varying from 0 (undamaged) to 1 (fully damaged). Also, is the elastic stiffness matrix which is based on the elastic modulus of the lattice material $ E$, and a parameter $ \gamma$ which is the ratio of the modulus of the shear and normal direction. The strength envelope is elliptic (Figure 12) and determined by three parameters, $ f_{\rm t}$, and . The evolution of the damage variable $ \omega$ is controlled by normal stress-normal crack opening law. The three possible laws are linear, bilinear and exponential (Figure 13).

Figure 12: Strength envelope of LatticeDamage2d.

Figure 13: Softening types of LatticeDamage2d: (a) linear softening, (b) bilinear softening, (c) exponential softening.

The model parameters are summarised in Tab. 50.

Table 50: Scalar damage model for 2d lattice elements - summary.
Description Saclar damage model for lattice2d
Record Format latticedamage2d (in) # d(rn) # talpha(rn) # e(rn) # a1(rn) # a2(rn) # e0(rn) # coh(rn) # ec(rn) # stype(rn) # wf(rn) # wf1(rn) #
Parameters - material number
  - d material density
  - talpha Thermal exansion coefficient
  - e normal modulus of lattice material
  - a1 ratio of shear and normal modulus
  - a2 ratio of rotational and normal modulus. Optional parameter. Default is 1.
  - e0 strain at tensile strength:
  - coh ratio of shear and tensile strength:
  - ec ratio of compressive and tensile strength:
  - stype softening types: 1-linear, 2-bilinear and 3-exponential
  - wf displacement threshold related to fracture energy used in all three softening types.
Supported modes 2dlattice

Borek Patzak