Skip to main content
Advanced Modeling and Simulation in Engineering Sciences

Table 1 The number of Gauss integration points for considered element types according to [21, Fig. 6.22], [20, Table 5.9]

From: Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

Element type

T3

T6

Q4

Q8

\({\varvec{\mathsf {B}}}^{\mathsf {T}}\overline{{\varvec{\mathsf {E}}}}{\varvec{\mathsf {B}}}\) (stiffness-matrix)

1

3

4 (\(1^{\mathrm{a}}\))

9 (\(4^{\mathrm{b}}\))

\({\varvec{\mathsf {N}}}^{\mathsf {T}}\overline{{\varvec{\mathsf {G}}}}{\varvec{\mathsf {N}}}\) (mass-matrix)

3

6

4

9

  1. T3 denotes three-node linear triangle, T6 six-node quadratic triangle, Q4 four-node bilinear quadrilateral, and Q8 eight-node serendipity quadratic quadrilateral. Numbers in parentheses specify the number of Gauss integration points for under-integrated versions in standard FE technology
  2. \(^{\mathrm{a}}\) In standard two-dimensional FEM, two spurious singular modes requiring hourglass control are observed
  3. \(^{\mathrm{b}}\) Induces one spurious singular mode in standard FEM; the mode is non-communicable, i.e. it typically does not occur in an element patch and hence no stabilization is usually required, cf. Fig. 4a, [20, Section 5.5.7.], and [22]
Back to article page