A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications

Stabilized mixed triangular elements with area bubble functions at small and large deformations

“…The drawback of the classical formulation of Simo and Rifai [14] is the evaluation of complex non-linear terms which arise due to the enriched part. Apart from stabilization methods of mixed finite elements, which will not be discussed in detail here, further methods like nodal pressures/ strains [22][23][24][25][26]17], or reduced integration [27,28], followed by recent works [29,30] only for quadrilaterals.…”

Stabilized mixed triangular elements with area bubble functions at small and large deformations

“…The drawback of the classical formulation of Simo and Rifai [14] is the evaluation of complex non-linear terms which arise due to the enriched part. Apart from stabilization methods of mixed finite elements, which will not be discussed in detail here, further methods like nodal pressures/ strains [22][23][24][25][26]17], or reduced integration [27,28], followed by recent works [29,30] only for quadrilaterals.…”

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

“…Figure 28 illustrates the deformation history of the water column, displaying pressure contour. As already reported in [47,54,80], pressure instabilities would be excited without incorporating any numerical damping to the Jacobian evolution (see Fig. 28a,b).…”

Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods

“…This stress component is theoretically supposed to be continuous across the horizontal interface between the materials. 7 Several points are noteworthy here:…”

Stabilized mixed triangular elements with area bubble functions at small and large deformations

“…The drawback of the classical formulation of Simo and Rifai [14] is the evaluation of complex non-linear terms which arise due to the enriched part. Apart from stabilization methods of mixed finite elements, which will not be discussed in detail here, further methods like nodal pressures/ strains [22][23][24][25][26]17], or reduced integration [27,28], followed by recent works [29,30] only for quadrilaterals.…”

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

“…Figure 28 illustrates the deformation history of the water column, displaying pressure contour. As already reported in [47,54,80], pressure instabilities would be excited without incorporating any numerical damping to the Jacobian evolution (see Fig. 28a,b).…”

Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods

“…This stress component is theoretically supposed to be continuous across the horizontal interface between the materials. 7 Several points are noteworthy here:…”

Stabilized mixed triangular elements with area bubble functions at small and large deformations

“…The drawback of the classical formulation of Simo and Rifai [14] is the evaluation of complex non-linear terms which arise due to the enriched part. Apart from stabilization methods of mixed finite elements, which will not be discussed in detail here, further methods like nodal pressures/ strains [22][23][24][25][26]17], or reduced integration [27,28], followed by recent works [29,30] only for quadrilaterals.…”

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

“…Figure 28 illustrates the deformation history of the water column, displaying pressure contour. As already reported in [47,54,80], pressure instabilities would be excited without incorporating any numerical damping to the Jacobian evolution (see Fig. 28a,b).…”

Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods

“…This stress component is theoretically supposed to be continuous across the horizontal interface between the materials. 7 Several points are noteworthy here:…”