PSI - Issue 14

Akhilesh Kumar Jha et al. / Procedia Structural Integrity 14 (2019) 416–428 Akhilesh Kumar Jha et al. / Structural Integrity Procedia 00 (2018) 000–000

421

6

Table 2. Properties of Rohacell 51WF foam. Rohacell 51WF

Values

E (MPa)

22

n

0

σ cy (MPa) P (MPa)

0.85 0.82

For woven fabric progressive damage modeling, Abaqus VUMAT subroutine has been implemented that is accessed by naming the user-defined material with the string ÁBQ_PLY_FABRIC. Continuum shell elements are used to models the target plates in ABAQUS. Continuum shell elements are the closest possible formulation that, being 3 dimensional in nature, can capture through thickness response for composite laminate structures. Table 3. Shows the formulation of the input deck of ABQ_PLY_FABRIC. The 1st and 2nd line contains, the elastic moduli, Poisson’s ratio and in-plane fiber strengths in the 1 and 2 directions. Line 3, represents the fracture energy released per unit area for loading along fiber direction 1 and 2. The ‘+’ and ‘-’ sign indicates, the mode of tensile and compressive loading respectively. Also, in Line 3, the material parameters that represent the shear damage parameter and maximum shear damage values are entered. Line 4 contains properties that are used to model plastic hardening of the matrix such as, the initial effective shear yield stress and the coefficient and power term in the hardening equation respectively, which is given by the formula, � � �� � � � �� � �� �� � � (7) Parameters in Line 5 are used as criteria for element deletion.

Table 3. Input deck for ABQ_PLY_FABRIC in ABAQUS. *MATERIAL, NAME=ABQ_PLY_FABRIC *DENSITY

*USER MATERIAL, CONSTANTS=40 ** Line 1 E 1+ E 1- ν E 2+ E 2- ** Line 2 X 1+ X 1- X 2+ X 2- S ** Line 3 G f 1+ G f 1- G f 2+ G f 2- α ** Line 4 σ y0 C p ** Line 5 1DelFlag d max ε max pl ε

12 d 12

max

max ε min

* DEPVAR DELETE 16 16

3.3. Methods of computation There are currently four modeling methods available, such as Lagrangian, Eulerian, Coupled Lagrangian Eulerian (CEL), and Smooth Particle Hydrodynamics, which are being used for the impact damage analyses. Each methodology has its own strengths and weaknesses. 3.3.1. Lagrangian Formulation In the Lagrangian formulation, the volume is divided into a large number of small geometries called elements. Mesh nodes are connected to a material by certain imaginary points called Integration points. The mesh follows the material, i.e. one material per element, during entire simulation. This formulation is generally used for solid materials.