Blast Mitigation Strategies in Marine Composite and Sandwich Structures by Srinivasan Gopalakrishnan & Yapa Rajapakse

Author:Srinivasan Gopalakrishnan & Yapa Rajapakse
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

2 Failure of Fiber-Reinforced Composite Laminate Due to Blast Loads

2.1 Material Models

2.1.1 Constitutive Relation

It is common to model, e.g., see [7, 8], the material nonlinearity by using a linear relation between the second Piola-Kirchhoff stress tensor, S, and the Green-St. Venant strain tensor, E. That is,

(1)

where C is the matrix of elasticities. The material described by Eq. (1) is called St. Venant-Kirchhoff. Here and below, a repeated index implies summation over the range of the index. We note that S has no physical meaning but is convenient to use, E includes all nonlinear terms in displacement gradients, and S and E are work-conjugate tensors. The stress–strain relation (1) is materially objective, and one can easily implement it in a software. From S and displacement gradients, one finds the true or the Cauchy stresses needed to ascertain damage initiation at a point.

A unidirectional fiber-reinforced lamina, modeled as a transversely isotropic material with the fiber along the axis of transverse isotropy, has five material constants. With S and E written as 6-D vectors, values of elasticities in the 6 × 6 matrix of material parameters are such that the matrix is positive-definite. For simple extensional deformations of a cylindrical isotropic body made of the St. Venant-Kirchhoff material, the structure becomes unstable in compression when the final length/initial length (or the axial stretch) equals 0.577 irrespective of values of material elasticities [9]. For simple shear deformations, this material exhibits strain hardening because the slope of the shear stress versus the shear strain curve increases with an increase in the shear strain [9]. For a transversely isotropic material loaded along the axis of transverse isotropy, the prismatic cylinder will become unstable at a compressive axial strain whose value depends upon the material elasticities.

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