scholarly journals Geometrically Nonlinear Stress Recovery in Composite Laminates

AIAA Journal ◽  
2012 ◽  
Vol 50 (5) ◽  
pp. 1156-1168 ◽  
Author(s):  
Timothy B. Hartman ◽  
Michael W. Hyer ◽  
Scott W. Case
Keyword(s):  
Composite Laminates ◽  
Stress Recovery ◽  
Geometrically Nonlinear ◽  
Nonlinear Stress

Stress Recovery in Composite Laminates Including Geometrically Nonlinear and Dynamic Effects

AIAA Journal ◽  
2016 ◽  
Vol 54 (8) ◽  
pp. 2521-2529 ◽  
Author(s):  
Timothy B. Hartman ◽  
Michael W. Hyer ◽  
Scott W. Case
Keyword(s):  
Composite Laminates ◽  
Stress Recovery ◽  
Geometrically Nonlinear ◽  
Dynamic Effects

Geometrically Nonlinear Stress-Deflection Relations for Thin Film/Substrate Systems With a Finite Element Comparison

1994 ◽  
Vol 61 (4) ◽  
pp. 872-878 ◽  
Author(s):  
C. B. Masters ◽  
N. J. Salamon
Keyword(s):  
Thin Film ◽  
Finite Element ◽  
Ritz Method ◽  
Spherical Shape ◽  
Free Edge ◽  
Boundary Region ◽  
Film Stress ◽  
Geometrically Nonlinear ◽  
Nonlinear Stress ◽  
Film Substrate

A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film /substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixthorder polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.

Practical Application of a Geometrically Nonlinear Stress-Curvature Relation

1991 ◽  
Vol 239 ◽  
Author(s):  
Christine B. Masters ◽  
N. J. Salamon
Keyword(s):  
Strain Energy ◽  
Film Stress ◽  
Silicon Substrates ◽  
Substrate Thickness ◽  
Geometrically Nonlinear ◽  
Practical Application ◽  
Total Strain Energy ◽  
Initial Film ◽  
Nonlinear Stress ◽  
Film Substrate

ABSTRACTA recently developed geometrically nonlinear stress-curvature relation based on a minimization of the total strain energy, which predicts a bifurcation in shape as the magnitude of intrinsic film stress increases, is discussed in this paper. It is compared with the linear theories of Stoney and Brenner & Senderoff for a thin molybdenum film on silicon substrates with various thicknesses. Although the ratio of film to substrate elastic modulus is only 2, Stoney's equation generates significant error for this film/substrate system and the Brenner & Senderoff relation should be used for calculating initial film stress when plate deflections are small. When deflections exceed approximately half the substrate thickness the Brenner & Senderoff equation produces over 10% error and consequently, the nonlinear stress-deflection relation should be used to relate plate curvatures to initial film stress.

A New Class of Damage Variables in Continuum Damage Mechanics

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
George Z. Voyiadjis ◽  
Peter I. Kattan
Keyword(s):  
Composite Laminates ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Higher Order ◽  
Cross Sectional Area ◽  
Scalar Case ◽  
Sectional Area ◽  
Cross Sectional ◽  
Nonlinear Stress

In this work various new proposed damage variables are introduced, examined and compared. Only the scalar case pertaining to isotropic damage is investigated here. Several types of new damage variables are proposed as follows: (1) damage variables that are defined in terms of cross-sectional area, (2) damage variables that are defined in terms of the elastic modulus or stiffness, and (3) composite damage variables that are defined in terms of two parameters relating to both cross-sectional area and stiffness. However, the generalization to tensors and general states of deformation and damage may be a straightforward process but is beyond the scope of this work. The damage variables introduced in this work can be applied to elastic materials including homogeneous materials like metals and heterogeneous materials like composite laminates. In the second part of this work, higher-order strain energy forms are proposed. It is seen that a specific nonlinear stress-strain relationship is associated with each higher-order strain energy form. These higher order strain energy forms along with some of the proposed damage variables are used in trying to lay the theoretical groundwork for the design of undamageable materials, i.e., materials that cannot be damaged where the value of the damage variable remains zero throughout the deformation process.

Sign in / Sign up

Export Citation Format

Share Document