On a finite-strain plate theory for growth-induced plane-strain deformations and instabilities of multi-layered hyperelastic plates

Author(s):  
Ping Du ◽  
Jiong Wang ◽  
Zhanfeng Li ◽  
Weicheng Cai
2000 ◽  
Vol 123 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Yarom Polsky ◽  
I. Charles Ume

The influence of transverse shear strain in the lamination theory modeling of Printed Wiring Board (PWB) deflection due to support conditions was examined. The in-plane mechanical properties of the core materials of a commercial PWB were measured as a function of temperature. Classical laminated plate theory and first-order shear deformation theory solutions for the out-of-plane deflection of a bare board configuration with two opposite edges simply supported and the remaining edges free were obtained. The weight of the board was approximated as a distributed transverse load. The effect of material property decrease with temperature and FR-4 layer thickness were examined to compare first-order shear and plane strain assumptions for the predicted warpage.


2016 ◽  
Vol 125 (2) ◽  
pp. 149-183 ◽  
Author(s):  
Zilong Song ◽  
Hui-Hui Dai
Keyword(s):  

Study of natural finite strain states in several oolitic limestones indicates that, unlike most rocks, many limestones have undergone deformation by a process of approximately plane strain. Accordingly, specimens of oolitic limestone were deformed experimentally in plane strain at confining pressures of 100 and 200 MPa, at temperatures of 25, 100, and 200 °G, and to total strains from 20 to 50 % by increments of 10 and 5 %. From subsequent strain analysis, utilizing thin sections of the deformed specimens, we find that the greatest strain heterogeneity exists, as is to be expected, for conditions under which the rock has low ductility, i.e. low confining pressure and low temperature. Increased pressure and temperature promotes a change in microscopic mechanism from cataclasis to intracrystalline gliding. The degree of strain heterogeneity is significantly decreased at higher confining pressure; it is affected to a lesser degree by higher temperature. From our results, it appears that the degree of strain heterogeneity remains sufficient within the deformational mode fields of uniform flow and ductile faulting to justify utilization of the deformation path concept.


Author(s):  
Hui-Hui Dai ◽  
Zilong Song

This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional potential energy under general loadings with a fourth-order error. Starting from the three-dimensional nonlinear elasticity (with both geometrical and material nonlinearity) and by a series expansion, we deduce a vector plate equation with three unknowns, which exhibits the local force-balance structure. The success relies on using the three-dimensional field equations and bottom traction condition to derive exact recursion relations for the coefficients. Associated weak formulations are considered, leading to a two-dimensional virtual work principle. An alternative approach based on a two-dimensional truncated energy is also provided, which is less consistent than the first plate theory but has the advantage of the existence of a two-dimensional energy function. As an example, we consider the pure bending problem of a hyperelastic block. The comparison between the analytical plate solution and available exact one shows that the plate theory gives second-order correct results. Compared with existing plate theories, it appears that the present one has a number of advantages, including the consistency, order of correctness, generality of loadings, applicability to finite-strain problems and no involvement of non-physical quantities.


2001 ◽  
Vol 38 (6) ◽  
pp. 1155-1165 ◽  
Author(s):  
Vincenzo Silvestri

This paper presents a method to obtain the constitutive relationships of sand from drained self-boring pressuremeter tests. Plane-strain conditions and Rowe's stress–dilatancy theory are assumed to hold to determine stress and finite strain distributions and paths. The proposed method, which has been validated using both calibration chamber studies and field tests, appears to correctly render the response behaviour of relatively loose to dense sands.Key words: stress–strain relations, self-boring pressuremeter tests, sands, finite strains, stress distributions, paths.


Sign in / Sign up

Export Citation Format

Share Document