The use of strain energy as a convergence criterion in the finite element modelling of bone and the effect of model geometry on stress convergence

1993 ◽  
Vol 15 (6) ◽  
pp. 474-476 ◽  
Author(s):  
L.W. Marks ◽  
T.N. Gardner
1991 ◽  
Vol 239 ◽  
Author(s):  
Dawei Luo ◽  
David J. Howard ◽  
David C. Paine

ABSTRACTFinite element modelling of strain-layer mesa structures shows that edge effects can contribute to the relaxation of in-plane misfit stress. Calculations were performed for a 200 nm thick layer of Si90Ge10 grown epitaxially on an <001> Si substrate which was patterned into 400-nm-high mesas ranging in diameter from 0.6 to 7 μm. These calculations were experimentally investigated using plan-view TEM to study relaxation in patterned and unpatterned material. This composition and film thickness exceeds the critical thickness predicted using simple strain energy considerations. In one experiment, an initially defect-free 200-nm-thick Si90Ge10 layer was annealed at 960°C for 1 hr to create a nearly fully relaxed layer which was then lithographically patterned into an array of sub-micron mesas. The wafer was then annealed for a second time and changes in the character of die pre-existing dislocations were studied.


2016 ◽  
Vol 25 (2) ◽  
pp. 096369351602500
Author(s):  
George S.E. Bikakis ◽  
Alexander Savaidis

In this paper, a finite element modelling procedure is implemented in order to predict the static load-indentation curves and the defection shape of simply supported circular GLARE fibre-metal laminates subjected to lateral indentation by a hemispherical indentor. ANSYS software is used and a non-linear analysis is employed with geometric and material non-linearities for FEM calculations. The finite element modelling procedure is applied to GLARE 2–2/1–0.3 and to GLARE 3–3/2–0.4 simply supported circular plates with various diameters. It is found that the simply supported circular GLARE plates deform axisymmetrically from the beginning of the indentation process up to the point of their first failure due to glass-epoxy tensile fracture. By comparison of the obtained load-indentation curves to corresponding previously published load-indentation curves of clamped circular GLARE plates, the effect of the different boundary conditions on their lateral indentation response is studied. Furthermore, the strain energy-indentation curves of the considered circular GLARE 2 and GLARE 3 plates with simply supported and clamped boundaries are calculated and compared. It is found that the simply supported GLARE plates have reduced stiffness and demonstrate an increased first failure defection due to glass-epoxy tensile fracture versus the clamped GLARE plates, whereas the first failure load is not significantly affected by the different boundary conditions. It is also found that for the same lateral indentation, simply supported GLARE plates absorb lower strain energy levels than clamped GLARE plates. Referring to a specific lateral indentation level, the influence of the different boundary support on the corresponding indentation load and the absorbed strain energy is strong and can reach a deviation level of 45 % between the two support types. To our knowledge, a research concerning the response of simply supported GLARE plates under lateral indentation has not been published elsewhere.


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