Bend stiffness of laminate microstructures containing three dissimilar materials
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Bend stiffness of laminate microstructures containing three dissimilar materials Damiano Pasini
Received: 14 July 2008 / Accepted: 1 December 2008 / Published online: 17 December 2008 Springer Science+Business Media, B.V. 2008
Abstract This article examines the effective flexural modulus of a multilayered micro-system evolving into alternative layered structures consisting of three dissimilar materials. A multiscale model of the bending stiffness is presented to capture the impact of changing the constituent materials, the layer architecture and the cross-section geometry. The results are plotted onto maps to show the existence of specific domains, within which fall the effective properties of all possible trimaterial multilayered configurations. The potential to stiffen a bi-material system is demonstrated by integrating additional layers of a more flexible material for given constraints on the volume fraction. The proposed scheme is conducive to contrast structural alternatives in constrained and unconstrained design. A case study shows how the maps enable optimum selection among various design concepts, which may range from monolithic materials with alternative shape geometries to systems consisting of two and three materials arranged in dissimilar multiple layer architectures. Keywords Multilayered system Flexural modulus modelling Layer geometry and material selection
D. Pasini (&) Department of Mechanical Engineering, Institute for Advanced Materials of McGill University, 817 Sherbrooke Street West, Montreal, QC, Canada H3A2K6 e-mail: [email protected]
Notations A Cross sectional area B Width (m) b Internal width (m) c Dimensionless multiplicator of cross-section internal width (c = b/B) c1 Beam curvature d Dimensionless multiplicator of cross-section internal height (d = h/H) D Rectangular cross-section envelope E Young’s modulus (GPa) ED, qD Effective of properties of prismatic beam ET, qT Effective of properties of shaped beam h Internal height (m) H Height (m) I Second moment of area (m4) JT Cross-section torsional constant (m4) l Beam length (m) Mb Bending moment per unit width m Mass (mg) n Exponent of Lame’ curves p Performance index q Scaling parameter of performance index rg Radius of gyration (m) u, v Envelope multiplicators S Shape V Volume (m3) q Material density (mg/m3) k Envelope efficiency parameter w Shape transformer
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1 Introduction Compared to monolithic materials, multilayered shaped structures have the potential to boost the performance of the next generation of micro-devices. The physical properties of these composites can be tailored to obtain optimized mechanical performance, often unachievable with the use of a single material. As monolithic structures, multilayered systems can work as transducers and, thus, be used in a large number of applications. For example, they are able to sense voltage, measure force and acceleration, move and control mechanisms, detect variations in current, pressure, temperature and other physical properties (Gad-el-Hak 2002; Senturi
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