The optimal density of cellular solids in axial tension

• Published in: Computer methods in biomechanics and biomedical engineering Vol. 20; no. 7; pp. 701 - 713
• Main Authors: Mihai, L. Angela, Alayyash, Khulud, Wyatt, Hayley
• Format: Journal Article
• Language: English
• Published: England Taylor & Francis 19.05.2017; Taylor & Francis Ltd
• Subjects: Axial stress; Cell size; Cell walls; Cellular solids; Elastic deformation; Elastic Modulus; Finite Element Analysis; Finite element method; large strain deformation; material density; Mathematical models; Mechanical properties; micro-structural behaviour; Modulus of elasticity; Nonlinear Dynamics; nonlinear hyperelastic material; optimisation; Optimization; Periodic structures; Plant Cells - metabolism; Plant Stems - physiology; Solids; Strain; Stress, Mechanical; Wall thickness; Cellular solids; material density; optimisation; nonlinear hyperelastic material; large strain deformation; micro-structural behaviour
• ISSN: 1025-5842; 1476-8259; 1476-8259
• DOI: 10.1080/10255842.2017.1292352

For cellular bodies with uniform cell size, wall thickness, and shape, an important question is whether the same volume of material has the same effect when arranged as many small cells or as fewer large cells. To answer this question, for finite element models of periodic structures of Mooney-type material with different structural geometry and subject to large strain deformations, we identify a nonlinear elastic modulus as the ratio between the mean effective stress and the mean effective strain in the solid cell walls, and show that this modulus increases when the thickness of the walls increases, as well as when the number of cells increases while the volume of solid material remains fixed. Since, under the specified conditions, this nonlinear elastic modulus increases also as the corresponding mean stress increases, either the mean modulus or the mean stress can be employed as indicator when the optimum wall thickness or number of cells is sought.