Composite Material Behavior Using a Homogenization Double Scale Method

• Published in: Journal of engineering mechanics Vol. 131; no. 1; pp. 65 - 79
• Main Authors: Oller, S, Miquel Canet, J, Zalamea, F
• Format: Journal Article
• Language: English
• Published: Reston, VA American Society of Civil Engineers 01.01.2005
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; TECHNICAL PAPERS; Constitutive equation; Periodicity; Homogenization; Modeling; Composite material; Boundary value problem; Composite materials; Computation; Internal structure; Homogenization methods; Homogeneity; Constitutive models; Composite structures
• ISSN: 0733-9399; 1943-7889
• DOI: 10.1061/(ASCE)0733-9399(2005)131:1(65)

In this paper, we present a two-scale numerical method in which structures made up of composite materials are simulated. The method proposed lies within the context of homogenization theory and assumes the periodicity of the internal structure of the material. The problem is divided into two scales of different orders of magnitude: A macroscopic scale in which the body and structure of the composite material is simulated, and a microscopic scale in which an elemental volume called a “cell” simulates the material. In this work, the homogenized strain tensor is related to the transformation of the periodicity vectors. The problem of composite materials is posed as a coupled, two-scale problem, in which the constitutive equation of the composite material becomes the solution of the boundary-value problem in the cell domain. Solving various examples found in the bibliography on this subject demonstrates the validity of the method.