Effective Elastic Stiffness for Periodic Masonry Structures via Eigenstrain Homogenization

The equivalent periodic eigenstrain method is used to evaluate the effective elastic stiffness of periodic masonry structure. An Eshelby tensor, for a unit cell of the periodic masonry structure, is derived analytically, and is combined with a strain energy approach to formulate the effective stiffness of the masonry. The new homogenization scheme is simple, one step, and closed form. The model described the periodicity and microstructure details of brick and mortar precisely and is compared to other analytical models. The improved accuracy of model prediction is validated through a finite-element simulation reported in literature. DOI: 10.1061/ ASCE 0899-1561 2007 19:3 269 CE Database subject headings: Elasticity; Stiffness; Masonry; Finite elements. Introduction Masonry is a two-phase material comprised of brick and mortar joints, normally arranged periodically. Studying the in-plane load deformation characteristics of the masonry is important for designing and retrofitting masonry structures. As a viable alternative to otherwise expensive and time-consuming laboratory and field experiments, numerical and analytical methods have attracted extensive attention in both industry and the research community. One of the most comprehensive approaches is to model each brick and each mortar joint in the assembly, where linear and nonlinear constitutive behaviors of bricks and mortar can be considered. Although detailed stress–strain and failure mechanism are well studied, methods of this category demand intensive computational efforts and usually rely on the expertise of finite element technique for example, in Gambarotta and Lagomarsino 1997; Michel et al. 1999; Giambanco et al. 2001; Formica et al. 2002 . The representation of each brick and each joint is essentially impractical for modeling a real large masonry structure, so this approach is only suitable to simulate a small specimen or a representative unit. The overall property of masonry can be derived accordingly from the numerical experiments Ma et al. 2001 . Graduate Researcher, Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley, CA 94720. Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley, CA 94720 corresponding author . E-mail: [email protected] Staff Engineer, Ball Aerospace & Technologies Corp., Systems Engineering Solutions, 2201 Buena Vista SE, Albuquerque, NM 87106; formerly, Graduate Student, Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley, CA 94720. Professor, Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley, CA 94720. Note. Associate Editor: Jason Weiss. Discussion open until August 1, 2007. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on January 13, 2004; approved on March 7, 2006. This paper is part of the Journal of Materials in Civil Engineering, Vol. 19, No. 3, March 1, 2007. ©ASCE, ISSN 0899-1561/ 2007/3-269–277/$25.00.