Nonlinear Modeling of Open Cell Solid Foams

Solid foams is a term commonly used to describe materials with a highly disperse solid phase arranged into cells which can be either open or closed. These materials can be found in many natural systems such as cork, wood, cancelleous bone and soft tissue among many others. Also, manufacturing of artificial foams such as honeycombs, foamed polymers, ceramics and metals has been promoted by some of distinctive characteristics of these systems including an excellent strength-to-density ratio. The topological arrangement of the cell structure in conjunction with the material behavior of the solid phase determine the macroscopic response of the foam. Since the early efforts of Gent and Thomas~(1959), who proposed one of the first models for cellular materials, many studies have followed correlating the micro to macro properties. Extensive reviews on the mechanics of cellular materials include Hilyard (1982), Hilyard and Cunningham (1994), and Gibson and Ashby (1997). With the advent of novel manufacturing processes which can produce foams with controlled topological features at small scale (see for example Jackman et al. 1998), more detailed formulations correlating explicitly foam structure and solid phase behavior to the constitutive relation are required in order to tailor the design of the micro features for specific applications.

In this talk, we present a hyperelastic model for light and compliant open cell foams with an explicit correlation between microstrucure and macroscopic behavior. The model describes a large number of three dimensional structures with regular and irregular cells. The theory is based on the formulation of general strain-energy function which accounts for localized bending and stretching. Within the same framework, however, general bending, shear and twisting energies can also be incorporated. The formulation incorporates nonlinear kinematics which traces the evolution of the structure during loading process and its effects on the constitutive behavior, including the cases where configurational transformations are present leading to non-convex strain-energy functions. The implications of the non-convexity are further explored by theoretical and experimental means to elucidate the spatially heterogeneous distributions of local stretch during compressive loading.