Three-dimensional finite-deformation multiscale modeling of elasto-viscoplastic open-cell foams in the dynamic regime

Cellular materials such as metallic and polymeric open-cell foams resemble a labyrinth of interconnected struts surrounded by air-filled voids however a closer inspection reveals a periodicity where a particular unit cell is repeated throughout a lattice inside a matrix of air. Depending on the loading rate and the specifics of the cellular topology and the material properties of the solid phase, the different stages of deformation can involve elasticity, plasticity, fracture, viscoelasticiy, thermoelasticity, strain rate effects, density (microinertia) etc. This dissertation contributes an approach for modeling dynamically loaded open-cell foam materials where the structure is mimicked with the replication of a periodic unit cell composed of a four ligament tetrahedron inside a dual tetrakaidecahedron volume element. Formulation of the Lagrangian for a representative unit cell comprising an imposed macroscopic deformation and enforcement of the principle of minimum action for dissipative systems results in a relation between the globally applied macroscopic deformation and the motion of the internal unit cell vertex, which uniquely defines the kinematic state of each cell and the effective stress state. By maintaining the history of local non-affine motion and the global affine deformation, the model is able to capture the microinertial and viscous effects important during dynamic loading of open-cell foams. The micromechanical formulation is used to predict the dynamic compressive uniaxial response of polymeric (visco-elastic) and metallic (elasto-plastic) open-cell foams for different loading rates and structural and material properties gauging the effects of strain rate, viscosity, plasticity and microinertia. The predictions capture the experimentally observed effects namely that as the strain rate increases the foam strength increases and that this effects are more pronounced for more viscous or more massive foams. The micromechanical alone provides the effective foam response in a numerically efficient manner allowing the user to probe a wide range of material properties and cellular dimensions in a short amount of time. However in order to predict the full field, full range response of an open-cell foam specimen, it is necessary to implement the micromechanical model as a constitutive update into implicit and/or explicit nonlinear dynamic finite element analysis FEA schemes. The FEA simulations clearly capture the experimentally observed signature response with the different stages including the heterogeneous bands of deformation during dynamic compression of cellular materials.Ph.D.Includes bibliographical references (p. 121-129)