Investigation and modeling of pressure dependent yield behavior of 3D stochastic and periodic foams.

摘要

With growing potential of cellular solids in a multitude of diverse engineering applications as lightweight alternatives and space filling cores in sandwich structures, need for predictive yield criteria for these load bearing members under multiaxial stress states becomes critical. Although there exist several yield criteria proposed in the literature for highly porous solid foams, majority are phenomenological in nature, rely on relatively long list of model parameters that require difficult experimentation not readily available to end user, and none of them can handle the anisotropy observed in commercially available solid foams. Further, it is by now well established that, the yield behavior of highly porous solid foams is significantly influenced by the hydrostatic component of stress. In majority of phenomenological yield criteria proposed for solid foams this dependence is expressed by a quadratic pressure term.;Present study integrates analytical and computational investigation of yield behavior in solid foams along with extensive validation by experimental results. It proposes a physics based approach by hypothesizing that the yielding of stochastic foams is governed by the total elastic strain energy density, which leads to an energy based yield criterion for transversely isotropic foams providing a physical basis for the quadratic pressure dependence. Also, it introduces new scalar measures of stress and strain, which are referred to as characteristic stress and characteristic strain, that are analogous to effective (von Mises) stress and strain commonly used in analyzing the yield and post-yield behavior of bulk metals. Proposed yield criterion also renders a unique advantage by relying only on the elastic properties and uniaxial yield strengths of the material, which makes the proposed yield criterion extremely practical for end user.;Results from experimental data obtained from multiaxial testing of Divinycell H100 and H130 foams as well as extensive computational simulations performed on periodic Kelvin and stochastic Voronoi foam models (both isotropic and transversely isotropic), point out to an additional linear pressure dependence in the yield behavior of solid foams. This dependence is observed to be more pronounced at lower relative densities. A simple quantitative technique which is based on the partition of elastic strain energy into bending and stretch components is used to identify the distribution of deformation modes at microstructural level, along with its influence on load sharing as a function of stress path. Furthermore, a plasticity model that incorporates a flow rule and hardening law are presented which allows the analysis of inelastic deformations in solid foams in a continuum framework. Such models facilitate development of user defined material model (UMAT) that allow evaluating the performance of proposed yield criterion under complex loading scenarios, such as indentation and punch loading.