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Quasi-static compression, tension and combined shear–compression tests were conducted to characterize the mechanical behavior of PMMA. The cylinder samples and dog-bone samples were used for uniaxial testing. The shear–compression samples of four different angles (15°, 30°, 45°, and 50°) were used to obtain the multiaxial stress state instead of complex loading equipment. The yield behaviors of PMMA cannot be described by the Tresca or Mises criterion due to the effects of both the first invariant of the stress and the third invariant of deviatoric stress. A criterion is proposed that includes the first invariant of the stress and the third invariant of deviatoric stress in this paper. In other word, the effects of hydrostatic pressure and Lode angle are considered. The proposed yield criterion has the capability to precisely capture the experimental yield loci of PMMA.

Based on the elongated Voronoi models, the yield behaviors of transversely isotropic foams have been explored by using finite element method. A pressure-dependent phenomenological constitutive model (stress potential function) has been established for transversely isotropic foams through the characteristic stress and strain. The stress potential function and its evolution can be determined in terms of the uniaxial and equi-triaxial tensile/compressive characteristic stress-strain curves. The stress potential function is expected to predict the elastoplastic mechanical responses of transversely isotropic foams. The material properties (i.e., relative density, transversely isotropic degree, matrix material and cell morphology) exhibit significant influence on the profile of initial yield surfaces. The pressure dependence of yield surfaces decreases as the relative density and transversely isotropic degree increase. The predictions of pressure-dependent constitutive model match excellently with the simulated yield data under different stress states and characteristic strain stages.

Based on the method of the geometric stretch, the elongated tetrakaidecahedron and Voronoi models in the rise direction have been established to investigate the multiaxial creep behavior of approximately transversely isotropic open-cell foams. A stretch factor R (the ratio of the cell length in the rise direction to that in the transverse direction) is introduced to quantificationally characterize the degree of transverse isotropy. Uniaxial simulation results indicate that, for the open-cell foams, the relative density has significant influence on the secondary creep rate and the effects of the microstructure cannot be ignored. Additionally, a modified phenomenological model is proposed to predict the multiaxial secondary creep rate of transversely isotropic foams, and the corresponding material constants are determined as a function of the stretch factor R by modifying the theoretical equations or fitting the FEA results. Then, the capability of the modified model is examined by simulating the creep behavior under axisymmetric loading. The simulation results indicate that the modified phenomenological model can give a good description of the uniaxial/multiaxial creep response of the transversely isotropic foams.

Finite element models, i.e. 2D honeycombs and 3D tetrakaidecahedron models, have been established to study defect-effect on the creep behavior of the cellular materials. Simulation results indicated that relative density have dominant effects on the steady state creep rate of the cellular materials. The creep behavior of the cellular materials is significantly correlated with the fraction of missing struts. A theoretical equation is proposed to predict the creep rate of cellular materials as a function of the ratio of different types of missing struts. The capability of the theoretical model was examined by simulating the creep behavior of two types of numerical models. The simulation results revealed that the theoretical model gives a good description of the creep response.

Three different types of tests, i.e. uniaxial compression, shear and combined shear-compression have been conducted on PMMA (polymethyl methacrylate) at different loading rates in order to investigate its failure behavior under different loading conditions. The experiment results show that the material exhibits the rate-dependent failure and post-failure behavior. Macroscopic failure loci of PMMA were was determined experimentally in the shear-normal stress space. Further, a macroscopic failure criterion was proposed to predict the material's failure locus as a function of the loading rate. The capability of the failure criterion was examined by simulating the failure behavior of the material at different load rates. The simulation results revealed very good agreement between the experimental data and the responses determined from the proposed failure criterion.