Volume Change of Heterogeneous Quasi-brittle Materials in Uniaxial Compression

The volumetric strain was categorized into elastic and plastic parts. The farmer camposed of axial and lateral strains is uniform and determined by Hooke＇s law ; however, the latter consisting of axial and lateral strains is a fuaction af thickness af shear band determined by grndieat-dependeat plasticity by cansidering the heterngeneity of quasi- brittle materials. The non- uniform lateral strain due to the fact that shear band was farmed in the middle of specimen was averaged within specimen to precisely assess the volumetric strain. Then, the analytical expression for volumetric strain was verified by comparison with two earlier experimental results for concrete and rack. Finally, a detailed parametric study was carried out to investigate effects of constitutive parameters （ shear band thickness, elastic and softening rnoduli ） and geometrical size of specimen（ height and width of specimen ） on the volume dilatancy.

"Extended" shear bands in interior of Pd-based bulk metallic glasses

Shear bands in the interior of Pd（79）Cu6Si（10）P5,Pd（79）Cu3Ag3Si（10）P5, and Pd（79）Cu4Au2Si（10）P5 bulk metallic glasses were investigated by optical microscopy（OM） and scanning electron microscopy（SEM）. No shear bands can be observed in the samples before etching. By etching in aqua regia solution, shear bands are found to be susceptible to preferential etching, and multiple etched bands could be observed. The thickness of the etched bands is about 1-7 μm. Therefore, the preferentially etched shear bands found in the study are called the ＂extended＂ shear bands.The ＂extended＂ shear bands can be divided into three classes according to their features： early, developing, and well-developed ＂extended＂ shear bands with thickness of about 1, 5, and 7 μm, respectively. The interface between the well-developed ＂extended＂ shear bands and the matrix is clearer than that of the others.

Effect of Relative Stress on Post-Peak Uniaxial Compression Fracture Energy of Concrete

Fracture energy in strain softening regime was investigated analytically by considering microstructures interaction and interplay.Based on gradient-dependent plasticity, the thickness of localized band was determined completely and strictly by characteristic length in relation to average grain diameter.After obtaining the plastic shear displacement of the band,the formula on axial response of concrete was proposed and the analytical post-peak fracture energy was deduced.A comparison between present theoretical results and earlier experimental results was carried out and the analytical result is reasonable and has a plausible foundation as considering the localized failure theoretically.Decreasing the relative stress leads to increasing the fracture energy non-linearly.The larger the shear elastic modulus and shear softening modulus,the lower the post-peak fracture energy.A larger fracture energy is caused by a larger thickness of shear band or a larger characteristic length of concrete material.If the inclination angle of the shear band and the compressive strength are not concerned with structural size of specimen,the post-peak fracture energy is size independent.