Constitutive modeling of geomaterials

"Preface When I was student (almost 40 years ago), my supervisor, Sakuro Murayama, often told us that the most important challenge in the field of soil mechanics was to establish the stress-strain-time-temperature relation of soils. Since the beginning of his academic carrier, he had pursued research on a constitutive model for soils, and he summarized his experience in a thick book of almost 800 pages (Murayama 1990) when he was almost 80 years old. In his book, the elastoplasticity theory was not used in a straightforward manner, but he discussed soil behavior, focusing his attention not on the plane where shear stress is maximized, called the tmax plane or 45ʻ plane, but rather on the plane where the shear-normal stress ratio is maximized, called the (t/s)max plane or mobilized plane, because the soil behavior is essentially governed by a frictional law. In retrospect, I realize how sharp was his vision to pay attention to the mobilized plane at a time when most people looked at the tmax plane. Now, in three-dimensional conditions in which the intermediate principal stress must be considered, the plane corresponding to the tmax plane in two-dimensional conditions is the commonly used octahedral plane because the shear stress on the octahedral plane is the quadratic mean of maximum shear stresses between two respective principal stresses. For three-dimensional constitutive modeling in this book, attention is paid to the so-called spatially mobilized plane (SMP) on which the shear-normal stress ratio is the quadratic mean of maximum shear-normal stress ratios between two respective principal stresses"--