Essential Concepts of Neohypoplasticity

Neohypoplasticity Revisited

“…The NHP was developed to overcome the disadvantages of the HP+IS mentioned in Section 1. The modified tensorial equation between the stress and the strain rate from the version of 21 $$$$\begin{equation} \mathring{\bm {\sigma }}=k \nobreakspace \overline{\mathsf {E}}:{\left(\dot{\bm {\varepsilon }}-\bm {m} Y\Vert \dot{\bm {\varepsilon }}\Vert -\omega \bm {m}^z\langle -\bm {z}: \dot{\bm {\varepsilon }}\rangle -\bm {m}^d Y_d\Vert \dot{\bm {\varepsilon }}\Vert \right)} \end{equation}$$$$resembles roughly the shape of Equation (1). However, the asymptotically hyperelastic stiffness $$\overline{\mathsf {E}}$$, the hypoplastic flow rule m and the degree of nonlinearity Y are redefined.…”

“…The components of Equation (2) are discussed in detail below. The improvements and modifications with respect to the version 21 are discussed in Sections 2.6 and 2.8.…”

“…In analogy to the Rodriguez formula, the operator $$R_{ijkl}$$ is introduced for the rotation of the fourth‐order stiffness tensors $$$$\begin{equation} R_{i j k l}=I_{i j k l}+(\operatorname{cos} \beta -1){\left(u_{i j} u_{k l}+v_{i j} v_{k l}\right)}-\sqrt {1-(\operatorname{cos} \beta )^2}{\left(u_{i j} v_{k l}-v_{i j} u_{k l}\right)} \end{equation}$$$$with the unit tensors $$u_{i j}=-\vec{\delta }_{i j}$$ and $$v_{i j}=\vec{z}_{i j}$$. The rotation angle β is given as a function of the current state of the soil by 21 …”

“…Influence of material constants $$B_Y$$, $$C_Y$$, $$n_Y$$ and the void ratio on degree of nonlinearity $$Y(e, \bm {\sigma })$$ 21 …”

“…The calculation of the rigid strip foundation is more realistic and tensile stresses are unachievable. Some further improvements to the version 21 are introduced in this paper. The neohypoplastic equations are presented in detail in Section 2.…”