15 problems

Consider a realistic self-driven solidification process, including the mechanical effects relevant to the formation of residual stresses. Incompatibility conjecture for self-driven…

Let $\textbf{V}_{\hspace{-1pt}\tau}(\boldsymbol{x},t)$ be the micro-displacement tensor field, decomposed into compatible and incompatible parts. Micro-displacement independence co…

Let a deformation have constant principal invariants of its deformation tensor. Ericksen's conjecture. Such a deformation must be homogeneous. Ericksen's conjecture concerns univer…

Chain-rule conjecture. Under this assumption, the objective rate $\frac{\mathrm{D}^{\sharp}}{\mathrm{D}t}$ is corotational. The claim characterizes corotational stress rates among…

Positive-corotational-rate conjecture. The equivalence is conjectured to hold for every such rate:

Corotational stability for the Green–Naghdi rate. The following equivalence is conjectured:

Corotational stability characterization. This characterization is conjectured to hold for a large class of reasonable corotational rates: the stability condition is equivalent to s…

Let $\mathcal{E}: \operatorname{Sym}^{++}(3) \to \operatorname{Sym}(3)$ be a spatial strain tensor with strongly monotone scale function $e: \mathbb{R}^+ \to \mathbb{R}$. For a cor…

Zero-background-modulus conjecture. The situation of a free-standing elastic sphere is simply found by setting the elastic modulus of the supporting background to zero.

Let $X\subset[0,1]\cap\mathbb Q$ be such that … for all $z$, and let $\theta^\ast\in X$ be an energy well satisfying … for some $z$. Non differentiability at the energy wells. The…

The atomistic chain is modeled by a higher-order continuum energy, with the order of the included gradient terms determining the model's accuracy. Higher-order gradient conjecture.…

The model describes a strain field whose linearized unstable modes may be oscillatory. Suppression-and-localization conjecture. The combined effect of instability and nonlinearity…

Colli–Mariano conjecture. A non-zero conservative phason self-action would avoid the non-physical instantaneous propagation at infinity of phason disturbances and assure phason dec…

Piola's conjecture. In the expression of Virtual Work, all quantities that undergo infinitesimal variation are either components of the deformation measure $C$ or components of one…

Let $G$ be a subgroup of $\mathrm{SO}(3)$, let $\mathbb{T}$ be a tensor space with its $G$-representation, and let $\mathrm{C}\in\left[\mathbb{T}\otimes^S\mathbb{T}\right]^G$. Writ…