THE PRINCIPLE of maximum energy dissipation rate is introduced as an energy criterion for crack dynamics. That allows us to explain observed limiting crack speeds in brittle materials, and to complete the crack dynamics formulation. The upper limits of the crack speed in perfectly elastic and elastic-plastic bodies are obtained. It is found that the theoretical maximum crack speed in an isotrop...

The natural way to find the most compliant design of an elastic plate, is to consider the three-dimensional elastic structures which minimize the work of the loading term, and pass to the limit when the thickness of the design region tends to zero. In this paper, we study the asymptotic of such compliance problem, imposing that the volume fraction remains fixed. No additional topological constr...

The contact angle that a liquid drop makes on a soft substrate does not obey the classical Young's relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact angles differently from those predicted by Neumann's law, which applies when the drop is floating on another liquid. Here, we derive an elastocapilla...

We derive expressions for the lowest nonlinear elastic constants of amorphous solids in athermal conditions (up to third order), in terms of the interaction potential between the constituent particles. The effect of these constants cannot be disregarded when amorphous solids undergo instabilities such as plastic flow or fracture in the athermal limit; in such situations the elastic response inc...

A variational limit defined on the space of one-dimensional Young measures is obtained from three-dimensional elasticity via dimension reduction. The physical requirement that the energy becomes infinite when the volume locally vanishes is taken into account. The rate at which it blows up characterizes the domain of the limit energy. The obtained limit problem uniquely determines the energy den...

In this paper we study the asymptotic behavior of two-dimensional transmission problems for the linear Koiter model of an elastic multi-structure composed of two thin shells with the same thickness ε 1. Contrary to the case of membrane shells, the formal limit problem, i.e., for ε = 0, fails to give a convenient approximate solution, as the limit problem is ill posed. An appropriate dilation le...

In earthquake-resistant design it is usually assumed that the structure is linearly elastic and remains linearly elastic throughout the duration of the seismic activity. This is not always a realistic assumption. Indeed, even well designed structures will yield during very strong shaking and endure stresses well beyond the elastic limit of the design material. It is neither necessary nor econom...

The bodies of the Solar System exist in a variety of irregular shapes. Studies of those shapes are conducted to infer information about the internal composition, structure, and history of those bodies. However, such inferences require knowing how the composition and structure or history relates to the shape and internal forces. That connection is known only for fluid bodies, where the permissib...