Solid stress and tissue stiffness affect tumour growth, invasion, metastasis and treatment. Unlike stiffness, which can be precisely mapped in tumours, the measurement of solid stresses is challenging. Here, we show that two-dimensional spatial mappings of solid stress and the resulting elastic energy in excised or in situ tumours with arbitrary shapes and wide size ranges can be obtained via t...

An ideal solid material will respond to an applied load by deforming ®nitely and recovering that deformation upon removal of the load. Such a response is called ``elastic''. Ideal elastic materials obey Hooke's law, which describes a direct proportionality between the stress ( ) and strain ( ) via a proportionality constant called modulus (G), i.e., ˆ G . An ideal ̄uid will deform and continue t...

We address the partial wetting of liquid drops on ultrathin solid sheets resting on a deformable foundation. Considering the membrane limit of sheets that can relax compression through wrinkling at negligible energetic cost, we revisit the classical theory for the contact of liquid drops on solids. Our calculations and experiments show that the liquid-solid-vapor contact angle is modified from ...

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We investigate hysteretic behavior in two dynamic models for solid-solid phase transitions. An elastic bar with a nonconvex double-well elastic energy density is subjected to time-dependent displacement boundary conditions. Both models include inertia and a viscous stress term that provides energy dissipation. The first model involves a strain-gradient term that models interfacial energy. In th...

Ab initio periodic Hartree-Fock (HF) theory was used to determine the elastic constants and selected phonon frequencies of bulk MgO; the accuracy of a posteriori correlation corrections to the periodic Hartree-Fock calculations is also discussed. Inc)usion of difFuse atomic orbitals in the MgO basis was necessary to accurately describe elastic distortions and phonon vibrations of the solid. The...

Elastic anticavitation is the phenomenon of a void in an elastic solid collapsing on itself. Under the action of mechanical loading alone typical materials do not admit anticavitation. We study the possibility of anticavitation as a consequence of an imposed differential growth. Working in the geometry of a spherical shell, we seek radial growth functions which cause the shell to deform to a so...

Precision measurements of the energy of keV electrons scattered ‘elastically’ over large angles from solid films or gas-phase molecules show that these electrons have lost some energy. In particular scattering from a system that contains hydrogen and carbon reveals two well-separated elastic peaks. The amount of energy lost in the deflection of the electron depends not only on the mass of the n...

Lubrication flows appear in many applications in engineering, biophysics, and in nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubrication fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loa...