Related papers: Formulation of Deformation Stress Fields and Const…
The purpose of this study is to propose a modified micromorphic continuum model for granular materials based on a micromechanics approach. In this model, Cauchy stress and the couple stress are symmetric conjugated with the symmetric strain…
We propose a thermodynamically based approach for constructing effective rate-type constitutive relations describing finite deformations of metamaterials. The effective constitutive relations are formulated as \emph{second-order} in time…
A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on…
In this paper, the concept of moment and couple in mechanics is examined from a fundamental perspective. It turns out that although representing a couple by its moment vector is very useful in rigid body mechanics and strength of materials,…
Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the…
The Cosserat solid is a theoretical model of a continuum whose elementary constituents are notional rigid bodies. Here we present a formulation of the mechanics of a Cosserat solid in the language of modern differential geometry and…
Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas…
We experimentally characterize the impact response of concentrated suspensions consisting of cornstarch and water. We observe that the suspensions support a large normal stress -- on the order of MPa -- with a delay after the impactor hits…
The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases. First for a spring hanging in a constant gravitational field, then for a spring which is at rest in a rotating system where it is…
The response of many materials to applied forces and boundary constraints depends upon internal geometric changes at multiple submacroscopic levels. Hierarchical structured deformations provide a mathematical setting for the description of…
Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and…
We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and…
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral…
The thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the…
For theories of relativistic matter fields there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two…
In order to reveal the coupling effect among the chemical activity and the hydraulic seepage as well as the mechanical properties, a constitutive theoretical framework considering the chemical activity for saturated porous media is derived…
In this paper, we examine the recently developed skew-symmetric couple stress theory and demonstrate its inner consistency, natural simplicity and fundamental connection to classical mechanics. This hopefully will help the scientific…
We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and…
Stress-tensor deformations suggest a geometric origin of emergent gravity but are typically non-local for $d>2$. We couple a seed QFT to Einstein gravity with deformation parameter $\lambda$ and evaluate the gravitational path integral at…
Tensor analysis provides a frame-invariant foundation for continuum mechanics, yet numerical implementations rely on matrix representations expressed in user-selected bases. When these bases are non-Cartesian and non-orthonormal, additional…