Related papers: Formulation of Deformation Stress Fields and Const…
We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…
Ordinarily, the stress tensor that one derives for a Madelung fluid is not regarded as being coupled to a strain tensor, which is consistent with the fluid hypothesis. However, based upon earlier work regarding the geometric nature of the…
A body immersed in a nematic liquid crystal disturbs the fluid's preferred molecular configuration and increases its stored elastic energy. In an active nematic, the fluid components also generate a stress in the bulk fluid. By introducing…
We derive a general expression for the deformation-gradient tensor by invoking the standard definition of a gradient of a vector field in curvilinear coordinates. This expression shows the connection between the standard definition of a…
Modeling coupled processes in fractured porous media -- flow, deformation, fracture mechanics, and thermal/chemical effects -- often relies on mixed dimensional multiphysics formulations. These systems are nonlinear and depend on physical…
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape?…
In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. A major drawback is the calibration of model parameters that depend on…
We propose a data-driven constitutive framework for anisotropic damage mechanics based on the second-order damage tensor approach for both compressible and incompressible materials. The formulation is thermodynamically consistent and…
Constitutive equations are developed for a polymer fluid, which is treated as a permanent network of strands bridged by junctions. The junctions are assumed to slide with respect to their reference positions under loading. Governing…
Considering the rheology of two-dimensional soft suspensions above the jamming density, we derive a tensorial constitutive model from the microscopic particle dynamics. Starting from the equation governing the $N$-particle distribution, we…
We derive the expressions for configurational forces in Kohn-Sham density functional theory, which correspond to the generalized variational force computed as the derivative of the Kohn-Sham energy functional with respect to the position of…
Mathematical models of biological growth commonly attempt to distinguish deformation due to growth from that due to mechanical stresses through a hypothesised multiplicative decomposition of the deformation gradient. Here we demonstrate…
We develop a generic geometric formalism that incorporates both $T\bar{T}$-like and root-$T\bar{T}$-like deformations in arbitrary dimensions. This framework applies to a wide family of stress-energy tensor perturbations and encompasses…
Compression experiments are widely used to study the mechanical properties of materials at micro- and nanoscale. However, the conventional engineering stress measurement method used in these experiments neglects to account for the…
Existence and uniqueness of solutions for a class of models for stress-modulated growth is proven in one spatial dimension. The model features the multiplicative decomposition of the deformation gradient $F$ into an elastic part $F_e$ and a…
This work is a continuation of the ongoing research on deformation behavior of reinforced concrete elements under tension. The previous studies have revealed that deformation behaviors of elements reinforced with multiple bars and the…
Electro-active materials are classified as electrostrictive and piezoelectric materials. They deform under the action of an external electric field. Piezoelectric material, as a special class of active materials, can produce an internal…
In this paper we formulate the theory of nonlinear elasticity in a geometrically intrinsic manner using exterior calculus and bundle-valued differential forms. We represent kinematics variables, such as velocity and rate-of-strain, as…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its…