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We develop a geometric and variational framework for nonlocal continuum mechanics in which nonlocal interaction kernels are reinterpreted as probabilistic transition structures on the configuration space, placing the theory within the setting of statistical manifolds equipped with the Fisher–Rao metric. After normalizing an interaction kernel into a probability transition densi…
We present a reduced-order theory for locally impenetrable elastic tubes with a uniform circular cross-section. The constraint of local impenetrability is incorporated into a variational scheme to derive a complete set of governing equations, jump conditions, and boundary conditions. We show that when local impenetrability is actively enforced, the configurations of the tube co…
We address a problem in the theory of elasticity motivated by the desire to reconstruct the point-wise strain field from partial information obtained using X-ray diffraction measurements. Referred to as either high-energy X-ray diffraction microscopy (HEDM) or three-dimensional X-ray diffraction microscopy (3DXRD), these methods provide diffraction images that, once processed, …
We show that certain mixed displacement/traction problems (including live pressure tractions) of nonlinear elastostatics that are solved by a homogeneous deformation admit no other classical equilibrium solution under suitable constitutive inequalities and domain boundary restrictions. This extends a well-known theorem of Knops and Stuart on the pure displacement problem.
Classical Lame equations of the theory of elasticity are considered from the point of view of the probabilistic Feynman-Kac formula, which delivers exact solutions of many elliptic and parabolic boundary value problems. Unlike other approaches which are applicable only for certain domains of special shape, the Feynman-Kac solutions are applicable to domains of practically arbit…
This paper examines the construction of continuous models for the dynamics of lattice meta-materials with long-range interactions. Lagrange lattices with nearest-neighbour and second-neighbour coupling, and with nearest-neighbour and third-nearest-neighbour coupling, are studied. Particular attention is paid to characteristic points on the dispersion curve, such as rotons, maxo…
In this paper, the thermoelastic behavior of an icosahedral quasicrystal thermoelectric thin film bonded to a homogeneous substrate is investigated. A one-dimensional temperature field is assumed, and the steady-state temperature distribution is obtained under applied thermal and electric loads. Adopting the perfect bonding condition and membrane assumption, the governing integ…
Soft materials embedded with liquid inclusions have been widely applied in the fields of biomedical engineering, flexible electronics and soft robotics owing to their unique mechanical properties, while classical linear elasticity solutions fail to accurately characterize their nonlinear mechanical response under finite deformation. In this paper, we develop a modified analytic…
This paper proposes a multivariable formulation with stress and displacement fields as primary unknowns to solve dynamical problems. Displacement is approximated by a time-dependent linear combination of {C}0 continuous basis functions over the spatial domain of the body. Strain is derived by differentiating the displacement field, which exists over each element. The acceler…
The radius of gyration is a fundamental quantity used to characterise mass distribution in a given geometrical shape, and is employed across a wide range of disciplines, including continuum mechanics, structural mechanics and polymer physics. Despite its widespread use, subtle differences in its mathematical definition and physical interpretation across fields lead to discrepan…
We apply the techniques of one-to-one mapping and analytic continuation to derive a closed-form solution to the anti-plane elasticity problem of a cracked anisotropic elastic elliptical inhomogeneity embedded in an infinite anisotropic elastic matrix subjected to uniform remote anti-plane shear stresses. The anisotropy of the elliptical inhomogeneity results in the finite crack…
We investigate transport in multilayer systems combining heterogeneous diffusion, interfacial resistance, and volumetric dissipation. Unlike classical diffusion models, the presence of dissipative bulk terms and imperfect interfaces leads to a dissipative diffusion–transmission operator structure. We show that the spectral properties of the associated diffusion–efflux operator …
This study investigates the coupled thermal and chemical interactions in a nonlocal homogeneous isotropic thermoelastic diffusive thick circular plate subjected to axisymmetric heat supply. Both surfaces of the plate are assumed to be stress free. Employing Laplace and Hankel transform techniques, analytical expressions for the field quantities are obtained in transformed domai…
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Abstract not available. Bibliographic information is searchable.
We develop a Bayesian operator-learning framework for nonlocal damage mechanics aimed at calibrating uncertain internal length scales and quantifying predictive uncertainty from limited observations. The deterministic forward model is based on an AT2-type gradient damage regularization, which introduces a finite localization width and provides a mesh-objective continuum descrip…
In a generalized plane stress state, the contact interaction of two identical stringers, symmetrically loaded by tangential forces, with an elastic infinite or semi-infinite plate is studied. A related problem of symmetric tangential force transfer from two reinforced strip-shaped stringers to an elastic half-space under antiplane deformation is also considered. Stringers are m…
Recently, the 40th anniversary of materials exhibiting negative characteristics was celebrated. The pioneering work began in 1984 when Herakovich [1] designed a layered composite with a negative Poisson’s ratio across the layers, followed in 1985 by inverse honeycomb designs [2, 3]. In 1986, Kolpakov and Rakin [4] introduced a layered composite with a negative coefficient of th…
In the context of linear thermoelasticity theories, we study the plane deformation of an arbitrarily shaped nano-inclusion embedded in an infinite isotropic matrix under uniform remote in-plane heat flux. The nanoscale thermoelastic effects are modeled using the theories of interface heat conduction, interface thermoelasticity and interface tension. An efficient series-based al…
This study investigates the planar transient dynamics of a linearized string interacting with a moving mass. Unlike conventional models that idealize the moving system as a point mass or particle, the mass is modeled more realistically as a finite body that maintains dual contact with the string at closely spaced points. This modeling choice naturally incorporates the rotationa…