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Showing 1 to 20 of 28 for “"Strain tensor"”.
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A strain tensor method for three-dimensional optimal Michell structures
… structures. It will be referred as the Michell strain tensor method (MSTM). First, the proof that MSTM is consistent with the existing theory in two dimensions is provided. Second, two-dimensional known solutions will be replicated based on MSTM. Finally, MSTM will be used to solve new three- …
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Enhanced Constitutive Theories for Classical Thermoviscoelastic Polymeric Fluids
… Constitutive theories for the Cauchy stress tensor are derived using the conjugate pair in the entropy inequality, additional desired physics, and the representation theorem. The constitutive theories for the Cauchy stress tensor consider convected time derivatives of Green’s strain tensor or …
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Biological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states
… tissue mechanics is modelled using anisotropic strain energy functions capturing the averaged behaviour of its fibrous microstructure. The strain energy function can be derived via representation theorems for anisotropic functions where a suitable nonlinear strain tensor, e.g. the Green strain …
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Calculating 3D intramyocardial strain tensors in a single slice of myocardium using MRI
Strain is a measure of cardiac deformation and provides information on the mechanical and functional properties of the heart. As this deformation occurs in three dimensions (3D), a 3D measure of strain is appropriate, however, currently the procedures for measuring 3D intramyocardial strain fields …
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In situ measurement of lattice strain using synchrotron radiation and a conical slit system
… synchrotron radiation to measure lattice strain components from an aluminum-lithium sample during tensile loading is presented in detail. The conical slit system at Argonne National Laboratory’s Advanced Photon Source is utilized to isolate a single grain with an orientation of interest …
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Nonlinear free vibration of beams by one-dimensional and elasticity solutions
… elasticity method based on the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. The outcomes of the approximated method have been compared by using the nonlinear Euler–Bernoulli theory depending on the Hermite and Lagrange interpolations. The solutions of both theories are …
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Atomistic simulations of grain boundary migration in face centred cubic metals
… decreasing to zero due to conversion effects of strain tensor components. It could be shown that strain tensor components necessary to yield an elastic DF were converted during the course of the simulations from being elastic into plastic strain components. This behaviour is connected to the …
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Coupled Hydro-Mechanical Modelling of Gas Migration in Saturated Bentonite
… is accounted for by introducing a modified strain tensor that is the sum of the strain tensor due to deformation and the strain tensor calculated from the initial stress. The numerical results showed that the developed coupled HM-PF framework can capture some important behaviors, such as the …
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Strongly orthotropic continuum mechanics
… derived entirely from an assertion of geometric strain indeterminacy. Implementable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This …
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Continuum mechanical analysis of space and time dependent deformation pattern of brain with blunt injury
… data was used to calculate 2D Lagrangian strain tensor and the principal strain. The temporal and spatial results of principal strain under different variables including impact velocity (5 mile/hour, 3 mile/ hour), impact location (crown head, front head) and concentration of gel used to …
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A Least Squares Closure Approximation for Liquid Crystalline Polymers
… Hinch-Leal II closure schemes. The orientation tensor and rate-of-strain tensor are fit separately using data generated from the kinetic solution of the Smoluchowski equation. The known behavior of the kinetic solution and existing closure schemes at equilibrium is compared with that of the new …
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An anisotropic damage model for rock
… definition of damage in a subdomain of the total strain and the characterisation of the directional microcracking by a fourth order tensor internal variable, the damaged secant stiffness of the 'crack' strain subdomain. Induced anisotropy results from the reduction of components of the initial …
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Arbitrarily curved and twisted space beams
… departures from the previous theory are that the strain - displacement relations are derived and that the expressions for the stress resultants are developed from the strain - displacement relations instead of assuming that the resultants are proportional to changes in the curvatures. It is shown …
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Enhancement of the Dynamic Buckling Load and Analysis of Active Constrained Layer Damping with Extension and Shear Mode Piezoceramic Actuators
… edges of the bottom surface of the plate are restrained from moving vertically. The two opposite edges of the plate are loaded by equal in-plane compressive loads that increase linearly with time and the other two edges are kept traction free. The plate material is modeled as orthotropic and …
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Theory of phase transitions in liquid crystals and plastic crystals
… order parameter to lattice distortions via the strain tensor is shown to make the methane J -methane II transition first order in this classical approximation. The symmetry breaking at a (001) surface of methane I is shown to result in (i) tetragonal surface distortions, (ii) rotational ordering …
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Molecular Dynamics and X-ray Powder Diffraction Simulations: Investigation of nano-polycrystalline microstructure at the atomic scale coupling local structure configurations and X-ray powder Diffraction techniques
… to equilibrate the system: the corresponding strain field was described both in the core and in surface regions of the different crystalline domains. New methods were developed to calculate the strain tensor at the atomic scale. Line Profile Analysis (LPA) was employed to retrieve the …
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Constitutive modeling and finite element analysis of the dynamic behavior of shape memory alloys
… of transformation, the analysis can account for strain-rate effects. Inspired by the deformation theory of plasticity, the 1-D model is extended to a 3-D macromechanical model of localized unstable pseudoelasticity. An important feature of this model is the reorientation of the transformation …
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Electrostatic effects of inhomogeneous strain in monolayer transition metal dichalcogenides
… properties due to their reduced dimensionality. Strain engineering can be used to modify optical and electronic properties, and highly inhomogeneous strain distributions in two-dimensional materials can be easily realized, allowing for their properties to be tuned on the nanoscale. This work is …
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Mathematical Challenges in Electron Microscopy
… new inverse problem for the reconstruction of 3D strain tensor fields from electron microscopy diffraction data. The remaining contributions target numerical aspects of inverse problems, from new algorithms for non-convex problems to convex optimisation with adaptive meshes.
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Thermodynamic modeling of martensitic transformations in shape memory alloys.
… to reasonable accuracy, the transformation strain tensor and captures the latent heat and thermal hysteresis to within an order of magnitude. The second part of this work consists of developing a lattice dynamics model to simulate the MTs. The atomic interactions are modeled using …
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