Hooke's law ≈ Hooke's law
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Breakdown of Hooke’s law of elasticity at the Mott critical endpoint in an organic conductor Open
The coupling of the critical electronic system to a compressible lattice is found to drastically alter the Mott criticality.
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Review on spectral decomposition of Hooke’s tensor for all symmetry groups of linear elastic material Open
The spectral decomposition of elasticity tensor for all symmetry groups of a linearly elastic material is reviewed. In the paper it has been derived in non-standard way by imposing the symmetry conditions upon the orthogonal projectors ins…
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Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials Open
The stress tensor is described as a symmetric tensor in all classical continuum mechanics theories and in most existing statistical mechanics formulations. In this work, we examine the theoretical origins of the symmetry of the stress tens…
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Lord–Shulman Nonlinear Generalized Thermoviscoelasticity of a Strip Open
In this paper, the response of a bounded one-dimensional medium (strip) subjected to a thermal shock is investigated. The strip is made of a linear visco-elastic material, of which the time-dependency of the elastic modulus is described by…
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The Green tensor of Mindlin’s anisotropic first strain gradient elasticity Open
We derive the Green tensor of Mindlin’s anisotropic first strain gradient elasticity. The Green tensor is valid for arbitrary anisotropic materials, with up to 21 elastic constants and 171 gradient elastic constants in the general case of …
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Elastic Anisotropy of Trabecular Bone in the Elderly Human Vertebra Open
Knowledge of the nature of the elastic symmetry of trabecular bone is fundamental to the study of bone adaptation and failure. Previous studies have classified human vertebral trabecular bone as orthotropic or transversely isotropic but ha…
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Method of approximate calculation of the stress tensor in layered elastic-creeping environments Open
The paper deals with the problem of constructing an effective model of a layered composite material. The layers consist of elastic-creeping materials, the creep kernels of which are exponents. The characteristics of the averaged model are …
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Robert Hooke: Tercentennial Studies Open
Book synopsis: Robert Hooke (1635-1703) was a genius whose wide-ranging achievements are at last receiving the recognition that they deserve. Long overshadowed by such eminent contemporaries as Sir Isaac Newton and Sir Christopher Wren, Ho…
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A note on Padé approximants of tensor logarithm with application to Hencky-type hyperelasticity Open
We show that the logarithmic (Hencky) strain and its derivatives can be approximated, in a straightforward manner and with a high accuracy, using Padé approximants of the tensor (matrix) logarithm. Accuracy and computational efficiency of …
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Discrete mechanical growth model for plant tissue Open
We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall's microstructure. To model plastic growth the resting lengths of springs are adjuste…
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Illustrating dimensionless scaling with Hooke’s law Open
Dimensionless variables and scalings are powerful tools for emphasising the universality of natural laws, but their application is typically restricted to topics in advanced physics. Here we describe how dimensionless scaling can be illust…
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Fabric Tensors in Bone Mechanics Open
Mechanical properties of cancellous and cortical bone have been investigated. The fabric tensors used in the relevant literature have been discussed. Nonlinear elastic and elastic-perfectly plastic constitutive relationships have been prop…
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The shear contribution to the equation of state: A universal law for the elastic moduli of solids Open
Cauchy's stress tensor, in the most generalized form, is known to be in two parts: a pressure plus octahedral shear stresses. Shear stress thermodynamics in pressurized and sheared systems are used to describe the physical shear properties…
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Determination of Springs Constant by Hooke’s Law and Simple Harmonic Motion Experiment Open
This study aims to calculate the spring constants of two types of stainless using Hooke’s Law principle and simple harmonic motion methods. Two types of springs (spring I and II) with different sizes in diameter have spring constant k valu…
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A Simple Theory of Asymmetric Linear Elasticity Open
Rotation is antisymmetric and therefore is not a coherent element of the classical elastic theory, which is characterized by symmetry. A new theory of linear elasticity is developed from the concept of asymmetric strain, which is defined a…
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On continuum damage mechanics Open
A material containing spherical microvoids with a Hookean matrix response was shown to take the appearance usually applied in continuum damage mechanics. However, the commonly used variable damage D was replaced with the void volume fracti…
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Perspective Chapter: Viscoelastic Mechanical Equivalent Models Open
Today, we are living in a polymeric era where thousands of daily used products are manufactured from some polymeric materials with different tasks and under a wide range of ambient conditions, including time duration of loading and working…
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Elastic symmetry with beachball pictures Open
SUMMARY The elastic map, or generalized Hooke’s Law, associates stress with strain in an elastic material. A symmetry of the elastic map is a reorientation of the material that does not change the map. We treat the topic of elastic symmetr…
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Stress tensor determination by modified hydraulic tests on pre-existing fractures: Method and stress constraints Open
The hydraulic testing of pre-existing fractures (HTPF) is one of the most promising in situ stress measurement methods, particularly for three-dimensional stress tensor determination. However, the stress tensor determination based on the H…
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Elasticity of Solids Open
If a solid is initially at rest and equal and opposing forces are applied to that object, Newton’s Second Law guarantees that the object will remain at rest because the net force on the sample is zero. If that object is an elastic solid, t…
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Elasticity of Auxetic Materials Open
The auxeticity of elastic materials is described and explained by the use of the linear and nonlinear models of elastic deformations for a wide range of strain values up to moderate levels. This chapter consists of three parts – general in…
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A Unified Nonlinear Elastic Model for Rock Material Open
Under conditions of low or medium stress, rocks that are in the compression state exhibit perceivable nonlinear elastic characteristics. After a comprehensive review of the existing nonlinear elastic models of rocks and joints, we proposed…
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Tensor compaction of porous rocks: theory and experimental verification Open
Compaction in sedimentary basins has been traditionally regarded as a one-dimensional process that ignores inelastic deformation in directions orthogonal to the active load. This study presents new experiments with sandstone demonstrating …
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On damage tensor in linear anisotropic elasticity Open
In this paper, the anisotropic linear damage mechanics is presented starting from the principle of strain equivalence. The authors have previously derived damage tensor components in terms of elastic parameters of undamaged (virgin) materi…
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Statistical criteria for the limits of application of Hooke’s law Open
Modern methods for studying the stress-strain state of solids use graphical methods based on a stress-strain curve to determine the transition from elastic deformation to plastic deformation. However, this approach is not formal and it is …
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Criterion for Verification of the Generalized Law of Hooke Open
Annotation.To discuss the generalized Hooke's law, we propose a new criterion derived for axial extension and compression of solid cylinders without the influence of the hypothesis of uniaxiality of the stressed state.Integration of the eq…
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On the Derivation of Hooke’s Law for Plane State Conditions Open
We discuss the derivation of Hooke’s law for plane stress and plane strain states from its general three-dimensional representation. This means that we consider the anisotropic case to ensure a certain generality of our representation. The…
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Material symmetry rotation for oblique 2D-elasticity Open
Definition of the material symmetry axes rotation in case of purely elastic finite-strain deformation is given. This rotation explains the rigid motion of the orthonormal vector frame, which coincides with the material symmetry axes in the…
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Vibration spectra of benzene-like models with Hooke’s law interactions Open
The harmonic oscillations of a spring-ball model of benzene-like nanosystems with Hooke’s law interactions between nearest, second, and third neighbors are explored. We show that in the cylindrical coordinates the dynamics of this cyclic h…
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Work conjugate strain of virial stress Open
Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor. Virial…