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Highly entangled hydrogels exhibit excellent mechanical properties, including high toughness, high stretchability, and low hysteresis. By considering the evolution of randomly distributed entanglements within the polymer network upon mechanical stretches, we develop a constitutive theory to describe the large stretch behaviors of these hydrogels. In the theory, we utilize a representative volume element (RVE) in the shape of a cube, within which there exists an averaged chain segment along each edge and a mobile entanglement at each corner. By employing an explicit method, we decouple the elasticity of the hydrogels from the sliding motion of their entanglements, and derive the stress-stretch relations for these hydrogels. The present theoretical analysis is in agreement with experiment, and highlights the significant influence of the entanglement distribution within the hydrogels on their elasticity. We also implement the present developed constitutive theory into a commercial finite element software, and the subsequent simulations demonstrate that the exact distribution of entanglements strongly affects the mechanical behaviors of the structures of these hydrogels. Overall, the present theory provides valuable insights into the deformation mechanism of highly entangled hydrogels, and can aid in the design of these hydrogels with enhanced performance. [ABSTRACT FROM AUTHOR]

Magnetoelasticity theories describe the behavior of solids in response to the application of a magnetic field. This paper presents a new thermodynamically consistent constitutive theory for simulating nonlinear responses of solids for which the strain energy density depends on the deformation gradient through the Biot strain tensor and specializes the theory for application to the problem of finite deformation of a circular cylindrical tube. The derived theory appears to be attractive for applications as it provides a relatively simple mathematical expression for modeling nonlinear magneto-mechanical responses of solids. For the considered problem, it is obtained that a higher modified pressure is required to maintain a specified azimuthal stretch when a magnetic field is applied. Finally, and among other things, it is observed that the influence of the magnetic field can either decline or progressively enhance with increasing azimuthal stretch. [ABSTRACT FROM AUTHOR]

A thermodynamic process is a solution of the balance equations fulfilling the second law of thermodynamics. This implies restrictions on the constitutive relations. The most general way to exploit these restrictions is the method introduced by Liu. This method is applied here, in contrast to most of the literature on relativistic thermodynamic constitutive theory, which goes back to a relativistic extension of the Thermodynamics of Irreversible Processes. In the present work, the balance equations and the entropy inequality are formulated in the special relativistic four-dimensional form for an observer with four-velocity parallel to the particle current. The restrictions on constitutive functions are exploited in the relativistic formulation. The domain of the constitutive functions, the state space, is chosen to include the particle number density, the internal energy density, the space derivatives of these quantities, and the space derivative of the material velocity for a chosen observer. The resulting restrictions on constitutive functions, as well as the resulting entropy production are investigated in the non-relativistic limit, and relativistic correction terms of the lowest order are derived. The restrictions on constitutive functions and the entropy production in the low energy limit are compared to the results of an exploitation of the non-relativistic balance equations and entropy inequality. In the next order of approximation our results are compared to the Thermodynamics of Irreversible Processes. [ABSTRACT FROM AUTHOR]

Motivated by recent strain-limiting models for solids and biological fibers, we introduce the first intrinsic set of nonlinear constitutive relations, between the geometrically exact strains and the components of the contact force and contact couple, describing a uniform, hyperelastic, strain-limiting special Cosserat rod. After discussing some attractive features of the constitutive relations (orientation preservation, transverse symmetry and monotonicity), we exhibit several explicit equilibrium states under either an isolated end thrust or an isolated end couple. In particular, certain equilibrium states exhibit Poynting like effects, and we show that under mild assumptions on the material parameters, the model predicts an explicit tensile shearing bifurcation: a straight rod under a large enough tensile end thrust parallel to its center line can shear. [ABSTRACT FROM AUTHOR]

The lung is the main organ of the respiratory system. Its purpose is to facilitate gas exchange (breathing). Mechanically, breathing may be described as the cyclic application of stresses acting upon the lung surface. These forces are offset by prominent stress-bearing components of lung tissue. These components result from the mechanical elastic properties of lung parenchyma. Various studies have been dedicated to understanding the macroscopic behaviour of parenchyma. This has been achieved through pressure-volume analysis, numerical methods, the development of constitutive equations or strain-energy functions, finite element methods, image processing and elastography. Constitutive equations can describe the elastic behaviour exhibited by lung parenchyma through the relationship between the macroscopic stress and strain. The research conducted within lung mechanics around the elastic and resistive properties of the lung has allowed scientists to develop new methods and equipment for evaluating and treating pulmonary pathogens. This paper establishes a review of mathematical studies conducted within lung mechanics, centering on the development and implementation of solid mechanics to the understanding of the mechanical properties of the lung. Under the classical theory of elasticity, the lung is said to behave as an isotropic elastic continuum undergoing small deformations. However, the lung has also been known to display heterogeneous anisotropic behaviour associated with large deformations. Therefore, focus is placed on the assumptions and development of the various models, their mechanical influence on lung physiology, and the development of constitutive equations through the classical and non-classical theory of elasticity. Lastly, we also look at lung blast mechanics. No explicit emphasis is placed on lung pathology. [ABSTRACT FROM AUTHOR]

How to directly relate frictions at the level of a single molecular chain to the viscoelasticity of soft materials is intriguing. Here, we choose to investigate classical elastomers, where molecular frictions are known to be generated when dangling chains move relatively to the surrounding polymer chain network. With explicit forms employed for the relationship between friction and velocity at the molecular scale, a constitutive theory is then developed for the coupling of molecular frictions and the macroscopic viscoelasticity of elastomers. With the utilization of this theory, viscoelastic behaviors of varied elastomeric materials are predicted, which agree well with existing experiments at both low and high strain rates under different loading conditions. The theory also reproduces the time-temperature equivalent principle of elastomers. We suggest that this work might have provided a modeling framework that directly couples frictions at the level of a single molecular chain to the viscoelasticity of soft materials. [ABSTRACT FROM AUTHOR]

Adaptive habitat construction is a process by which individuals alter their environment so as to increase their (inclusive) fitness. Such alterations are a subset of the myriad ways that individuals condition their environment. We present an individual‐based model of habitat construction to explore what factors might favor selection when the benefits of environmental alterations are shared by individuals of the same species. Our results confirm the predictions of inclusive fitness and group selection theory and expectations based on previous models that construction will be more favored when its benefits are more likely to be directed to self or near kin. We found that temporal variation had no effect on the evolution of construction. For spatial heterogeneity, construction was disfavored when the spatial pattern of movement did not match the spatial pattern of environmental heterogeneity, especially when there was spatial heterogeneity in the optimal amount of construction. Under those conditions, very strong selection was necessary to favor genetic differentiation of construction propensity among demes. We put forth a constitutive theory for the evolution of adaptive habitat construction that unifies our model with previous verbal and quantitative models into a formal conceptual framework. [ABSTRACT FROM AUTHOR]

In this work, a thermodynamically consistent three-dimensional (3D) small strain-based theory to describe the deformation and fracture in quasi-brittle and brittle elastic solids is presented. The description of fracture at a material point resembles the microplane fracture approach developed by Bažant et al. (J Eng Mech 126(9):944–953, 2000, J Eng Mech 122(3): 245–254, 1996), but the present theory has the following novel features: (a) a probabilistic description of fracture propagation is used, developing evolution equations for the probability of a microcrack occurring at a given location and (b) a kinematical approach to modeling crack opening and closing. The new 3-D constitutive theory, in which elements were recently proposed by Srinivasa et al. (Mech Adv Mater Struct 80(27–30):2099–2108, 2020), has been computationally implemented within a Graph-based Finite-Element Analysis (GraFEA) framework developed by Reddy and colleagues (Khodabakhshi et al. in Meccanica 51:3129–3147, 2016, Acta Mech 230:3593–3612, 2019), and it has also been implemented into the dynamics-based Abaqus/Explicit (Reference manuals. Simulia-Dassault Systémes, 2020) finite element program through a vectorized user–material subroutine interface. Our computational approach for fracture modeling is intra-element-based, which is central to the GraFEA approach rather than inter-element fracture, as is done in cohesive zone-based numerical methods, together with selective non-locality where the non-locality is only for probability evolution motivated by population dynamic models that allows us to perform efficient implementation of the code without special elements or other numerical artifacts. Several homogeneous deformation cases for fracture in cementitious and brittle elastic materials were modeled, and the response obtained from the constitutive theory and its finite element implementation are qualitatively similar to that obtained in the literature. In particular, we show that our computational procedure is able to model crack closure in solids in a robust, relatively simple and elegant manner instead of relying on a previously developed method of decomposing the stored energy into "positive" and "negative" portions (Amor et al. in J Mech Phys Solids 57(8):1209–1229, 2009, Miehe et al. in Int J Numer Meth Eng 83:1273–1311, 2010). [ABSTRACT FROM AUTHOR]

We present a recently developed three-dimensional-finite-deformation-rate form-based constitutive theory to describe the deformation and fracture of viscoelastic solids. The constitutive theory was also implemented into a commercial finite-element program. Damage and fracture in viscoelastic solids is simulated using the element failure method coupled with a Gibbs free energy-based nonlocal fracture criterion. By numerically simulating selected boundary value problems, we show that our newly developed computational framework is able to reproduce the correct stress-strain response, force–displacement response and crack propagation characteristics in viscoelastic solids undergoing fracture, when compared to the response obtained using the extended finite-element method implementation in a commercially available finite element program. [ABSTRACT FROM AUTHOR]

Rock anisotropy is an intrinsic property of natural rock mass, and layered rock has the most significant effect on the stress distribution and deformation of a rock mass. With the development of rock mechanics theory and constitutive theory, the study of rock anisotropy has become one of the focuses and hotspots in the field of rock mechanics. Based on the rock isotropic self-consistent theory, the rock anisotropy theory of different media such as triclinic anisotropy, monoclinic anisotropy, and orthorhombic anisotropy has been greatly developed. Rock mechanical property test, not only limited to the traditional single-axis, triaxial compression test, Brazilian split test and pure bending beam tensile test, and meso-structural characteristic test (XRD, ultrasonic test, etc.), is also widely used. With the development of numerical analysis theory and computer technology, numerical analysis methods such as finite difference method, discrete element method, finite element method, boundary element method, and interface element method have played an important role in the study of rock anisotropy characteristics. According to the assumptions and reasoning methods of anisotropic failure criterion, it can be classified into two categories: continuous failure criterion and discontinuous piecewise failure criterion. Continuous medium failure criterion can also be classified into mathematical and empirical ones. Because of the complexity of rock anisotropy, the research on yield criterion and constitutive relation of rock anisotropy is still in the stage of theoretical research, and it is seldom applied in actual rock engineering. The physics model of rock has an important influence on the study of the anisotropic characteristics of rock. Therefore, the establishment of an appropriate rock physics model has a direct impact on the accurate determination of rock anisotropy parameters and P-S wave velocity. Finally, the key and difficult points of anisotropic rock research and the direction of future research are discussed and analyzed to provide a reference for engineering practice and related problems. [ABSTRACT FROM AUTHOR]

One of the long-standing problems in continuum damage mechanics is accurate prediction of damage evolution that accounts for the distribution of microstructural features. This is particularly true for microcracking solids, such as concrete, where non-uniformity in the size and spatial distribution of defects can lead to non-uniqueness in the continuum-averaged energy release rate (and free surface area creation) for cases where local microcrack growth occurs. In this work, a novel theoretical framework for quantifying the crack free surface area creation is formulated and used along with a previously developed non-local numerical technique known as Graph-based Finite Element Analysis (GraFEA). Using the 2D GraFEA approach and its implementation into a finite element code, the invariance of the crack free surface area created and the total amount of energy dissipated due to fracture was demonstrated. This research aims to honor the lifelong accomplishments of Professor Alan Needleman in computational modeling of deformation and fracture. • 2D GraFEA extended to estimate free surface area creation in microcracking concrete. • Used a non-local, stochastic model with population dynamics and survival probability. • Calibrated non-local characteristic length for concrete to estimate fracture energy. • Calculated fracture energy absorbed in concrete quasi-static boundary value problems. • This approach eliminated non-uniqueness in free surface area creation in GraFEA. [ABSTRACT FROM AUTHOR]

The following study intends to analyse the evolution of theories regarding the recognition of states in international law. Whereas the Montevideo Criteria contains the legal requirements for statehood, recognition is largely dependent on the political will of the other states. The question faced by the contemporary international community is whether a state is held to recognise another if it meets the said requirements. While the Constitutive Theory insists that a state could only exist as an international legal person if it is recognised by previously-established states, the Declarative Theory rejects such a discretionary process. While the common practice among states was argued to be somewhere in the middle of these two theories, the declarative conception is much closer to the current model followed by the international community as it is also enshrined in the rules contained in the Montevideo Convention and reiterated by the Badinter Commission.

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We derive a thermodynamically-consistent, three-dimensional, rate form-based finite-deformation constitutive theory and computational approach for damage & fracture in nonlinear viscoelastic materials. The key ingredient that allows us to develop a physical criterion for fracture is the use of a Gibbs potential-based multinetwork formulation of viscoelasticity. An approach that is based on the use of the criticality of the averaged Gibbs potential over a fracture process zone is used for the initiation & propagation of cracks in a body. The rate form-based constitutive theory and fracture criterion are implemented into the Abaqus (2018) finite-element program through a user-material subroutine interface. Crack propagation is modeled as the failure of elements leading to loss of mechanical resistance to deformation. The tearing & fracture response of a viscoelastic material using a notch-in-plate sample deformed in simple tension is also simulated. By comparing the simulation results for a local damage criterion versus a truly nonlocal damage criterion, we show how the spread of Gibbs free energy around the crack tip influences the nature of the crack growth. As expected, the material fracture response described by a local damage criterion exhibits pathological mesh dependence whereas the response obtained using the nonlocal damage criterion is mesh objective regardless of mesh density, element type and orientation. This work presents two major computational advances: (1) the conversion of the rate form-based finite-deformation constitutive theory into an objective time-integration procedure is straightforward because the material time derivative-based constitutive equations are frame-invariant, and (2) the physically-observed crack initiation & propagation process in solids can be accurately & robustly simulated using simple numerical techniques such as the element failure method if a truly nonlocal fracture criterion is utilized. Finally, we benchmark results obtained from our computational framework and numerical simulations for modeling crack initiation & propagation to physical experimental data of mixed-mode crack propagation in a viscoelastic material. • A new advance to modeling the fracture of viscoelastic solids is presented. • A novel rate form-based finitedeformation constitutive theory is derived. • A new computational framework for damage in viscoelastic solids is developed. • The crack propagation process in viscoelastic solids can be accurately simulated. [ABSTRACT FROM AUTHOR]

A soft solid is said to be initially stressed if it is subjected to a state of internal stress in its unloaded reference configuration. In physical terms, its stored elastic energy may not vanish in the absence of an elastic deformation, being also dependent on the spatial distribution of the underlying material inhomogeneities. Developing a sound mathematical framework to model initially stressed solids in nonlinear elasticity is key for many applications in engineering and biology. This work investigates the links between the existence of elastic minimizers and the constitutive restrictions for initially stressed materials subjected to finite deformations. In particular, we consider a subclass of constitutive responses in which the strain energy density is taken as a scalar-valued function of both the deformation gradient and the initial stress tensor. The main advantage of this approach is that the initial stress tensor belongs to the group of divergence-free symmetric tensors satisfying the boundary conditions in any given reference configuration. However, it is still unclear which physical restrictions must be imposed for the wellposedness of this elastic problem. Assuming that the constitutive response depends on the choice of the reference configuration only through the initial stress tensor, under given conditions we prove the local existence of a relaxed state given by an implicit tensor function of the initial stress distribution. This tensor function is generally not unique, and can be transformed according to the symmetry group of the material at fixed initial stresses. These results allow one to extend Ball's existence theorem of elastic minimizers for the proposed constitutive choice of initially stressed materials. [ABSTRACT FROM AUTHOR]

The article presents Charles Taylor's critical philosophy of language and it reviews his recent book on the human linguistic capacity. Critical philosophy of language is understood here as a broad (philosophical, social and political) perspective on language characterized by multifaceted concern with the linguistic and cognitive mechanisms involved in language use. The paper discusses Taylor's interest in language and philosophy of language, and focuses on his seminal distinction between the 'designative-instrumental' and 'constitutive-expressive' theories of language. In the former theory language is understood within the confines of Cartesian representational epistemology, whereas in the latter language constitutes meaning and shapes human experience (one of the features important for defining the critical approach to philosophy of language). [ABSTRACT FROM AUTHOR]

This article starts from the observation that International Relations scholars do not agree on what they mean by theory. The declining popularity of grand theory and the celebration of theoretical pluralism are accompanied by the relative absence of a serious conversation about what ‘theory’ is or should be. Taking the view that we need such a conversation, especially given the shallow theorizing of modern scholarship that conflates theory with method, and the postmodern view that abstract narratives must be deconstructed and rejected, this article puts forward the notion of ‘deep theorizing’ as the ground for grand theory. Specifically, it argues that deep theorizing is the conceptual effort of explaining (inter)action by developing a reading of drives/basic motivations and the ontology of its carrier through an account of the human condition, that is, a particular account of how the subject (the political actor) is positioned in social space and time. The article illustrates this angle through a discussion of realist, liberal and postcolonial schools of thought. It basically argues that, through their particular readings of the human condition, these approaches develop distinct conceptions of political agency and, hence of the nature and location of world politics. [ABSTRACT FROM AUTHOR]

Shape memory polymers (SMPs) are a class of active, deformable materials that can switch between a temporary shape, which can be freely designed, and their original shape. With their large deformation, low density, various stimulation methods, good biocompatibility and other advantages, SMPs have become widely accepted as smart materials. However, SMPs have many limitations and weaknesses that are exposed in engineering applications. For this reason, the significance of SMP composites (SMPCs) has been analyzed in terms of four aspects: reinforcement, innovation and improvement of driving methods, the creation of specific deformations and the creation of multifunctional materials. We then introduce the constitutive theory of SMPs and the post-buckling analysis of SMPCs. Afterward, we introduce the extensive applications of SMPCs in the fields of aerospace, biomedical equipment, self-finishing, deformable mandrels and the 4D printing of active origami structures, demonstrating their ability to undergo active driving and deformation, their adaptiveness, their ease of transport and their rapid production capacity, which fully demonstrate the unique advantages of SMPs in solving application problems. Finally, the advantages and disadvantages of SMPCs in applications are summarized, and the prospects for new SMPCs and new SMPC structures are described. [ABSTRACT FROM AUTHOR]