Constitutive modelling of non-crystalline solids using Van der Waals Potential

Non-crystalline molecular solid materials have many scientific and engineering applications. This study develops a constitutive equation for understanding stress-stretch behaviour of non-crystalline molecular solid using Lennard-Jones (LJ) intermolecular interaction. The strain energy derived from Lennard-Jones interactions between molecules. Based on the excluded volume (spherical volume occupied by the molecules maintaining centre to centre distance with a reference molecule) and density of the molecules, strain energy density is developed. In order to relate the molecular approach with continuum approximation, the excluded volume and density are expressed as a function of strain invariants of right Cauchy-Green deformation tensor. Finally, the constitutive equation in the form of Cauchy stress tensor is developed using the present strain energy density function. The present constitutive model is used to study finite deformations of the molecular solid like uniaxial extension. We compare our theoretical results with the experimental data of flexible polyurethane foams and obtain very good agreements. The current constitutive model can predict the deformation of micro/nano engineering system components.

Soil compaction is widely applied in geotechnical engineering practice. It is used to maximise the dry density of soils to reduce subsequent settlement under working loads or to reduce the permeability of soils. The durability and stability of structures are highly related to the appropriate compaction achievement. The structural failure of roads and airfields, and the damage caused by foundation settlement can often be traced back to the failure in achieving adequate compaction. For that reason, soil compaction is important for engineering activities involving earthworks. Compacted soils are unsaturated by nature, which includes both air and water within their voids. Thus, unsaturated soil mechanics principles are crucial in understanding the compaction behaviour of soils. There are several qualitative studies, which attempt to explain the compaction behaviour of soils and there is a vast body of literature covering the behaviour of compacted soils. Still, fundamental research on the compaction process is limited. In addition, the current constitutive models available for unsaturated soils assume that the soil state after compaction is the initial state of the soil. However, compacted soils undergo a stress history which influences the post compaction behaviour. Considering these facts, it still remains that the compaction of soil is a complex phenomenon, which is not well explained, particularly from a quantitative sense. Further understanding of the compaction behaviour during the compaction process will provide important insights on the behaviour of compacted soils. The main aim of this research project is to extend the current understanding of the compaction process of soils. The research focuses on three different areas: investigating the experimental behaviour of soils during the static compaction process and obtaining data for compaction modelling; developing a compaction model using the existing constitutive models for unsaturated soils; and evaluating the performance of this model in predicting the compaction behaviour of soils. In the experimental part, static compaction tests were conducted on two different granular soils, sand with 2% and 5% bentonite content by weight. The tests were undertaken on samples with different water contents in order to observe the effect of matric suction on the compaction behaviour. The initial matric suction of the specimens was measured using the null type axis translation technique and the matric suction variations were monitored during the compaction process. It was found that the unsaturated samples were always more compressible than the saturated sample. This finding is contrary to the assumption made in most constitutive models, and thus modelling the compaction behaviour using these models may result in some deficiencies. In addition, in granular soils with low water content the axis translation technique was found to be very time consuming for the suction measurements. This was attributed to the discontinuous water phase within the samples. To develop a compaction model, a volume change constitutive relationship for unsaturated soils, defined in terms of two independent stress variables, was incorporated with pore pressure predictions. The model was developed for undrained, semi-drained and drained loading conditions. Initially, compressibility coefficients in the volume change relationship were considered as constant parameters, i.e., the compressibility of a soil element does not change with increasing vertical stress. Using constant compressibility coefficients, the compaction curve can be predicted only for the wet side of the curve, not the dry side. Thus, variable compressibility coefficients were derived from constitutive models proposed in the literature, and using these coefficients, the well-known shape of the compaction curve was predicted on both dry and wet side of the compaction curve. It was found that the shape of the compaction curve can be the theoretically predicted using unsaturated soil mechanics principles. The main insight gained from the model development was that the influence of matric suction on the material compressibility with respect to net stress is the governing factor determining the inverted parabolic shape of the compaction curve. The performance of the compaction models were examined on their ability to predict the compaction behaviour of soils. Data for four different soils, two sand-bentonite mixtures tested in this study, and Boom clay and Speswhite kaolin data from literature, were used for models evaluation. Two different constitutive modelling approaches were analysed, which are the separate stress state variables approach and combined stress state approach. It was concluded that the samples prepared from initially slurry soils and from initially dry soils could not be treated the same and would require the use of different sets of soil parameters. In addition, the compaction behaviour of soils, prepared from initially dry samples, could only be modelled over a narrow range of water contents using a single set of soil parameters. Minimum two sets of soil parameters are required to model the compaction behaviour over a wide range of water contents with the current constitutive models.

Derivation of higher order gradient continuum theories in 2,3-d non-linear elasticity from periodic lattice models

Springer handbook of enzymes, 2nd edn

Constitutive restrictions for a hyperelastic material, based upon strain invariants yielding orthogonal stress response terms

On internal dissipation inequalities and finite strain inelastic constitutive laws: Theoretical and numerical comparisons

The upper triangular decomposition has recently been proposed to multiplicatively decompose the deformation gradient tensor into a product of a rotation tensor and an upper triangular tensor called the distortion tensor, whose six components can be directly related to pure stretch and simple shear deformations, which are physically measurable. In the current paper, constitutive equations for hyperelastic materials are derived using strain energy density functions in terms of the distortion tensor, which satisfy the principle of material frame indifference and the first and second laws of thermodynamics. Being expressed directly as derivatives of the strain energy density function with respect to the components of the distortion tensor, the Cauchy stress components have simpler expressions than those based on the invariants of the right Cauchy-Green deformation tensor. To illustrate the new constitutive equations, strain energy density functions in terms of the distortion tensor are provided for unconstrained and incompressible isotropic materials, incompressible transversely isotropic composite materials, and incompressible orthotropic composite materials with two families of fibers. For each type of material, example problems are solved using the newly proposed constitutive equations and strain energy density functions, both in terms of the distortion tensor. The solutions of these problems are found to be the same as those obtained by applying the polar decomposition-based invariants approach, thereby validating and supporting the newly developed, alternative method based on the upper triangular decomposition of the deformation gradient tensor.

Micromechanical modelling of mortar joints and brick-mortar interfaces in masonry Structures: A review of recent developments

The mechanical properties of Ti-6Al-4V alloy are sensitive to strain rate and temperature load. The finite element simulation results of high-speed machining Ti-6Al-4V alloy depend on the accurate description of dynamic deformation. However, it is hard to describe the flow stress behavior in current constitutive models in a complex high-speed machining process for Ti-6Al-4V alloy. In this paper, the stress-strain curves of Ti-6Al-4V alloy under the wide ranges of strain rate and temperature are obtained by high-velocity uniaxial impact tests. The apparent coupling between temperature and strain is observed, which proves that the temperature is dependent on a hardening effect for Ti-6Al-4V alloy. A function describing the coupling between temperature and strain is then introduced into the modification for the original Johnson-Cook (JC) constitutive model. The maximum deviation between the predicted data from using the proposed modified JC constitutive model and experimental data is reduced from 10.43% to 4.19%. It can be concluded that the modified JC constitutive model is more suitable to describe the temperature-dependent hardening effect, which provides strong support for accurate finite element simulation of high-speed machining Ti-6Al-4V alloy.

The mechanical response of most soft tissue is considered to be viscohyperelastic, making the development of accurate constitutive models a challenging task. In this article, we present a constitutive model for bovine liver tissue that utilizes a viscous dissipation potential, and use it to model the response of bovine liver tissue at strain rates ranging from 0.001 to 0.04 s(-1). On the material modeling front of this study, the free energy is assumed to depend on the right Cauchy-Green deformation tensor, whereas a separate rate-dependent viscous potential is posited to characterize viscoelasticity. This viscous dissipation component is a function of the time rate of change of the right Cauchy-Green deformation tensor. On the experimental front, no-slip uniaxial compression experiments are conducted on bovine liver tissue at various strain rates. A numerical correction approach is used to account for the no-slip edge conditions, and the constitutive model is fit to the resulting corrected stress-strain data. The complete derivation of the material model, its implementation in the finite element software package ABAQUS, and a validation study are presented in this article. The results show that bovine liver tissue exhibits a strong strain-rate dependence even at the low strain rates considered here and that the proposed constitutive model is able to accurately describe this response.

The nonlinear viscoelastic properties of a fairly large class of polymeric fluids can be described with the factorable single integral constitutive equation. For this class of fluids, a connection between the rheological behaviour in different flow geometries can be defined if the strain tensor (or the damping function) is expressed as a function of the invariants of a tensor which describes the macroscopic strain, such as the Finger tensor. A number of these expressions, proposed in the literature, are tested on the basis of the measuring data for a low-density polyethylene melt. In the factorable BKZ constitutive equation the strain-energy function must be expressed as a function of the invariants of the Finger tensor. The paper demonstrates that the strain-energy function can be calculated from the simple shear and simple elongation strain measures, if it is assumed to be of the shape proposed by Valanis and Landel. The measuring data for the LDPE melt indicate that the Valanis-Landel hypothesis concerning the shape of the strainenergy function is probably not valid for polymer melts.

Cemented sand and gravel (CSG) is a kind of green building material that has emerged in recent years. The cement content has a great impact on the deformation characteristics of CSG, but the current constitutive models cannot reflect this problem. Based on the previous research results, this paper depicted the volume strain and shear strain of CSG, established a nonlinear constitutive model of CSG, and finally verified the new constitutive model with experimental data. Results showed that the model could well simulate the deformation characteristics of the CSG with cement content of more than 40 kg/m3, and the entire stress–strain relationship was basically consistent with the experimental value, reflecting the adaptability and superiority of the nonlinear constitutive model of CSG.

With the interaction in automobile manufacturing technology, products made of integrated die-cast aluminum alloy are becoming more and more widespread. However, engineers frequently ignore the impact of structural features on mechanical properties when utilizing simulation software to determine a product's strength, and current constitutive models do not account for structural flaw studies. To examine the correlation between structural flaws and mechanical properties of the die-cast aluminum alloy, quasi-static tensile tests were performed on JDA1b alloy specimens. The defect rates were varied by adding circular holes with varying diameters at the center of the specimens. The results showed that the JDA1b alloy’s tensile strength and elongation significantly decreased as the fault rate increased. A constitutive model with defect rates is proposed, which has higher accuracy than the J–C model. Simulations and experimental findings effectively validated the accuracy of the proposed constitutive model. The proposed model provides support for high-precision computing for analyzing the mechanical performance of materials.

Effects of crystal content on the mechanical behaviour of polyethylene under finite strains: Experiments and constitutive modelling

Some issues about anisotropic elastic–plastic models at finite strain