Showing papers on "Constitutive equation published in 2020"

A statistical damage constitutive model considering whole joint shear deformation

Abstract: The whole shear deformation of rock joints significantly affects the long-term behavior and safety of engineering projects. In this paper, a new damage constitutive model related to the Weibull dis...

Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study.

Abstract: The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings.

A constitutive model for 3D printed continuous fiber reinforced composite structures with variable fiber content

Abstract: 3D printing provides a new technical means for the preparation of functionally controlled continuous fiber reinforced composites (CFRCs) with variable fiber content. The constitutive model of 3D printed CFRCs with different fiber contents are the basis for establishing mechanical analysis models and design methods of functionally regulated CFRCs based on 3D printing. In this paper, stiffness and strength properties of 3D printed CFRCs with different fiber contents were systematically studied, and the mapping relationship between material properties and fiber content was obtained. The failure processes of 3D printed CFRCs under different loads were studied by microstructural morphology and interfacial performance analysis, revealing the formation mechanisms of the material properties. The constitutive model and finite element analysis method of 3D printed CFRCs were established by using the material properties of 3D printed CFRCs with different fiber contents. The mechanical analysis mode was used to predict and analyze the performance of functionally graded CFRCs with variable fiber content. The results show that the mechanical analysis mode can be used for the optimization design and mechanical analysis of functionally controlled CFRCs.

Power-Law Scaling in Granular Rheology across Flow Geometries

Abstract: Based on discrete element method simulations, we propose a new form of the constitutive equation for granular flows independent of packing fraction. Rescaling the stress ratio μ by a power of dimensionless temperature Θ makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number I. The basic power-law structure appears robust to varying particle properties (e.g., surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the nonlocal granular fluidity model.

New perspective of fracture mechanics inspired by gap test with crack-parallel compression.

Abstract: The line crack models, including linear elastic fracture mechanics (LEFM), cohesive crack model (CCM), and extended finite element method (XFEM), rest on the century-old hypothesis of constancy of materials' fracture energy. However, the type of fracture test presented here, named the gap test, reveals that, in concrete and probably all quasibrittle materials, including coarse-grained ceramics, rocks, stiff foams, fiber composites, wood, and sea ice, the effective mode I fracture energy depends strongly on the crack-parallel normal stress, in-plane or out-of-plane. This stress can double the fracture energy or reduce it to zero. Why hasn't this been detected earlier? Because the crack-parallel stress in all standard fracture specimens is negligible, and is, anyway, unaccountable by line crack models. To simulate this phenomenon by finite elements (FE), the fracture process zone must have a finite width, and must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening, and splitting with microbuckling. This is best accomplished by the FE crack band model which, when coupled with microplane model M7, fits the test results satisfactorily. The lattice discrete particle model also works. However, the scalar stress-displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate. The experiment is proposed as a standard. It represents a simple modification of the three-point-bend test in which both the bending and crack-parallel compression are statically determinate. Finally, a perspective of various far-reaching consequences and limitations of CCM, LEFM, and XFEM is discussed.

A continuum constitutive model for FDM 3D printed thermoplastics

Abstract: Fused deposition modelling (FDM) is the most common additive manufacturing technology used for thermoplastic components. This layers-based manufacturing process results into direct links between printing parameters and the polymer mesostructure by means of porosity and structural anisotropy. These dependencies along with other features of thermoplastic polymers (i.e., nonlinearities, viscous and thermal responses) makes its constitutive modelling very challenging. This work distances from studies that model the 3D printing process. Instead, we aim at complementing such approaches with a continuum model to describe the macroscopic behaviour of FDM thermoplastics while preserving links with printing parameters. Prior to the modelling conceptualisation, experimental characterisation tests are conducted on ABS specimens to evaluate the influence of printing parameters on the macroscopic mechanical response. The physical fundamentals behind the deformation and failure mechanisms are identified and motivate the new constitutive model. This model is formulated for finite deformations within a thermodynamically consistent framework. The model accounts for: nonlinear response; anisotropic hyperelasticity related to a transversely isotropic distribution of porous; strain rate dependency; macroscopic stiffness dependent on 3D printing processing. Finally, the model is numerically implemented and calibrated for ABS with original experiments, demonstrating its suitability.

A Physics-Informed Assembly of Feed-Forward Neural Network Engines to Predict Inelasticity in Cross-Linked Polymers.

Abstract: In solid mechanics, data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and accuracy. However, the implementation of machine-learned approaches in material modeling has been modest due to the high-dimensionality of the data space, the significant size of missing data, and limited convergence. This work proposes a framework to hire concepts from polymer science, statistical physics, and continuum mechanics to provide super-constrained machine-learning techniques of reduced-order to partly overcome the existing difficulties. Using a sequential order-reduction, we have simplified the 3D stress–strain tensor mapping problem into a limited number of super-constrained 1D mapping problems. Next, we introduce an assembly of multiple replicated neural network learning agents (L-agents) to systematically classify those mapping problems into a few categories, each of which were described by a distinct agent type. By capturing all loading modes through a simplified set of dispersed experimental data, the proposed hybrid assembly of L-agents provides a new generation of machine-learned approaches that simply outperform most constitutive laws in training speed, and accuracy even in complicated loading scenarios. Interestingly, the physics-based nature of the proposed model avoids the low interpretability of conventional machine-learned models.

Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model

Abstract: Several studies indicate that Eringen’s nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both Euler-Bernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.

Non-standard and constitutive boundary conditions in nonlocal strain gradient elasticity

Abstract: Zaera et al. (Int J Eng Sci 138:65–81, 2019) recently showed that the nonlocal strain gradient theory (NSGT) is not consistent when it is applied to finite solids, since all boundary conditions associated to the corresponding problems cannot be simultaneously satisfied. Given the large number of works using the NSGT being currently published in the field of generalized continuum mechanics, it is pertinent to evince the shortcomings of the application of this theory. Some authors solved the problem omitting the constitutive boundary conditions. In the current paper we show that, in this case, the equilibrium fields are not compatible with the constitutive equation of the material. Other authors solved it omitting the non-standard boundary conditions. Here we show that, in this case, the solution does not fulfil conservation of energy. In conclusion, the inconsistency of the NSGT is corroborated, and its application must be prevented in the analysis of the mechanical behaviour of nanostructures.