Two-field variational formulations for a class of nonlinear mechanical models

A nonlinear boundary value problem arising from continuum mechanics is considered. The nonlinearity of the model arises from the constitutive law which is described by means of the subdifferential of a convex constitutive map. A bipotential [Formula: see text], related to the constitutive map and its Fenchel conjugate, is considered. Exploring the possibility to rewrite the constitutive law as a law governed by the bipotential [Formula: see text], a two-field variational formulation involving a variable convex set is proposed. Subsequently, we obtain existence and uniqueness results. Some properties of the solution are also discussed.

Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>

Rotation of the Stress Tensor in a Westerly Granite Sample During the Triaxial Compression Test

We simulated the spatiotemporal modelling of 3D stress and strain distributions during the triaxial compression laboratory test on a westerly granite sample using finite-difference numerical modelling implemented with FLAC3D software. The modelling was performed using a ubiquitous joint constitutive law with strain softening. The applied procedure is capable of reproducing the macroscopic stress and strain evolution in the sample during triaxial deformation until a failure process occurs. In addition, we calculated focal mechanisms of acoustic emission (AE) events and resolved local stress field orientations. This detailed stress information was compared with that from numerical modelling. The comparison was made based on the 3D rotation angle between the cardinal axes of the two stress tensors. To infer the differences in rotation, we applied ANOVA. We identified the two time levels as the plastic deformation phase and the after-failure phase. Additionally, we introduced the bin factor, which describes the location of the rotation scores in the rock sample. The p values of the test statistics F for the bin and phase effects are statistically significant. However, the interaction between them is insignificant. We can, therefore, conclude that there was a significant difference in the time between the rotation means in the particular bins, and we ran post hoc tests to obtain more information where the differences between the groups lie. The largest rotation of the stress field provided by the focal mechanisms of AE events from the numerically calculated stress field is observed in the edge bins, which do not frame the damage zone of the sample.

Complex Behavior in the Dynamics of a Polymeric Biocomposite Material—“Liquid Wood”. Experimental and Theoretical Aspects

The purpose of the present paper is to analyze, both experimentally and theoretically, the behavior of the polymeric biocomposite generically known as “liquid wood”, trademarked as Arbofill. The experimental part refers to the mechanical performance in tension and compression, having as finality the possibility of using “liquid wood” as a material suitable for the rehabilitation of degraded wooden elements in civil structures (ex. use in historical buildings, monuments etc.,). The theoretical part refers to computer simulations regarding the mechanical behavior of “liquid wood” as well as to a theoretical model in the paradigm of motion, which describes the same behavior. This model is based on the hypothesis that “liquid wood” can be assimilated, both structurally and functionally, to a multifractal object, situation in which its entities are described through continuous, non-differentiable curves. Then, descriptions of the behavior of “liquid wood”, both in the Schrödinger-type and in hydrodynamic-type representations at various scale resolutions, become operational. Since in the hydrodynamic-type representation, the constitutive law of “liquid wood” can be highlighted, several operational procedures (Ricatti-type gauge, differential geometry in absolute space etc.,) will allow correlations between the present proposed model and the experimental data. The obtained results, both practical (81% bearing capacity in compression and 36% bearing capacity in tension, compared to control samples) and theoretical (validation of material performance in virtual environment simulations, stresses and strains correlations in a theoretical model) indicate that “liquid wood” could be used in the construction industry, as a potential rehabilitation material, but with more development clearly needed.

The Influence of the Material Properties on the Ultimate Behaviour of Aluminium H-shaped Beams

Background: In this paper, the influence of the Ramberg-Osgood exponent on the ultimate behaviour of the H-shaped (or I-shaped) aluminium beams subjected to non-uniform bending moment is investigated. Methods: In particular, the results of a wide parametric analysis recently carried out by the authors are herein exploited to point out the influence of the material properties. The flange slenderness, the flange-to-web slenderness ratio, and the non-dimensional shear length, accounting for the moment gradient, are the main non-dimensional parameters governing the ultimate resistance and the rotation capacity of H-shaped aluminium beams. Results: The influence of these parameters was investigated considering four different materials covering both low yielding-high hardening alloys and high yielding-low hardening alloys, which are characterised by significant differences in the values of the Ramberg-Osgood exponent of the stress-strain constitutive law of the material. Conclusion: Finally, empirical formulations for predicting the non-dimensional ultimate flexural strength and the plastic rotation capacity of H-section aluminium beams under moment gradient have been provided as a function of the Ramberg-Osgood exponent and all the above non-dimensional parameters.

A novel strain-based finite element family for mesh-independent analysis of the tensile failure of reinforced concrete bars

The paper presents a novel family of strain-based beam finite elements (FE) for analysis of tensile failure of a reinforced concrete bar (RC bar), with results of the analysis being independent of the applied FE mesh. The composite bar consists of a continuous longitudinal ductile reinforcing bar(s) surrounded by brittle concrete cover, which are considered separately in the model. Longitudinal slip at the contact between the concrete cover and reinforcing bars is allowed, while their relative displacements perpendicular to the axis of the RC bar are prevented. Cracks in concrete cover occur when tensile stress in concrete exceeds its tensile strength. Propagation of partially connected crack, that is, softening of the material at the crack, is described through constitutive law in form of nonlinear relationship between stresses in concrete at the crack and the width of the crack. Each separate crack is considered discretely as a discontinuity in geometry of the element. In the analysis of cracking of concrete, it is commonly assumed that the discrete crack can occur at the nodes of FE only. However, this assumption leads to dependence of the analysis results on the employed FE mesh. The presented family of FE enables occurrence of the crack anywhere along the FE. In order to achieve this, the discrete crack is excluded from equations of FE and additional boundary conditions are introduced at the discontinuity. This approach ensures that the location of the cracks, their number and their propagation are independent of the applied FE mesh. Advantages of the novel family of FE are thoroughly presented in a parametric study which investigates influence of number of FE as well as influence of degrees of interpolation and integration on the cracking of RC bar under tensile loading. Experimental results of tensile tests on the analysed bar are available in literature. It can be concluded that the results obtained with the minimal possible number of novel FE and sufficiently high degree of numerical integration scheme, applied for solving integrals in equations of FE, are considerably more accurate than the results of previous analyses with model of discrete crack at the nodes of FE only.

Mechanical analysis of heterogeneous materials with higher-order parameters

Even though heterogeneous porous materials are widely used in a variety of engineering and scientific fields, such as aerospace, energy-storage technology, and bio-engineering, the relationship between effective material properties of porous materials and their underlying morphology is still not fully understood. To contribute to this knowledge gap, this paper adopts a higher-order asymptotic homogenization method to numerically investigate the effect of complex micropore morphology on the effective mechanical properties of a porous system. Specifically, we use the second-order scheme that is an extension of the first-order computational homogenization framework, where a generalized continuum enables us to introduce length scale into the material constitutive law and capture both pore size and pore distribution. Through several numerical case studies with different combinations of porosity, pore shapes, and distributions, we systematically studied the relationship between the underlying morphology and effective mechanical properties. The results highlight the necessity of higher-order homogenization in understanding the mechanical properties and reveal that higher-order parameters are required to capture the role of realistic pore morphologies on effective mechanical properties. Furthermore, for specific pore shapes, higher-order parameters exhibit dominant influence over the first-order continuum.

A dynamic electroviscoelastic problem with thermal effects

We consider a mathematical model which describes the dynamic pro- cess of contact between a piezoelectric body and an electrically conductive foun- dation. We model the material's behavior with a nonlinear electro-viscoelastic constitutive law with thermal e ects. Contact is described with the Signorini condition, a version of Coulomb's law of dry friction. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear rst order evolution inequali- ties, the equations with monotone operators, and the xed point arguments.