iRheoFoam: A package for simulating complex planar interfaces by Adolfo Esteban, Julio Hernández, Javier Tajuelo, Miguel Ángel Rubio

“…It is based on the Boussinesq–Scriven constitutive law and the Navier–Stokes equations, includes various solvers for both time-dependent and steady problems, and allows easy incorporation of new interface models and solvers, making it a versatile and powerful tool.…”
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Lie groups and continuum mechanics: where do we stand today? by de Saxcé, Géry, Razafindralandy, Dina

“…We explore the classical symmetry groups of the mechanics, the covariant form of the equations and the symmetry group of constitutive laws. We consider the Lie symmetry group of the equations of a mechanical problem and investigate how to take advantage of them in developping analytical models (self-similar solutions, conservation laws, turbulence, ...) of the physical phenomena encoded in these equations. …”
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On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials by Luciano Feo, Rosa Penna

“…The Bernoulli-Euler kinematic assumption and the Eringen nonlocal constitutive law are assumed in the formulation of the elastic equilibrium problem. …”
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On the frictionless unilateral contact of two viscoelastic bodies by M. Barboteu, T.-V. Hoarau-Mantel, M. Sofonea

“…The bodies are assumed to have a viscoelastic behavior that we model with Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the classical Signorini condition with zero-gap function. …”
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Church and State Relations in the Constitution of Malta by Kevin Aquilina

“… This paper discussed the relationship between the Catholic Church and the State of Malta as evidenced primarily in the Constitution of Malta and secondarily in other Constitutional Laws. It is noted that the Roman Catholic Apostolic Religion is the national religion of Malta. …”
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Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory by Ahmed Hamidat, Hakim Bagua, Adel Aissaoui

“…The material behaviour is explained using a viscoelastic constitutive law that includes long-term memory and damage. …”
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A frictionless contact problem for viscoelastic materials by Mikäel Barboteu, Weimin Han, Mircea Sofonea

“…The body is assumed to have a viscoelastic behavior that we model with the Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the well-known Signorini condition in a form with a zero gap function. …”
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Study on Impact Behavior and Impact Force of Bridge Pier Subjected to Vehicle Collision by Deyuan Zhou, Ruiwen Li, Juan Wang, Changtuan Guo

“…Nonlinear material constitutive laws considering the strain-rate effect were used. …”
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Fracture toughness of rough and frictional cracks emanating from a re-entrant corner by Andrea Carpinteri, Andrea Spagnoli, Michele Terzano, Sabrina Vantadori

“…The crack surfaces are assumed to be globally smooth, and roughness and friction are incorporated through a constitutive law between opposite crack surfaces. The solution is found using the distributed dislocation method, and an iterative algorithm is needed due to the non-linearity of the model. …”
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Mechanical Performance and Design Method of Improved Lead Shear Damper with Long Stroke by Baoshun Wang, Weiming Yan, Haoxiang He

“…Based on the ideal rigid-plastic constitutive law of lead, a mechanical model of the ILSD-LS is established. …”
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Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media by Dolbeau, Martin, Bleyer, Jérémy, Sab, Karam

“…Sab et al. (2024) have recently proposed an FFT-based iterative algorithm, termed Adaptive Eyre–Milton (AEM), for solving the Lippmann–Schwinger equation in the context of periodic homogenization of infinitely double contrasted linear elastic composites (heterogeneous materials with linear constitutive laws that contain both pores and rigid inclusions). …”
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Flow optimization in vascular networks by Radu C. Cascaval, Ciro D'Apice, Maria Pia D'Arienzo, Rosanna Manzo

“…Detailed $3$D studies of flow in the arterial system based on the Navier-Stokes equations require high computational power, hence reduced models are often used, both for the constitutive laws and the spatial domain. In order to capture the major features of the phenomena under study, such as variations in arterial pressure and flow velocity, the resulting PDE models on networks require appropriate junction and boundary conditions. …”
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An Analytical Step-by-Step Procedure to Derive the Flexural Response of RC Sections in Compression by Piero Colajanni, Marinella Fossetti, Maurizio Papia

“…The formulation is developed in dimensionless terms, after a preliminary definition of the geometrical and mechanical parameters involved, so that the results are valid for classes of RC sections. The constitutive laws of the materials include confinement effect on the concrete and postyielding behaviour of the steel reinforcement, which can be assumed to be softening behaviour for buckled reinforcing bars. …”
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Experimental and Numerical Study on Tensile Strength of Concrete under Different Strain Rates by Fanlu Min, Zhanhu Yao, Teng Jiang

“…The implementation of material constitutive law is of capital importance for the numerical simulation of the dynamic processes as those caused by earthquakes. …”
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Gradient enriched linear-elastic crack tip stresses to estimate the static strength of cracked engineering ceramics by Harm Askes, Luca Susmel

“…This peculiar modus operandi results in stress fields in the vicinity of sharp cracks which are no longer singular, even though the assessed material is assumed to obey a linear-elastic constitutive law. Given both the geometry of the cracked component being assessed and the value of the material length scale, the magnitude of the corresponding gradient enriched linear-elastic crack tip stress is then finite and it can be calculated by taking full advantage of those computational methods specifically devised to numerically implement gradient elasticity. …”
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Gradient-enriched linear-elastic tip stresses to perform the highcycle fatigue assessment of notched plain concrete by C. Bagni, H. Askes, L. Susmel

“…This is done by simply assuming that the material under investigation obeys a linear-elastic constitutive law, albeit equipped with additional spatial strain gradients. …”
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Dynamic Characteristics of Blade with Viscoelastic Damping Block Based on Complex Eigenvalue Method by Jiao Wang, Yue-hao Zhang, Tao Yu, Qing-kai Han

“…Complex modulus model is applied to represent the constitutive law of viscoelastic material and shear force acting on the VE-blade formulates the effect of viscoelastic damping at the root interfaces. …”
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A numerical model based on ALE formulation to predict crack propagation in sandwich structures by Marco Francesco Funari, Fabrizio Greco, Paolo Lonetti, Saverio Spadea

“…Debonding phenomena are simulated by weak based connections, in which moving interfacial elements with damage constitutive laws are able to reproduce the crack evolution. …”
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Influence of the Constitutive Flow Law in FEM Simulation of the Radial Forging Process by Olivier Pantalé, Babacar Gueye

“…As the deformation of the workpiece, during the process, is a consequence of a large number of high-speed strokes, the Johnson-Cook constitutive law (taking into account the strain rate) seems to be well adapted for representing the material behavior even if the process is performed under cold conditions. …”
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Modelling of Rough Contact between Linear Viscoelastic Materials by Sergiu Spinu, Delia Cerlinca

“…The spatial discretization needs to be supported by temporal sampling of the simulation window when time-dependent viscoelastic constitutive laws are considered in the description of the material response. …”
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