Nonlinear Models of Thermo-Viscoelastic Materials

Giorgi, Claudio; Morro, Angelo

doi:10.3390/ma14247617

Cited by 11 publications

(10 citation statements)

References 31 publications

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“…The approach through rate equations turn out to be advantageous thanks as well to some ideas and results established in [ 8 ], in which the entropy production is viewed as a constitutive function, while a representation formula yields the general result ( 28 ) for solids and the analogue for fluids. The completeness of the scheme allows us to find the stress rate in magneto-hypoelasticity, magneto-hyperelasticity, and (dissipative) magneto-viscoelasticity.…”

Section: Discussionmentioning

confidence: 99%

“…If

and

are arbitrary and independent, then it follows that

(and

). If, instead,

and

are not independent, then we can determine the relation between

and

through a representation formula [ 8 , 9 ].…”

Section: Balance Equationsmentioning

confidence: 99%

“…Recently, we have developed a systematic approach to nonlinear materials with memory [ 8 , 9 ]. The crucial points are that the models are thermodynamically consistent; the entropy production is a constitutive quantity that characterizes the dissipative properties; the entropy inequality allows us eventually to derive a representation formula for the pertinent function; and the nonlinear rate equations are derived with an objective time derivative.…”

Section: Introductionmentioning

confidence: 99%

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Magneto-Viscoelastic Materials: Memory Functionals and Rate Equations

Giorgi

Morro

2022

Materials

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The properties of viscoelastic solids subject to a magnetic field are modelled within two thermodynamically consistent approaches that are typical of models with a non-instantaneous response. One is based on memory functionals: the reversible changes are described by the instantaneous response, while the dissipativity is expressed by the dependence on histories. The other approach involves objective rate equations. While memory functionals lead to the difficulty of determining thermodynamically consistent free energy functionals, rate equations result in a simpler scheme. The greater simplicity allows the discovery of, in particular, models of magneto-hyperelastic materials, magneto-hypoelastic materials, and various forms of magneto-viscoelastic behaviour. The novelty of the procedure is based on two features: a representation formula, originating from the entropy inequality, and the use of the entropy production as a constitutive function. Relations with other approaches in the literature are examined in detail.

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Section: Discussionmentioning

confidence: 99%

“…If

and

are arbitrary and independent, then it follows that

(and

). If, instead,

and

are not independent, then we can determine the relation between

and

through a representation formula [ 8 , 9 ].…”

Section: Balance Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Magneto-Viscoelastic Materials: Memory Functionals and Rate Equations

Giorgi

Morro

2022

Materials

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“…of the constitutive law (26), which corresponds to a Kelvin-Voigt model for the material, see for instance [GM21,LLT13].…”

Section: Analysis Of Displacements and Vibrationsmentioning

confidence: 99%

Simulations in a Digital Twin of an Electrical Machine

Cherifi¹,

Mehrmann²,

Schulze³

2022

Preprint

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Digital twins have become popular for their ability to monitor and optimize a process or a machine during its lifetime using simulations and sensor data. In this paper, we focus on the challenge of the implementation of accurate and real time simulations for digital twins in the context of electrical machines.In general, this involves not only computational models for the electromagnetic aspects, but also mechanical and thermal effects need to be taken into account. We address mathematical tools that can be employed to carry out the required simulations based on physical laws as well as surrogate or data-driven models. One of those tools is a model hierarchy of very fine to very course models as well model reduction which is required for obtaining real-time simulations.We discuss in detail the coupling of electromagnetic, mechanical, and thermal models of an electrical machine to obtain a simulation model which is able to describe the interaction of those different physical components. In this context, a very promising setting is provided by energy-based formulations within the port-Hamiltonian framework, which has received much attention in the past years, especially in the context of multiphysics modeling. We present such port-Hamiltonian formulations for the considered electromagnetic, mechanical, and thermal models as well as for the coupled overall system.

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“…The mathematical complexity of this formulation is too complicated for use in many situations. Another approach involves objective rate equations by means of a thermodynamically consistent scheme which naturally allows the construction of nonlinear viscoelastic models (see [ 8 ]). More recently, in [ 9 , 10 ], nonlinear mechanical viscous effects are described by assuming a semi-continuum theoretical model with a geometric nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic and Electromagnetic Materials with Nonlinear Memory

Giorgi

Golden

2022

Materials

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A method is presented for generating free energies relating to nonlinear constitutive equations with memory from known free energies associated with hereditary linear theories. Some applications to viscoelastic solids and hereditary electrical conductors are presented. These new free energies are then used to obtain estimates for nonlinear integro-differential evolution problems describing the behavior of nonlinear plasmas with memory.

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Nonlinear Models of Thermo-Viscoelastic Materials

Cited by 11 publications

References 31 publications

Magneto-Viscoelastic Materials: Memory Functionals and Rate Equations

Magneto-Viscoelastic Materials: Memory Functionals and Rate Equations

Simulations in a Digital Twin of an Electrical Machine

Viscoelastic and Electromagnetic Materials with Nonlinear Memory

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