Rate-Independent Damage in Thermo-Viscoelastic Materials with Inertia

Lazzaroni, Giuliano; Rossi, Riccarda; Thomas, Marita; Toader, Rodica

doi:10.1007/s10884-018-9666-y

Cited by 30 publications

(54 citation statements)

References 63 publications

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“…□ Minimizers of (43) satisfy the following first order optimality conditions. Let ( , el, , ) be the minimizing triple of (43). Then there exists ∈ 1, (Ω) ∩ ∞ (Ω) solving (37c), and satisfying 0 ≤ ≤ 1.…”

Section: Existence Of Weak Solutionsmentioning

confidence: 99%

“…We are now in a position of providing, in the following lemmas and corollary, further optimality conditions for triples ( , , ) solving (43). Let ( , el, , ) be the minimizing triple of (43), and let be the quantity defined in (42). Then, there holds…”

Section: A-priori Energy Estimatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…A vast literature concerning damage in viscoelastic materials, both in the quasistatic and the dynamical setting is currently available. We refer, e.g., to [42,43,45,50,57,59] and the references therein for an overview of the main results.The interplay between plasticity and damage has been already extensively investigated, prominently in the quasistatic framework. The interaction between damage and strain gradient plasticity is addressed in [21] whereas a perfect-plastic model has been proposed in [1], where the one-dimensional response is also studied.…”

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confidence: 99%

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Dynamic perfect plasticity and damage in viscoelastic solids

2019

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In this paper we analyze an isothermal and isotropic model for viscoelastic media combining linearized perfect plasticity (allowing for concentration of plastic strain and development of shear bands) and damage effects in a dynamic setting. The interplay between the viscoelastic rheology with inertia, elasto‐plasticity, and unidirectional rate‐dependent incomplete damage affecting both the elastic and viscous response, as well as the plastic yield stress, is rigorously characterized by showing existence of weak solutions to the constitutive and balance equations of the model. The analysis relies on the notions of plastic‐strain measures and bounded‐deformation displacements, on sophisticated time‐regularity estimates to establish a duality between acceleration and velocity of the elastic displacement, on the theory of rate‐independent processes for the energy conservation in the dynamical‐plastic part, and on the proof of the strong convergence of the elastic strains. Existence of suitably defined weak solutions (even conserving energy) is proved rather constructively by using a staggered two‐step time discretization scheme.

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Section: Existence Of Weak Solutionsmentioning

confidence: 99%

Section: A-priori Energy Estimatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Dynamic perfect plasticity and damage in viscoelastic solids

2019

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“…e.g. [2,9,[12][13][14]). We remark that in [2] viscosity can be neglected under suitable assumptions.…”

Section: Introductionmentioning

confidence: 99%

A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations

Nardini

2016

J Dyn Diff Equat

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In this paper we study the limit as ε → 0 of the singularly perturbed second orderis a potential. We assume that u 0 (t) is one of its equilibrium points such that ∇ x V (t, u 0 (t)) = 0 and ∇ 2x V (t, u 0 (t)) > 0. We find that, under suitable initial data, the solutions u ε converge uniformly to u 0 , by imposing mild hypotheses on V . A counterexample shows that they cannot be weakened.

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Dynamic Phase‐Field Fracture in Viscoelastic Materials using a First‐Order Formulation

Friebertshäuser

Thomas

Tornquist

et al. 2023

Proc Appl Math and Mech

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In this contribution we present analytical results on a model for dynamic fracture in viscoelastic materials at small strains that have been obtained in full depth in [1]. In the model, the sharp crack interface is regularized with a phase‐field approximation, and for the phase‐field variable a viscous evolution with a quadratic dissipation potential is employed. A non‐smooth penalization prevents material healing. The viscoelastic momentum balance is formulated as a first order system and coupled in a nonlinear way to the non‐smooth evolution equation of the phase field. We give a full discretization in time and space using a discontinuous Galerkin method for the first‐order system. We discuss the existence of discrete solutions and, with the step size in space and time tending to zero, their convergence to a suitable notion of weak solution of the system. Eventually, we provide a numerical benchmark and compare it with simulation results found in [2].

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Rate-Independent Damage in Thermo-Viscoelastic Materials with Inertia

Cited by 30 publications

References 63 publications

Dynamic perfect plasticity and damage in viscoelastic solids

Dynamic perfect plasticity and damage in viscoelastic solids

A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations

Dynamic Phase‐Field Fracture in Viscoelastic Materials using a First‐Order Formulation

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