Damage of nonlinearly elastic materials at small strain – Existence and regularity results –
نویسنده
چکیده
In this paper an existence result for energetic solutions of rate-independent damage processes is established and the temporal regularity of the solution is discussed. We consider a body consisting of a physically nonlinearly elastic material undergoing small deformations and partial damage. The present work is a generalization of [MiR06] concerning the properties of the stored elastic energy density as well as the suitable Sobolev space for the damage variable: While previous work assumes that the damage variable z satisfies z ∈ W 1,r(Ω) with r > d for Ω ⊂ Rd, we can handle the case r > 1 by a new technique for the construction of joint recovery sequences. Moreover, this work generalizes the temporal regularity results to physically nonlinearly elastic materials by analyzing Lipschitzand Hölder-continuity of solutions with respect to time.
منابع مشابه
Viscous Approximation of Quasistatic Evolutions for a Coupled Elastoplastic-damage Model
Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.
متن کاملGlobally Stable Quasistatic Evolution for Strain Gradient Plasticity Coupled with Damage
We consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin-Anand formulation [19]. The aim of the present model is to account for different phenomena: on the one hand the elastic stiffness reduces and the plastic yield surface shrinks due to material’s degradation, on ...
متن کاملThis preprint will appear in final form in Strain LONGITUDINAL STRAIN SOLITARY WAVE IN A TWO-LAYERED POLYMERIC BAR
Both theoretical investigations and successful experimental research were performed recently, confirming the existence and demonstrating the main properties of bulk strain solitary waves in nonlinearly elastic solid wave guides. Our current research is devoted to non-linear wave processes in layered elastic wave guides with inhomogeneities modelling damage/delamination. Here, we present first e...
متن کاملFinite element analysis of elastic-plastic solids under Vickers indentation: surface deformation
Finite element modeling has been used to study the development of surface deformation during indentation with a Vickers indenter. A wide range of materials with different elastic modulus and yield stresses are examined. Results show that in a pyramidal indentation process, for a perfectly plastic material, sinking-in during loading can change to pile-up in unloading. This phenomenon depends on ...
متن کامل