相关论文: Complete damage in linear elastic materials - Mode…
In this work we study global boundedness and exponential integrability of weak solutions to degenerate $p$-Poisson equations using an iterative method of De Giorgi type. Given a symmetric, non-negative definite matrix valued function $Q$…
The structured deformation theory is used within the thermodynamics of irreversible processes framework in order to build a damage model relevant for quasi-brittle materials. The cracks are supposed smeared in the body and their shape is…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of…
In this paper we derive a new model for visco-elasticity with large deformations where the independent variables are the stretch and the rotation tensors which intervene with second gradients terms accounting for physical properties in the…
In this work we investigate a phase field model for damage processes in two-dimensional viscoelastic media with nonhomogeneous Neumann data describing external boundary forces. In the first part we establish global-in-time existence,…
We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating…
Controlling the growth of material damage is an important engineering task with plenty of real world applications. In this paper we approach this topic from the mathematical point of view by investigating an optimal boundary control problem…
This study addresses ductile fracture of single grains in metals by modeling of the formation and propagation of transgranular cracks. A proposed model integrates gradient extended hardening, phase-field modeling for fracture, and crystal…
The motivation of this work is to produce an integrated formulation for material response due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we are interested to capture miscible and…
We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect on the deformation of cardiac tissue. The system governs…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
Accurate prediction of damage and fracture evolution is critical for the safety design and preventive maintenance of engineering structures, however existing computational methods face significant limitations. On one hand, discrete damage…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
In this thesis we develop a functional analytic framework for shape optimization with elliptic partial differential equation (PDE) constraints in classical function spaces (H\"older spaces). This approach is motivated by shape optimization…
In this paper, a thermodynamic analysis of Bouc-Wen models endowed with both strength and stiffness degradation is provided. It is based on the relationship between the flow rules of these models and those of the endochronic plasticity…
Compartmental models are widely used in mathematical epidemiology to describe dynamics of infection disease. A new SIS-PDE model, recently derived by Chalub and Souza, is based on a diffusion-drift approximation of probability density in a…
We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the…
We present a quasi-static elasticity model that accounts for damage evolution based on the ideas of Kachanov 1958 and and Rabotnov 1968. We analyze the resulting strongly nonlinear system of differential equations in view of well-posedness.…
A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum variant of Newton's second law, uses integral rather than…