Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials

We consider a non-negative and one-homogeneous energy functional $${{\mathcal {J}}}$$ J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional $${{\mathcal {E}}}(t,u)= t {{\mathcal {J}}}(u)$$ E ( t , u ) = t J ( u ) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system.

DIAGNÓSTICO AMBIENTAL PARA AVES DE CORTE NO MUNICÍPIO DE CAMPINA GRANDE (PB)

DIAGNÓSTICO AMBIENTAL PARA AVES DE CORTE NO MUNICÍPIO DE CAMPINA GRANDE (PB) RAÍSSA GONÇALVES CAVALCANTI¹, JOSÉ WALLACE BARBOSA DO NASCIMENTO¹, DERMEVAL ARAÚJO FURTADO¹, JOELMA VIEIRA DO NASCIMENTO DUARTE¹, POLYANA MARTA DA SILVA¹ 1 Departamento de Engenharia Agrícola, Universidade Federal de Campina Grande, rua Aprígio Veloso, 882, Bairro Universitário, 58429-900, Campina Grande, Paraíba, Brasil. [email protected]; [email protected]; [email protected]; [email protected]; [email protected] RESUMO: A pesquisa teve como objetivo realizar o diagnóstico ambiental para frangos de corte com três semanas de vida no município de Campina Grande (PB), região do Agreste Paraibano. Onde foram sistematizados os dados climáticos do município, comparando com as exigências dos animais, determinando os limites de aceitabilidade ambiental, identificando os pontos críticos e por fim, foram disponibilizados soluções construtivas e energéticas para correção das instalações. Foram utilizados os dados de série histórica de temperatura do ar, umidade e ITGU para o município, obtidos por meio do software Estima_T, disponibilizado pelo Departamento de Ciências Atmosféricas da Universidade Federal de Campina Grande. Observou-se que o ITGU, apenas na primeira semana, obteve um índice inferior ao ITGU ideal. Já para as demais semanas, o valor do ITGU permaneceu confortável em todos os meses do ano. Assim, o presente diagnóstico indica que há necessidade de correções nas instalações para proporcionar aos animais um maior conforto térmico, para que os mesmos possam expressar todo seu potencial dentro das instalações que estão inseridos. Palavras-chave: Avicultura, Instalações, Conforto térmico, Diagnóstico. ENVIRONMENTAL DIAGNOSIS FOR BROILERS CHICKENS IN THE MUNICIPALITY OF CAMPINA GRANDE ABSTRACT: The research aimed to carry out the environmental diagnosis for broilers chickens with three weeks of life in the municipality of Campina Grande (PB), region of Agreste Paraibano. Where the municipality climatic data were systematized, comparing with the requirements of animals, determining the limits of environmental acceptability, identifying the critical points and finally, constructive and energetic solutions were made available to correct the installations. Historical data on air temperature, humidity and ITGU for the municipality were used, obtained using the Estima_T software, made available by the Department of Atmospheric Sciences at the Federal University of Campina Grande. It was observed that the ITGU, only in the first week, obtained a lower index than the ideal ITGU. For the other weeks, the ITGU value remained comfortable in all months of the year. Thus, the present diagnosis indicates that there is a need for corrections in the facilities to provide animals with greater thermal comfort, so that they can express their full potential within the facilities that are inserted. Keywords: Poultry, Facilities, Thermal comfort, Diagnosis.

Visco-energetic solutions to some rate-independent systems in damage, delamination, and plasticity

This paper revolves around a newly introduced weak solvability concept for rate-independent systems, alternative to the notions of Energetic ([Formula: see text]) and Balanced Viscosity ([Formula: see text]) solutions. Visco-Energetic ([Formula: see text]) solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for [Formula: see text] solutions, but perturbed by a “viscous” correction term, as in the case of [Formula: see text] solutions. However, for VE solutions this viscous correction is tuned by a fixed parameter. The resulting solution notion turns out to describe a kind of evolution in between Energetic and BV evolution. In this paper we aim to investigate the application of [Formula: see text] solutions to nonsmooth rate-independent processes in solid mechanics such as damage and plasticity at finite strains. We also address the limit passage, in the [Formula: see text] formulation, from an adhesive contact to a brittle delamination system. The analysis of these applications reveals the wide applicability of this solution concept, in particular to processes for which [Formula: see text] solutions are not available, and confirms its intermediate character between the [Formula: see text] and [Formula: see text] notions.

Convergence analysis of time-discretisation schemes for rate-independent systems

It is well known that rate-independent systems involving nonconvex energy functionals in general do not allow for time-continuous solutions even if the given data are smooth. In the last years, several solution concepts were proposed that include discontinuities in the notion of solution, among them the class of global energetic solutions and the class of BV-solutions. In general, these solution concepts are not equivalent and numerical schemes are needed that reliably approximate that type of solutions one is interested in. In this paper, we analyse the convergence of solutions of three time-discretisation schemes, namely an approach based on local minimisation, a relaxed version of it and an alternate minimisation scheme. For all three cases, we show that under suitable conditions on the discretisation parameters discrete solutions converge to limit functions that belong to the class of BV-solutions. The proofs rely on a reparametrisation argument. We illustrate the different schemes with a toy example.

Social investigations as a measuring instrument of construction industry in the areas of Polish districts with prefabricated buildings

We analyze Town area with prefabricated buildings of poor energetic quality. We survey opinions on possible energetic improvements according to inhabitants´ age. Inhabitants are interested in improvements and willing to pay. Inhabitants want information on possible pro-energetic solutions. Surveys like this encourage people to think of benefits of energetic improvements.

Rate-independent elastoplasticity at finite strains and its numerical approximation

Gradient plasticity at large strains with kinematic hardening is analyzed as quasistatic rate-independent evolution. The energy functional with a frame-indifferent polyconvex energy density and the dissipation is approximated numerically by finite elements and implicit time discretization, such that a computationally implementable scheme is obtained. The nonself-penetration as well as a possible frictionless unilateral contact is considered and approximated numerically by a suitable penalization method which keeps polyconvexity and simultaneously bypasses the Lavrentiev phenomenon. The main result concerns the convergence of the numerical scheme toward energetic solutions. In the case of incompressible plasticity and of nonsimple materials, where the energy depends on the second derivative of the deformation, we derive an explicit stability criterion for convergence relating the spatial discretization and the penalizations.