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Asymptotic analysis of a clamped thin multidomain allowing for fractures and discontinuities
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abstract
We consider a thin multidomain of $\mathbb R^3,$ consisting of a vertical rod upon a horizontal disk. The equilibrium configurations of the thin hyperelastic multidomain, allowing for fracture and damage, are described by means of a bulk energy density of the kind $W(\nabla U)$, where $W$ is a Borel function with linear growth and $\nabla U$ denotes the gradient of the displacement, i.e. a vector valued function $U:\Omega \to \mathbb R^3$. By assuming that the two volumes tend to zero, under suitable boundary conditions and loads, and suitable assumptions of the rate of convergence of the two volumes, we prove that the limit model is well posed in the union of the limit domains, with dimensions, respectively, $1$ and $2$.
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Beyond the model: Key differentiators in large language models and multi-agent services
A review arguing that ecosystem factors such as data management, computational efficiency, latency, and evaluation frameworks, not model size, will determine the value of LLM-based services.