---
name: "2D"
section: "3rheolef"
platform: "linux"
package: "librheolef-dev"
version: "6.1-2.1"
release: "Debian 7 (Wheezy)"
platforms: ["linux"]
url: "https://new.carta.tech/2D"
---

# 2D(3rheolef)

## NAME

**2D** -- rate of deformation tensor

## SYNOPSIS

```
        form (const space V, const space& T, "2D");

```

## DESCRIPTION

Assembly the form associated to the rate of deformation tensor, i.e. the symmetric part of the gradient of a vector field. These derivative are usefull in fluid mechanic and elasticity.

```
                 /
                 |
      b(u,tau) = | 2 D(u) : tau dx,
                 |
                 / Omega

```

where

```
     2 D(u) = grad u + (grad u)^T

```

If the V space is a vector-valued **P1** (resp. **P2**) finite element space, the T space may be a tensor-valued **P0** (resp. **P1d**) one.

## EXAMPLE

The following piece of code build the Laplacian form associated to the P1 approximation:

```
        geo omega ("square");
        space V (omega, "P1", "vector");
        space T (omega, "P0", "tensor");
        form  b (V, T, "2D");

```