What is this plant?

It is in my mother's yard and we actually like it. It grows very thick but lays flat and does not need to be mowed. How do I encourage it to spread? 

Here is a healthier looking version of the same plant. 

does it have a smell if you crush it's leaves?

Pennyroyal?

If it's minty - it could be pennyroyal. Thx bigben - was blanking on the name

If it smells pepperminty, pennyroyal would be my guess and if that's what it is, you can buy seeds for it or you can get some plants at Well Sweep Herb Farm in Port Murray. Pennyroyal is supposed to deter fleas but the irony is it's toxic to pets so you shouldn't use it topically on them as a flea preventative.  Pennyroyal is quite easily grown and is perennial.

No peppermint smell. It smells very "green," like a super concentrated mesclun salad. 

I looked on the stem for a line of little hairs to see if it was chickweed but it doesn't have that either. 

I have googled for weeds found in NJ yards. Rutger's has a good page of images. It is slow going. Perhaps it is purslane? 

https://njaes.rutgers.edu/weeds/full.asp?purslane

Looks like purslane to me...

Various members of the RIO series of purslanes did well for me for several years. Original plants kept going, year over year,  in pots left outdoors. Self-seeding. Until all failed last spring.

Big flowers (for purslane). Bright colors. Unfazed by heat/sun/dry. Long, continuous bloom until frost (once they got started).  Big boxes should have started plants soon (if not already).

Alas, what you have may not be exactly what I had. Did the NYT urban  forager person say they are edible?

spontaneous said:

 How do I encourage it to spread? 

I used to break off pieces and stick broken end in soil. Might also root if just dropped haphazardly onto soil. Self-seeding should spread it, too (over time). Could also locate center of root system of substantial "clump" and use sharp spade to divide (then lift up, and  plant, upended half).

not purslane. Purslane is more of a succulent.

Joy I think you are right.

No, definitely not a succulent. I will try to remember to pick a few pieces tomorrow and get a better picture.

I'll try dividing it and seeing if it takes. Whatever it is, it makes a beautiful thick ground cover but doesn't grow too tall. 

It also looks like it may flower soon, which may also help in identifying it.   

Common chickweed? https://en.wikipedia.org/wiki/Stellaria_media#/media/File:StellariaMedia001.JPG

I looked and it doesn't have the line of hair on the stem, but I do keep coming back to chickweed, so maybe that is what it is.  I don't care that it is a weed, it looks good for our intended purpose.  In the areas where it is well established it has formed a thick mat, no dirt at all is visible underneath it, which is what we want.

Have you asked Lynn?  She would know.

It seems it is a variety of chickweed, just not the one with hairs going up the stem.  I'm also told that though it is lush now, it will be straggly and bare by mid summer.  My search for a good, thick, walkable ground cover continues.  

Do you need the ground cover to be free?  Farm at Green Village had a lot of great ground covers. Irish moss. I think some are oreganos. 

It doesn't have to be free, but we don't have a large budget, so price per plant is a concern.  

ETA: We put creeping thyme and phlox in parts of the yard that do not get foot traffic, but I don't believe they would do well in parts of the yard that get foot traffic.